{"id":208449,"date":"2026-10-01T19:00:00","date_gmt":"2026-10-01T10:00:00","guid":{"rendered":"https:\/\/ichizenholdings.co.jp\/media\/?p=208449"},"modified":"2026-09-25T19:36:55","modified_gmt":"2026-09-25T10:36:55","slug":"var-and-expected-shortfall","status":"publish","type":"post","link":"https:\/\/ichizenholdings.co.jp\/media\/trading\/financial-engineering\/var-and-expected-shortfall\/","title":{"rendered":"\u7b2c42\u56de VaR \u3068 Expected Shortfall \u2015 \u30ea\u30b9\u30af\u30921\u3064\u306e\u6570\u5b57\u306b\u3059\u308b\u4ee3\u511f"},"content":{"rendered":"\n<blockquote class=\"is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u4f4d\u7f6e: \u7b2c4\u90e8 \u7b2c42\u56de \/ \u524d\u63d0: \u7b2c20\u56de\u3001\u7b2c35\u56de \/ \u6570\u5b66\u7de8: M29 \/ \u3053\u306e\u56de\u3067\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068: \u640d\u5931\u5206\u5e03\u304b\u3089 VaR \u3068 Expected Shortfall \u3092\u8a08\u7b97\u3057\u3001VaR \u304c\u5206\u6563\u6295\u8cc7\u306e\u52b9\u679c\u3092\u6b63\u3057\u304f\u6620\u3055\u306a\u3044\u4f8b\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5b9f\u8df5: \u53e3\u5ea7\u306e\u6708\u6b21\u30c7\u30fc\u30bf\u304b\u3089\u30ea\u30bf\u30fc\u30f3\u30fb\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u30fb\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa\u3092 Excel \u3067\u8a08\u7b97\u3057\u3001\u5165\u51fa\u91d1\u306e\u5f71\u97ff\u3092\u53d6\u308a\u9664\u3044\u3066\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u308b<\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">0. \u7269\u8a9e \u2015 \u5206\u6563\u6295\u8cc7\u3057\u305f\u306e\u306b VaR \u304c\u4e0a\u304c\u308b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u624b\u5143\u306b1\u5104\u5186\u306e\u904b\u7528\u8cc7\u91d1\u304c\u3042\u3063\u3066\u30012\u3064\u306e\u5546\u54c1\u306b\u5206\u3051\u3066\u6295\u8cc7\u3059\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5546\u54c1A\u306f\u5343\u56de\u306e\u3046\u30618\u56de\u3060\u3051\u5927\u304d\u306a\u640d\u5931\u304c\u51fa\u307e\u3059\u304c\u3001\u305d\u308c\u4ee5\u5916\u306f\u640d\u5931\u30bc\u30ed\u3067\u3059\u3002\u5546\u54c1B\u3082\u540c\u3058\u69cb\u9020\u3067\u3001\u3084\u306f\u308a\u5343\u56de\u306e\u3046\u30618\u56de\u3060\u3051\u640d\u5931\u304c\u51fa\u307e\u3059\u3002\u305f\u3060\u3057\u3001A\u3068B\u304c\u640d\u5931\u3092\u51fa\u3059\u65e5\u306f\u5b8c\u5168\u306b\u305a\u308c\u3066\u3044\u3066\u3001\u540c\u3058\u65e5\u306b\u4e21\u65b9\u304c\u5927\u640d\u3059\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30ea\u30b9\u30af\u7ba1\u7406\u90e8\u9580\u306b\u300c\u767e\u56de\u306b99\u56de\u306f\u640d\u5931\u304c\u3053\u306e\u91d1\u984d\u306b\u53ce\u307e\u308b\u300d\u3068\u3044\u3046\u57fa\u6e96\u3067\u30ea\u30b9\u30af\u3092\u6e2c\u3063\u3066\u3082\u3089\u3046\u3068\u3001\u5546\u54c1A\u306f\u30bc\u30ed\u3001\u5546\u54c1B\u3082\u30bc\u30ed\u3068\u51fa\u307e\u3059\u3002\u5343\u56de\u306e\u3046\u30618\u56de\u3068\u3044\u3046\u983b\u5ea6\u306f\u767e\u56de\u306b1\u56de\u3088\u308a\u5c11\u306a\u3044\u306e\u3067\u300199\u30d1\u30fc\u30bb\u30f3\u30c8\u306e\u7dda\u3092\u5f15\u3044\u305f\u5185\u5074\u306b\u306f\u640d\u5931\u304c\u898b\u3048\u306a\u3044\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3067\u306f\u3001\u5206\u6563\u6295\u8cc7\u306e\u3064\u3082\u308a\u3067\u4e21\u65b9\u3092\u6301\u3063\u305f\u3089\u3069\u3046\u306a\u308b\u304b\u3002\u5927\u304d\u306a\u640d\u5931\u304c\u51fa\u308b\u65e5\u306f\u5408\u8a0816\u56de\u306b\u5897\u3048\u307e\u3059\u3002\u5343\u56de\u306e\u3046\u306116\u56de\u306f\u767e\u56de\u306b1.6\u56de\u3067\u3059\u304b\u3089\u3001\u3055\u3063\u304d\u306e\u57fa\u6e96\u3067\u6e2c\u308b\u3068\u30ea\u30b9\u30af\u306e\u6570\u5b57\u306f\u7a81\u7136\u30bc\u30ed\u304b\u3089100\u306b\u8df3\u306d\u4e0a\u304c\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u500b\u5225\u306b\u306f\u30bc\u30ed\u3060\u3063\u305f\u30ea\u30b9\u30af\u304c\u3001\u5206\u6563\u3057\u305f\u3089\u5897\u3048\u3066\u3057\u307e\u3044\u307e\u3057\u305f\u3002\u30ea\u30b9\u30af\u3092\u6e1b\u3089\u3059\u305f\u3081\u306e\u5206\u6563\u6295\u8cc7\u304c\u3001\u6307\u6a19\u306e\u4e0a\u3067\u306f\u9006\u52b9\u679c\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u6307\u6a19\u306f\u3001\u640d\u5931\u5206\u5e03\u306e\u3042\u308b\u4e00\u70b9\u3060\u3051\u3092\u898b\u3066\u300c\u3053\u3053\u307e\u3067\u306f\u5927\u4e08\u592b\u300d\u3068\u7dda\u3092\u5f15\u304f\u4ed5\u7d44\u307f\u3067\u3059\u3002\u7dda\u306e\u5185\u5074\u306b\u96a0\u308c\u3066\u3044\u305f\u5c0f\u3055\u306a\u78ba\u7387\u306e\u640d\u5931\u304c\u3001\u5408\u7b97\u3059\u308b\u3068\u7dda\u306e\u5916\u306b\u51fa\u3066\u304d\u3066\u3057\u307e\u3046\u306e\u304c\u539f\u56e0\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u65b9\u3001\u7dda\u3092\u8d85\u3048\u305f\u5148\u306e\u5e73\u5747\u7684\u306a\u640d\u5931\u3092\u6e2c\u308b\u5225\u306e\u6307\u6a19\u306a\u3089\u3001\u5546\u54c1A\u304c80\u3001\u5546\u54c1B\u308280\u3067\u3001\u5408\u8a08\u306f160\u3067\u3059\u3002\u4e21\u65b9\u3092\u5408\u308f\u305b\u305f\u3068\u304d\u306e\u5024\u306f100\u3067\u3059\u304b\u3089\u3001\u5408\u8a08\u3088\u308a\u5c0f\u3055\u3044\u3002\u5206\u6563\u6295\u8cc7\u306e\u52b9\u679c\u304c\u304d\u3061\u3093\u3068\u6570\u5b57\u306b\u73fe\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u56de\u3067\u306f\u3001\u4e00\u70b9\u3060\u3051\u3092\u898b\u308b\u6307\u6a19\u304c\u306a\u305c\u5206\u6563\u6295\u8cc7\u3068\u76f8\u6027\u304c\u60aa\u3044\u306e\u304b\u3092\u8a3c\u660e\u3057\u3001\u5c3e\u90e8\u306e\u5e73\u5747\u3092\u898b\u308b\u6307\u6a19\u304c\u3069\u306e\u3088\u3046\u306a\u4ed5\u7d44\u307f\u3067\u6574\u5408\u6027\u3092\u4fdd\u3064\u306e\u304b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1. \u52d5\u6a5f \u2015 \u30ea\u30b9\u30af\u30921\u3064\u306e\u6570\u5b57\u306b\u3067\u304d\u308b\u304b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u56de\u3092\u8aad\u307f\u7d42\u3048\u308b\u3068\u3001\u640d\u5931\u5206\u5e03\u304b\u3089 VaR \u3068 Expected Shortfall \u3092\u8a08\u7b97\u3057\u3001VaR \u304c\u5206\u6563\u6295\u8cc7\u306e\u52b9\u679c\u3092\u6b63\u3057\u304f\u6620\u3055\u306a\u3044\u4f8b\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u3053\u306e\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u30ea\u30b9\u30af\u306f\u3044\u304f\u3089\u3067\u3059\u304b\u300d\u3068\u554f\u308f\u308c\u3066\u30011\u3064\u306e\u6570\u5b57\u3092\u8fd4\u3057\u305f\u3044\u306e\u306f\u81ea\u7136\u306a\u6b32\u6c42\u3067\u3059\u3002\u5206\u6563\u306f\u6b63\u3068\u8ca0\u306e\u305a\u308c\u3092\u533a\u5225\u3057\u307e\u305b\u3093\u3002\u640d\u5931\u306e\u5074\u3060\u3051\u3092\u6e2c\u308b\u6307\u6a19\u3068\u3057\u3066\u5e83\u304f\u4f7f\u308f\u308c\u3066\u3044\u308b\u306e\u304c <strong>VaR\uff08Value at Risk\uff09<\/strong> \u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">VaR \u306f\u660e\u5feb\u3067\u3059\u3002\u300c99% \u306e\u78ba\u7387\u3067\u3001\u640d\u5931\u306f\u3053\u306e\u91d1\u984d\u306b\u53ce\u307e\u308a\u307e\u3059\u300d\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u8a00\u3044\u5207\u308a\u306b\u306f\u4ee3\u511f\u304c\u3042\u308a\u307e\u3059\u3002\u53ce\u307e\u3089\u306a\u304b\u3063\u305f\u6b8b\u308a 1% \u3067\u4f55\u304c\u8d77\u304d\u308b\u304b\u3092\u3001VaR \u306f\u4e00\u5207\u8a9e\u308a\u307e\u305b\u3093\u3002\u3055\u3089\u306b\u5384\u4ecb\u306a\u3053\u3068\u306b\u30012\u3064\u306e\u6301\u3061\u9ad8\u3092\u5408\u7b97\u3057\u305f VaR \u304c\u3001\u500b\u5225\u306e VaR \u306e\u548c\u3092\u4e0a\u56de\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001VaR \u306e\u5b9a\u7fa9\u3092\u5206\u4f4d\u70b9\u3068\u3057\u3066\u6b63\u78ba\u306b\u8ff0\u3079\u305f\u3046\u3048\u3067\u3001\u52a3\u52a0\u6cd5\u6027\u304c\u7834\u308c\u308b\u4f8b\u3092\u5177\u4f53\u7684\u306b\u69cb\u6210\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u5c3e\u90e8\u306e\u5e73\u5747\u3092\u53d6\u308b <strong>Expected Shortfall\uff08ES\uff09<\/strong> \u304c\u52a3\u52a0\u6cd5\u6027\u3092\u6e80\u305f\u3059\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u3053\u306e\u8a18\u4e8b\u3067\u8a3c\u660e\u3059\u308b\u3053\u3068<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li><strong>THM-VAR-1<\/strong> VaR \u306f\u640d\u5931\u5206\u5e03\u306e\u5206\u4f4d\u70b9\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u305d\u308c\u3092\u8d85\u3048\u308b\u640d\u5931\u306e\u5927\u304d\u3055\u306b\u3064\u3044\u3066\u306f\u4f55\u3082\u8a9e\u308a\u307e\u305b\u3093\u3002<\/li>\n\n\n<li><strong>THM-VAR-2<\/strong> 2\u3064\u306e\u6301\u3061\u9ad8\u3092\u5408\u7b97\u3057\u305f VaR \u304c\u500b\u5225\u306e VaR \u306e\u548c\u3092\u4e0a\u56de\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u5206\u6563\u6295\u8cc7\u304c VaR \u3092\u60aa\u5316\u3055\u305b\u305f\u3088\u3046\u306b\u898b\u3048\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n<li><strong>THM-VAR-3<\/strong> Expected Shortfall \u306f\u5e38\u306b\u52a3\u52a0\u6cd5\u7684\u3067\u3042\u308a\u3001\u5408\u7b97\u3057\u305f\u5024\u304c\u500b\u5225\u306e\u548c\u3092\u8d85\u3048\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/li>\n\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u8a2d\u5b9a\u3068\u4eee\u5b9a \u2015 \u640d\u5931\u5206\u5e03\u306e\u5206\u4f4d\u70b9<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306e\u4eee\u5b9a\u3092\u7f6e\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n\n<li>\u640d\u5931\u306f\u6b63\u306e\u5024\u3067\u8868\u3057\u307e\u3059\u3002\u5229\u76ca\u306f\u8ca0\u3067\u3059\u3002<\/li>\n\n\n<li>\u4fe1\u983c\u6c34\u6e96\u3092\u660e\u793a\u3057\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f <strong>99%<\/strong> \u3092\u6a19\u6e96\u3068\u3057\u307e\u3059\u3002<\/li>\n\n\n<li>\u5206\u5e03\u306f\u65e2\u77e5\u3068\u3057\u3066\u4e0e\u3048\u307e\u3059\u3002\u63a8\u5b9a\u306e\u554f\u984c\u306f\u6271\u3044\u307e\u305b\u3093\u3002<\/li>\n\n\n<li>\u4fdd\u6709\u671f\u9593\u3092 <strong>1\u65e5<\/strong> \u3068\u3057\u307e\u3059\u3002<\/li>\n\n<\/ul>\n\n\n\n<p>\u640d\u5931\u3092\u78ba\u7387\u5909\u6570 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/eq> \u3067\u8868\u3057\u307e\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/eq> \u306e\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathbb\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3068\u66f8\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4fe1\u983c\u6c34\u6e96 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq>\uff08\u4f8b\u3048\u3070 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.99<\/span><\/span><\/span><\/span><\/eq>\uff09\u306b\u5bfe\u3059\u308b VaR \u306f\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u5206\u4f4d\u70b9\u3067\u3059\u3002<\/p>\n\n\n\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">in<span style=\"margin-right:0.0778em;\">f<\/span><\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mclose\">}<\/span><\/span><span class=\"katex-tag\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord text\"><span class=\"mord\">(<\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><span class=\"mord\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n\n\n\n<p>\u3053\u308c\u306f\u300c\u640d\u5931\u304c <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u4ee5\u4e0b\u306b\u53ce\u307e\u308b\u78ba\u7387\u304c\u5c11\u306a\u304f\u3068\u3082 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u3067\u3042\u308b\u300d\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Expected Shortfall \u306f\u3001VaR \u3092\u8d85\u3048\u305f\u90e8\u5206\u306e\u5e73\u5747\u640d\u5931\u3067\u3059\u3002<\/p>\n\n\n\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.476em;vertical-align:-0.9119em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.564em;\"><span style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.8129em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9119em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><\/span><span class=\"katex-tag\"><span class=\"katex-strut\" style=\"height:2.476em;vertical-align:-0.9119em;\"><\/span><span class=\"mord text\"><span class=\"mord\">(<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><span class=\"mord\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n\n\n\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/eq> \u304c\u9023\u7d9a\u5206\u5e03\u306b\u5f93\u3046\u5834\u5408\u3001\u3053\u308c\u306f\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\"><\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/eq> \u3068\u4e00\u81f4\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">VaR \u306f\u5206\u4f4d\u70b9\u3001ES \u306f\u5c3e\u90e8\u306e\u5e73\u5747\u3002\u3053\u306e\u9055\u3044\u304c\u3053\u306e\u8a18\u4e8b\u306e\u5168\u3066\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3. \u4e3b\u5f35 \u2015 VaR \u306f\u5206\u6563\u6295\u8cc7\u3068\u76f8\u6027\u304c\u60aa\u3044<\/h2>\n\n\n\n<blockquote>\n<p><strong>\u5b9a\u7406 THM-VAR-1\uff08VaR \u306e\u5b9a\u7fa9\uff09<\/strong>\n\u4fe1\u983c\u6c34\u6e96 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u306e VaR \u306f\u3001\u640d\u5931\u5206\u5e03\u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u5206\u4f4d\u70b9\u3067\u3042\u308b\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">in<span style=\"margin-right:0.0778em;\">f<\/span><\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/eq>\u3002\u3053\u306e\u5024\u306f\u3001\u640d\u5931\u304c <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3092\u8d85\u3048\u305f\u5834\u5408\u306b\u3069\u308c\u3060\u3051\u5927\u304d\u304f\u306a\u308b\u304b\u306b\u3064\u3044\u3066\u306f\u4f55\u3082\u8a9e\u3089\u306a\u3044\u3002<\/p>\n<\/blockquote>\n\n\n\n<blockquote>\n<p><strong>\u5b9a\u7406 THM-VAR-2\uff08VaR \u306f\u52a3\u52a0\u6cd5\u7684\u3067\u306a\u3044\uff09<\/strong>\n2\u3064\u306e\u640d\u5931 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u5bfe\u3057\u3066<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/eqn><\/section><p>\u304c\u6210\u308a\u7acb\u3064\u5834\u5408\u304c\u3042\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u5206\u6563\u6295\u8cc7\u304c VaR \u3092\u60aa\u5316\u3055\u305b\u305f\u3088\u3046\u306b\u898b\u3048\u308b\u3053\u3068\u304c\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<blockquote>\n<p><strong>\u5b9a\u7406 THM-VAR-3\uff08ES \u306e\u52a3\u52a0\u6cd5\u6027\uff09<\/strong>\n\u4efb\u610f\u306e\u640d\u5931 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u5bfe\u3057\u3066<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/eqn><\/section><p>\u304c\u5e38\u306b\u6210\u308a\u7acb\u3064\u3002<\/p>\n<\/blockquote>\n\n\n\n<details class=\"finmath-proof\"><summary>\u8a3c\u660e\u3092\u8aad\u3080\uff08\u8aad\u307e\u306a\u304f\u3066\u3082\u8a18\u4e8b\u306f\u5b8c\u7d50\u3057\u307e\u3059\uff09<\/summary>\n<h2>4. \u8a3c\u660e \u2015 \u52a3\u52a0\u6cd5\u6027\u304c\u7834\u308c\u308b\u4f8b\u3092\u69cb\u6210\u3059\u308b<\/h2>\n<p>\u3053\u306e\u7bc0\u306f\u8aad\u307e\u306a\u304f\u3066\u3082\u8a18\u4e8b\u306f\u5b8c\u7d50\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u8a3c\u660e\u3092\u8ffd\u3044\u305f\u3044\u4eba\u306f\u3001<a href=\"https:\/\/ichizenholdings.co.jp\/media\/column\/financial-math\/math-convexity-jensen\/\">\u6570\u5b66\u7de8 \u7b2c29\u56de\u300c\u51f8\u6027\u3068\u6700\u9069\u5316\u300d<\/a>\u3078\u3002<\/p>\n<h3>THM-VAR-1 \u306e\u8a3c\u660e<\/h3>\n<p>VaR \u306e\u5b9a\u7fa9\u3092\u53b3\u5bc6\u306b\u8ffd\u3044\u307e\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3092\u56fa\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<p>\u5206\u4f4d\u70b9\u306e\u5b9a\u7fa9 (1) \u3088\u308a\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">in<span style=\"margin-right:0.0778em;\">f<\/span><\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">:<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u3002\u3053\u308c\u306f\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306e\u4e00\u822c\u9006\u95a2\u6570\u3067\u3042\u308a\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u304c\u9023\u7d9a\u304b\u3064\u72ed\u7fa9\u5358\u8abf\u5897\u52a0\u306a\u3089\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u3092\u6e80\u305f\u3059\u552f\u4e00\u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u4e00\u81f4\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u5b9a\u7fa9\u304c\u8a9e\u308b\u306e\u306f\u300c\u640d\u5931\u304c <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3092\u8d85\u3048\u308b\u78ba\u7387\u306f\u9ad8\u3005 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq>\u300d\u3068\u3044\u3046\u4e00\u70b9\u3060\u3051\u3067\u3059\u3002\u8d85\u3048\u305f\u5148\u306e\u640d\u5931\u304c\u3044\u304f\u3089\u306b\u306a\u308b\u304b\uff08100 \u304b 10000 \u304b\uff09\u306f\u3001\u5206\u4f4d\u70b9\u306e\u8a08\u7b97\u306b\u4e00\u5207\u5165\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u5206\u5e03\u95a2\u6570 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u3088\u308a\u53f3\u5074\u306e\u5f62\u72b6\u3092\u5168\u304f\u53c2\u7167\u3057\u306a\u3044\u3053\u3068\u304c\u3001\u5b9a\u7fa9\u306b\u5206\u4f4d\u70b9\u3057\u304b\u73fe\u308c\u306a\u3044\u3053\u3068\u304b\u3089\u5206\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u304c VaR \u306e\u672c\u8cea\u7684\u306a\u9650\u754c\u3067\u3059\u3002 \u220e<\/p>\n<h3>THM-VAR-2 \u306e\u8a3c\u660e<\/h3>\n<p>\u53cd\u4f8b\u30921\u3064\u69cb\u6210\u3059\u308c\u3070\u5341\u5206\u3067\u3059\u3002<\/p>\n<p>\u7b49\u78ba\u7387\u306e 1000 \u30b7\u30ca\u30ea\u30aa\uff08\u5404\u78ba\u7387 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1\/1000<\/span><\/span><\/span><\/span><\/eq>\uff09\u3092\u8003\u3048\u307e\u3059\u30022\u3064\u306e\u6301\u3061\u9ad8 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u3081\u307e\u3059\u3002<\/p>\n<ul>\n<li><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq>: \u30b7\u30ca\u30ea\u30aa 1\u301c8 \u3067\u640d\u5931 100\u3001\u305d\u308c\u4ee5\u5916\u3067\u640d\u5931 0\u3002\u5927\u640d\u306e\u78ba\u7387\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">8\/1000<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8056em;vertical-align:-0.0556em;\"><\/span><span class=\"mord\">0.8%<\/span><\/span><\/span><\/span><\/eq>\u3002<\/li>\n<li><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq>: \u30b7\u30ca\u30ea\u30aa 9\u301c16 \u3067\u640d\u5931 100\u3001\u305d\u308c\u4ee5\u5916\u3067\u640d\u5931 0\u3002\u5927\u640d\u306e\u78ba\u7387\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">8\/1000<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8056em;vertical-align:-0.0556em;\"><\/span><span class=\"mord\">0.8%<\/span><\/span><\/span><\/span><\/eq>\u3002<\/li>\n<li><strong><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3068 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306e\u5927\u640d\u30b7\u30ca\u30ea\u30aa\u306f\u91cd\u306a\u3089\u306a\u3044\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/strong><\/li>\n<\/ul>\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.99<\/span><\/span><\/span><\/span><\/eq> \u3067\u306e VaR \u3092\u6c42\u3081\u307e\u3059\u3002\u5206\u4f4d\u70b9\u306e\u5b9a\u7fa9\u3088\u308a\u3001\u640d\u5931\u3092\u5c0f\u3055\u3044\u9806\u306b\u4e26\u3079\u305f\u3068\u304d\u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">\u2308<\/span><span class=\"mord\">0.99<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1000<\/span><span class=\"mclose\">\u2309<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">990<\/span><\/span><\/span><\/span><\/eq> \u756a\u76ee\u306e\u5024\u3092\u53d6\u308a\u307e\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.99<\/span><\/span><\/span><\/span><\/eq> \u3068\u306a\u308b\u306b\u306f\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l<\/span><\/span><\/span><\/span><\/eq> \u4ee5\u4e0b\u306e\u640d\u5931\u304c 990 \u30b7\u30ca\u30ea\u30aa\u4ee5\u4e0a\u5fc5\u8981\u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u3064\u3044\u3066\u3001\u4e0a\u4f4d 8 \u500b\u304c 100\u3001\u6b8b\u308a 992 \u500b\u304c 0 \u3067\u3059\u3002990 \u756a\u76ee\u306f 0 \u306e\u9818\u57df\u306b\u3042\u308b\u306e\u3067 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/eq>\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3082\u540c\u69d8\u306b <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u3002<\/p>\n<p>\u5408\u7b97 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u3064\u3044\u3066\u3001\u30b7\u30ca\u30ea\u30aa 1\u301c16 \u3067\u640d\u5931 100\u3001\u305d\u308c\u4ee5\u5916\u3067 0 \u3067\u3059\u3002\u4e0a\u4f4d 16 \u500b\u304c 100 \u3067\u3059\u304b\u3089\u3001990 \u756a\u76ee\u306f 100 \u306e\u9818\u57df\u306b\u3042\u308a\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">100<\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u3002<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.7em;vertical-align:-1.1em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6em;\"><span style=\"top:-3.6em;\"><span class=\"pstrut\" style=\"height:2.84em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-2.1em;\"><span class=\"pstrut\" style=\"height:2.84em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.1em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6em;\"><span style=\"top:-3.76em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\">100<\/span><\/span><\/span><span style=\"top:-2.26em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.1em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>\u52a3\u52a0\u6cd5\u6027\u304c\u7834\u308c\u307e\u3057\u305f\u3002\u500b\u5225\u3067\u306f VaR \u306b\u5f15\u3063\u304b\u304b\u3089\u306a\u304b\u3063\u305f\u7a00\u306a\u640d\u5931\u304c\u3001\u5408\u7b97\u3059\u308b\u3068\u78ba\u7387\u306e\u95be\u5024\u3092\u8d85\u3048\u3066 VaR \u306b\u73fe\u308c\u307e\u3059\u3002 \u220e<\/p>\n<h3>THM-VAR-3 \u306e\u8a3c\u660e\uff08\u8981\u70b9\uff09<\/h3>\n<p>ES \u306e\u5b9a\u7fa9 (2) \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.476em;vertical-align:-0.9119em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.564em;\"><span style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.8129em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9119em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>\u4efb\u610f\u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/eq> \u306b\u5bfe\u3057\u3066\u3001\u5206\u4f4d\u70b9\u306f\u51f8\u6027\u304b\u3089<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>\u304c<strong>\u4e00\u822c\u306b\u306f\u6210\u308a\u7acb\u3061\u307e\u305b\u3093<\/strong>\uff08THM-VAR-2 \u3067\u793a\u3057\u305f\u901a\u308a\uff09\u3002\u3067\u3059\u304b\u3089 VaR \u306e\u7a4d\u5206\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u305f ES \u306e\u52a3\u52a0\u6cd5\u6027\u306f\u3001VaR \u306e\u52a3\u52a0\u6cd5\u6027\u304b\u3089\u306f\u5f93\u3044\u307e\u305b\u3093\u3002<\/p>\n<p>\u8a3c\u660e\u306e\u9375\u306f\u3001ES \u3092\u5225\u306e\u5f62\u306b\u66f8\u304d\u76f4\u3059\u3053\u3068\u3067\u3059\u3002\u671f\u5f85\u5024\u304c\u6709\u9650\u306a\u4efb\u610f\u306e\u640d\u5931 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/eq> \u306b\u3064\u3044\u3066\u3001\u9023\u7d9a\u5206\u5e03\u3067\u3082\u96e2\u6563\u5206\u5e03\u3067\u3082<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6679em;\"><span style=\"top:-2.3518em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">c<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mathbb mtight\">R<\/span><\/span><\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7756em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8213em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">}<\/span><\/span><\/span><\/span><span class=\"katex-tag\"><span class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\"><\/span><span class=\"mord text\"><span class=\"mord\">(<\/span><span class=\"mord\"><span class=\"mord\">3<\/span><\/span><span class=\"mord\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff08<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq>\uff09\u3002\u6700\u5c0f\u5024\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3067\u9054\u6210\u3055\u308c\u307e\u3059\u3002\u96e2\u6563\u5206\u5e03\u3067\u306f\u6700\u5c0f\u5024\u3092\u4e0e\u3048\u308b <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/eq> \u304c\u533a\u9593\u306b\u306a\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u304c\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u306f\u305d\u306e1\u3064\u3067\u3059\u3002\u5f8c\u3067 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u3082 (3) \u3092\u4f7f\u3046\u306e\u3067\u3001\u9023\u7d9a\u5206\u5e03\u306b\u9650\u3089\u306a\u3044\u3053\u3068\u304c\u5927\u5207\u3067\u3059\u3002\u9023\u7d9a\u306a <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3092\u8db3\u3057\u3066\u3082\u3001\u305f\u3068\u3048\u3070 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306a\u3089\u548c\u306f\u5b9a\u6570\u306b\u306a\u308a\u3001\u9023\u7d9a\u5206\u5e03\u3067\u306f\u306a\u304f\u306a\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>(3) \u3092\u78ba\u304b\u3081\u307e\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U<\/span><\/span><\/span><\/span><\/eq> \u3092 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u4e0a\u306e\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u3068\u3059\u308b\u3068\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">U<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/eq> \u3068\u540c\u3058\u5206\u5e03\u3092\u6301\u3061\u307e\u3059\uff08\u5206\u4f4d\u70b9\u5909\u63db\uff09\u3002\u3053\u308c\u3092\u4f7f\u3063\u3066\u671f\u5f85\u5024\u3092\u5206\u4f4d\u70b9\u306e\u7a4d\u5206\u306b\u66f8\u304d\u76f4\u3059\u305f\u3081\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">:=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3068\u304a\u304f\u3068<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0713em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8213em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.476em;vertical-align:-0.9119em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.564em;\"><span style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><span style=\"top:-3.8129em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9119em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0713em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8213em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>\u3067\u3059\u3002\u53f3\u8fba\u306e\u4e2d\u62ec\u5f27\u3092 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3068\u66f8\u304d\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3092\u4ee3\u5165\u3057\u307e\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/eq> \u306b\u3064\u3044\u3066\u975e\u6e1b\u5c11\u306a\u306e\u3067\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u3067\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/eq>\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><\/eq> \u3067\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:5.2519em;vertical-align:-2.376em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.876em;\"><span style=\"top:-4.876em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.1em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.376em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.876em;\"><span style=\"top:-4.876em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.564em;\"><span style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.8129em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9119em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><span style=\"top:-2.1em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.564em;\"><span style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.8129em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9119em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.376em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>\u6b21\u306b\u4efb\u610f\u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/eq> \u3067 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3092\u793a\u3057\u307e\u3059\u3002\u88ab\u7a4d\u5206\u95a2\u6570\u306f\u975e\u8ca0\u306a\u306e\u3067\u7a4d\u5206\u533a\u9593\u3092 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/eq> \u306b\u7e2e\u3081\u3066\u3082\u5024\u306f\u5897\u3048\u305a\u3001\u3055\u3089\u306b <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/eq> \u306a\u306e\u3067<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:3.976em;vertical-align:-1.738em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.238em;\"><span style=\"top:-4.238em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.186em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.738em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.238em;\"><span style=\"top:-4.238em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">\u222b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.564em;\"><span style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.8129em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9119em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><span style=\"top:-2.186em;\"><span class=\"pstrut\" style=\"height:3.564em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.738em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>2\u3064\u3092\u5408\u308f\u305b\u308b\u3068\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g<\/span><\/span><\/span><\/span><\/eq> \u306e\u6700\u5c0f\u5024\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3067\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3067\u9054\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u304c (3) \u3067\u3059\u3002<\/p>\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9368em;vertical-align:-0.2481em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3092\u305d\u308c\u305e\u308c <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u5bfe\u3059\u308b\u6700\u9069\u306a <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/eq> \u3068\u3057\u307e\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9368em;vertical-align:-0.2481em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9368em;vertical-align:-0.2481em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u5bfe\u3059\u308b\u6700\u9069\u89e3\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u304c\u3001\u5b9f\u884c\u53ef\u80fd\u306a\u5024\u3067\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9368em;vertical-align:-0.2481em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u304c\u6210\u308a\u7acb\u3064\u306e\u3067\uff08<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8547em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7713em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306e\u4e0d\u7b49\u5f0f\uff09\u3001<\/p>\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:11.6261em;vertical-align:-5.563em;\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:6.063em;\"><span style=\"top:-8.6714em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-7.1714em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-5.1899em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-2.6723em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-0.1546em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:1.7547em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:5.563em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:6.063em;\"><span style=\"top:-8.6714em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-7.1714em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7387em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7387em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-5.1899em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7387em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7387em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8213em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><span style=\"top:-2.6723em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7387em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4483em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-0.1546em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7387em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4483em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6887em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2217<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:1.7547em;\"><span class=\"pstrut\" style=\"height:3.4483em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">\u03b1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:5.563em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n<p>\u7b2c1\u306e\u4e0d\u7b49\u5f0f\u306f\u6700\u5c0f\u5316\u554f\u984c\u306b\u6700\u9069\u3067\u306a\u3044 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/eq> \u3092\u4ee3\u5165\u3057\u305f\u3053\u3068\u3001\u7b2c2\u306e\u4e0d\u7b49\u5f0f\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8547em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7713em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7713em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u306b\u3088\u308b\u3082\u306e\u3067\u3059\u3002 \u220e<\/p>\n<\/details>\n\n\n\n<h2 class=\"wp-block-heading\">5. \u53cd\u4f8b \u2015 VaR \u3092\u8d85\u3048\u305f\u5148\u306f\u6e2c\u308c\u306a\u3044<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">CEX-VAR-1: VaR \u3092\u8d85\u3048\u3066\u3082\u5927\u3057\u305f\u3053\u3068\u306a\u3044\u3001\u3068\u306f\u9650\u3089\u306a\u3044<\/h3>\n\n\n\n<p>VaR \u3092\u8d85\u3048\u305f\u5834\u5408\u306e\u5e73\u5747\u640d\u5931\uff08ES\uff09\u306f\u3001VaR \u306e\u4f55\u500d\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002\u6a19\u6e96\u504f\u5dee 1 \u306e\u6b63\u898f\u5206\u5e03\u3068\u3001\u540c\u3058\u6a19\u6e96\u504f\u5dee\u3092\u6301\u3064\u81ea\u7531\u5ea6 5 \u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\u3067\u6bd4\u8f03\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th>\u6b63\u898f\u5206\u5e03<\/th>\n<th><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\uff08\u81ea\u7531\u5ea6 5\uff09<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>99% VaR<\/td>\n<td>2.3263<\/td>\n<td>2.6065<\/td>\n<\/tr>\n<tr>\n<td>99% ES<\/td>\n<td>2.6652<\/td>\n<td>3.4488<\/td>\n<\/tr>\n<tr>\n<td>ES \/ VaR<\/td>\n<td>1.1457<\/td>\n<td>1.3232<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<p>\u6b63\u898f\u5206\u5e03\u3067\u306f\u3001VaR \u3092\u8d85\u3048\u305f\u5834\u5408\u306e\u5e73\u5747\u640d\u5931\u306f VaR \u306e\u7d04 1.15 \u500d\u3067\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\u3067\u306f\u7d04 1.32 \u500d\u306b\u8df3\u306d\u4e0a\u304c\u308a\u307e\u3059\u3002\u88fe\u304c\u91cd\u3044\u5206\u5e03\u3067\u306f\u3001VaR \u3092\u8d85\u3048\u305f\u5148\u306e\u640d\u5931\u304c VaR \u304b\u3089\u60f3\u50cf\u3059\u308b\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002VaR \u306e\u6570\u5b57\u3060\u3051\u898b\u3066\u5b89\u5fc3\u3057\u3066\u3044\u308b\u3068\u3001\u5b9f\u969b\u306b\u8d85\u3048\u305f\u3068\u304d\u306e\u75db\u307f\u3092\u898b\u8aa4\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">CEX-VAR-2: \u5206\u6563\u6295\u8cc7\u304c VaR \u3092\u60aa\u5316\u3055\u305b\u308b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">THM-VAR-2 \u306e\u8a3c\u660e\u3067\u69cb\u6210\u3057\u305f\u4f8b\u304c\u305d\u306e\u307e\u307e\u53cd\u4f8b\u3067\u3059\u30021000 \u30b7\u30ca\u30ea\u30aa\u306e\u96e2\u6563\u5206\u5e03\u3067\u3001<\/p>\n\n\n\n<ul>\n<li><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/eq>\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/eq><\/li>\n<li><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">VaR<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">100<\/span><\/span><\/span><\/span><\/eq><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5408\u7b97\u3057\u305f\u3053\u3068\u3067 VaR \u304c 0 \u304b\u3089 100 \u306b\u8df3\u306d\u4e0a\u304c\u308a\u307e\u3057\u305f\u3002\u500b\u5225\u3067\u306f\u78ba\u7387 0.8% \u306e\u7a00\u306a\u4e8b\u8c61\u304c VaR \u306e\u95be\u5024\uff081%\uff09\u306e\u5185\u5074\u306b\u96a0\u308c\u3066\u3044\u305f\u306e\u306b\u3001\u5408\u7b97\u3059\u308b\u3068\u78ba\u7387 1.6% \u3068\u306a\u3063\u3066\u95be\u5024\u3092\u8d85\u3048\u305f\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u65b9\u3001\u540c\u3058\u8a2d\u5b9a\u3067 ES \u3092\u8a08\u7b97\u3059\u308b\u3068\u3001<\/p>\n\n\n\n<ul>\n<li><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">80.0<\/span><\/span><\/span><\/span><\/eq>\u3001<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">80.0<\/span><\/span><\/span><\/span><\/eq><\/li>\n<li><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">ES<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.99<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">100.0<\/span><\/span><\/span><\/span><\/eq><\/li>\n<\/ul>\n\n\n\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7804em;vertical-align:-0.136em;\"><\/span><span class=\"mord\">100.0<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\">80.0<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">80.0<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">160.0<\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u304b\u3089\u3001ES \u306f\u52a3\u52a0\u6cd5\u6027\u3092\u6e80\u305f\u3057\u3066\u3044\u307e\u3059\u3002ES \u306f\u5c3e\u90e8\u306e\u5e73\u5747\u3092\u53d6\u308b\u305f\u3081\u3001\u500b\u5225\u306b\u898b\u305f\u3068\u304d\u304b\u3089\u5927\u304d\u306a\u5024\u304c\u51fa\u3066\u304a\u308a\u3001\u5408\u7b97\u3057\u3066\u3082\u548c\u3092\u8d85\u3048\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">CEX-VAR-3: \u6b63\u898f\u5206\u5e03\u3092\u4eee\u5b9a\u3057\u3066\u3088\u3044\u306e\u304b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6a19\u6e96\u504f\u5dee\u304c\u540c\u3058 1 \u3067\u3082\u3001\u5206\u5e03\u306e\u5f62\u304c\u9055\u3048\u3070 99% VaR \u306f\u7570\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th>\u6b63\u898f\u5206\u5e03<\/th>\n<th><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\uff08\u81ea\u7531\u5ea6 5\uff09<\/th>\n<th>\u6bd4\u7387<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>99% VaR<\/td>\n<td>2.3263<\/td>\n<td>2.6065<\/td>\n<td>1.1204<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\u306e VaR \u306f\u6b63\u898f\u5206\u5e03\u306e\u7d04 1.12 \u500d\u3067\u3059\u3002\u6a19\u6e96\u504f\u5dee\u3060\u3051\u3067\u5206\u5e03\u3092\u7279\u5b9a\u3057\u305f\u3064\u3082\u308a\u306b\u306a\u308b\u3068\u3001\u88fe\u306e\u30ea\u30b9\u30af\u3092\u904e\u5c0f\u8a55\u4fa1\u3057\u307e\u3059\u3002\u5b9f\u969b\u306e\u640d\u76ca\u30c7\u30fc\u30bf\u306f\u6b63\u898f\u5206\u5e03\u3088\u308a\u88fe\u304c\u91cd\u3044\u3053\u3068\u304c\u591a\u304f\u3001\u6b63\u898f\u5206\u5e03\u3092\u4eee\u5b9a\u3057\u305f VaR \u306f\u697d\u89b3\u7684\u306a\u6570\u5b57\u306b\u306a\u308a\u304c\u3061\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">6. \u6570\u5024\u4f8b \u2015 2\u3064\u306e\u5206\u5e03\u3067 VaR \u3068 ES \u3092\u6bd4\u3079\u308b<\/h2>\n\n\n\n<p>\u6a19\u6e96\u504f\u5dee 1 \u306e\u6b63\u898f\u5206\u5e03\u3068\u3001\u540c\u3058\u6a19\u6e96\u504f\u5dee\u3092\u6301\u3064\u81ea\u7531\u5ea6 5 \u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\u3092\u6bd4\u8f03\u3057\u307e\u3059\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\u306e\u30b9\u30b1\u30fc\u30eb\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.24em;vertical-align:-0.305em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.935em;\"><span class=\"svg-align\" style=\"top:-3.2em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"mord\" style=\"padding-left:1em;\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0637em;\">\u03bd<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0637em;\">\u03bd<\/span><\/span><\/span><span style=\"top:-2.895em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.305em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.24em;vertical-align:-0.305em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.935em;\"><span class=\"svg-align\" style=\"top:-3.2em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"mord\" style=\"padding-left:1em;\"><span class=\"mord\">3\/5<\/span><\/span><\/span><span style=\"top:-2.895em;\"><span class=\"pstrut\" style=\"height:3.2em;\"><\/span><span class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.305em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u3068\u3057\u3066\u6a19\u6e96\u504f\u5dee\u3092 1 \u306b\u63c3\u3048\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5206\u5e03\u3054\u3068\u306e VaR \u3068 ES<\/strong><\/p>\n\n\n\n<table>\n<thead>\n<tr>\n<th>\u6307\u6a19<\/th>\n<th>\u6b63\u898f\u5206\u5e03<\/th>\n<th><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\uff08\u81ea\u7531\u5ea6 5\uff09<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>99% VaR<\/td>\n<td>2.3263<\/td>\n<td>2.6065<\/td>\n<\/tr>\n<tr>\n<td>99% ES<\/td>\n<td>2.6652<\/td>\n<td>3.4488<\/td>\n<\/tr>\n<tr>\n<td>ES \/ VaR<\/td>\n<td>1.1457<\/td>\n<td>1.3232<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<p>\u6b63\u898f\u5206\u5e03\u3067\u306f ES \u3068 VaR \u306e\u5dee\u306f\u5c0f\u3055\u304f\u3001VaR \u3092\u8d85\u3048\u305f\u5148\u3082\u305d\u308c\u307b\u3069\u60aa\u304f\u3042\u308a\u307e\u305b\u3093\u3002<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/eq> \u5206\u5e03\u3067\u306f ES \/ VaR \u6bd4\u304c 1.32 \u306b\u4e0a\u304c\u308a\u3001VaR \u3092\u8d85\u3048\u305f\u5148\u306e\u640d\u5931\u304c\u76f8\u5bfe\u7684\u306b\u5927\u304d\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u52a3\u52a0\u6cd5\u6027\u306e\u78ba\u8a8d\uff081000 \u30b7\u30ca\u30ea\u30aa\u306e\u96e2\u6563\u4f8b\uff09<\/strong><\/p>\n\n\n\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq><\/th>\n<th><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq><\/th>\n<th><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq><\/th>\n<th>\u500b\u5225\u306e\u548c<\/th>\n<th>\u52a3\u52a0\u6cd5\u7684\u304b<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>99% VaR<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>100<\/td>\n<td>0<\/td>\n<td>\u7834\u308c\u308b<\/td>\n<\/tr>\n<tr>\n<td>99% ES<\/td>\n<td>80.0<\/td>\n<td>80.0<\/td>\n<td>100.0<\/td>\n<td>160.0<\/td>\n<td>\u6e80\u305f\u3059<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<p class=\"wp-block-paragraph\">VaR \u306f\u5408\u7b97\u3067\u60aa\u5316\u3057\u307e\u3057\u305f\u304c\u3001ES \u306f\u5408\u7b97\u5024\u304c\u500b\u5225\u306e\u548c\u4ee5\u4e0b\u306b\u53ce\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u30ea\u30b9\u30af\u306e\u5408\u7b97\u3092\u6b63\u3057\u304f\u53cd\u6620\u3059\u308b\u6307\u6a19\u3068\u3057\u3066\u306f\u3001ES \u304c\u512a\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">7. \u5b9f\u8df5 \u2015 \u53e3\u5ea7\u306e\u30ea\u30bf\u30fc\u30f3\u3068\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u3092 Excel \u3067\u51fa\u3059<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u307e\u3067\u306e\u7b2c3\u90e8\u30fb\u7b2c4\u90e8\u3067\u7a4d\u307f\u4e0a\u3052\u305f\u30ea\u30bf\u30fc\u30f3\u306e\u5b9a\u7fa9\uff08\u7b2c19\u56de\uff09\u3001\u5e73\u5747\u3068\u5206\u6563\uff08\u7b2c29\u56de\uff09\u3001\u5bfe\u6570\u30ea\u30bf\u30fc\u30f3\uff08\u7b2c31\u56de\uff09\u3001\u5e73\u65b9\u6839\u5247\uff08\u7b2c32\u56de\uff09\u3001\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u5206\u6563\uff08\u7b2c36\u56de\uff09\u3001\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa\uff08\u7b2c40\u56de\uff09\u3092\u3001\u67b6\u7a7a\u306e\u53e3\u5ea7\u30c7\u30fc\u30bf\u306b\u5f53\u3066\u3066\u624b\u3092\u52d5\u304b\u3057\u307e\u3059\u3002\u3053\u306e\u5b9f\u8df5\u3092\u7d42\u3048\u308b\u3068\u3001\u53e3\u5ea7\u306e\u6708\u6b21\u30c7\u30fc\u30bf\u304b\u3089\u30ea\u30bf\u30fc\u30f3\u30fb\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u30fb\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa\u3092 Excel \u3067\u8a08\u7b97\u3057\u3001\u5165\u51fa\u91d1\u306e\u5f71\u97ff\u3092\u53d6\u308a\u9664\u3044\u3066\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u624b\u9806<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u67b6\u7a7a\u306e\u53e3\u5ea7\uff0813\u304b\u6708\u5206\u306e\u6708\u672b\u6b8b\u9ad8\u30fb\u5165\u51fa\u91d1\u30fb2\u8cc7\u7523\u306e\u57fa\u6e96\u4fa1\u984d\uff09\u3092\u7528\u610f\u3057\u307e\u3059\u3002\u6570\u5024\u306f\u8aac\u660e\u7528\u306e\u67b6\u7a7a\u306e\u3082\u306e\u3067\u3001\u5b9f\u5728\u306e\u53e3\u5ea7\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u67086\u306b100\u4e07\u5186\u306e\u5165\u91d1\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30b9\u30c6\u30c3\u30d71: \u5165\u51fa\u91d1\u3092\u9664\u3044\u305f\u6708\u6b21\u5358\u7d14\u30ea\u30bf\u30fc\u30f3<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b8b\u9ad8\u306e\u5909\u5316\u984d\u304b\u3089\u5165\u51fa\u91d1\u3092\u5f15\u3044\u3066\u524d\u6708\u672b\u6b8b\u9ad8\u3067\u5272\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.2547em;vertical-align:-0.8943em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3603em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u6b8b\u9ad8<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u6b8b\u9ad8<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u5165\u51fa\u91d1<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u6b8b\u9ad8<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8943em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n\n\n\n<p>Excel \u3067\u306f <code>=(C3-D3-C2)\/C2<\/code> \u3067\u3059\u3002\u67086\uff08\u5165\u91d1100\u4e07\u5186\u306e\u6708\uff09\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">6<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">625.30<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\">100.00<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">530.60<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\/530.60<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">0.009989<\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30b9\u30c6\u30c3\u30d72: \u5bfe\u6570\u30ea\u30bf\u30fc\u30f3<\/strong><\/p>\n\n\n\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">ln<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002Excel \u3067\u306f <code>=LN(1+(C3-D3-C2)\/C2)<\/code> \u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30b9\u30c6\u30c3\u30d73: \u5e74\u7387\u306e\u5e73\u5747\u30ea\u30bf\u30fc\u30f3\u3068\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3<\/strong><\/p>\n\n\n\n<p>\u6708\u6b21\u306e\u5e73\u5747\u30ea\u30bf\u30fc\u30f3\u3092 <code>=AVERAGE(E2:E13)<\/code> \u3067\u3001\u6a19\u672c\u6a19\u6e96\u504f\u5dee\u3092 <code>=STDEV.S(E2:E13)<\/code> \u3067\u6c42\u3081\u307e\u3059\u3002\u5e74\u7387\u63db\u7b97\u306f\u5e73\u5747\u3092 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">12<\/span><\/span><\/span><\/span><\/eq> \u500d\u3001\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u3092 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.04em;vertical-align:-0.1328em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9072em;\"><span class=\"svg-align\" style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\" style=\"padding-left:0.833em;\"><span class=\"mord\">12<\/span><\/span><\/span><span style=\"top:-2.8672em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1328em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u500d\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30b9\u30c6\u30c3\u30d74: \u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa<\/strong><\/p>\n\n\n\n<p>\u8d85\u904e\u30ea\u30bf\u30fc\u30f3\u3092\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u3067\u5272\u308a\u307e\u3059\u3002\u7121\u30ea\u30b9\u30af\u91d1\u5229\u306f\u5e74 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8056em;vertical-align:-0.0556em;\"><\/span><span class=\"mord\">0.5%<\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u3002<\/p>\n\n\n\n<section><eqn><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">SR<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.3331em;vertical-align:-0.836em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4971em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">annual<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8201em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1667em;\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">annual<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/eqn><\/section>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30b9\u30c6\u30c3\u30d75: \u5171\u5206\u6563\u884c\u5217\u3068\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u5206\u6563<\/strong><\/p>\n\n\n\n<p>2\u8cc7\u7523\u306e\u6708\u6b21\u30ea\u30bf\u30fc\u30f3\u304b\u3089 <code>=COVARIANCE.S(F2:F13,G2:G13)<\/code> \u3067\u5171\u5206\u6563\u3092\u3001<code>=CORREL(F2:F13,G2:G13)<\/code> \u3067\u76f8\u95a2\u4fc2\u6570\u3092\u6c42\u3081\u307e\u3059\u3002\u30a6\u30a7\u30a4\u30c8 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0.60<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">0.40<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u306e\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u5206\u6563\u306f <code>=SUMPRODUCT(H2:H3,MMULT(I2:J3,H2:H3))<\/code> \u3067\u51fa\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30b3\u30fc\u30c9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Excel \u306e\u8a08\u7b97\u3092 Python \u3067\u691c\u7b97\u3057\u307e\u3059\u300250\u884c\u4ee5\u5185\u3001\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u307f\u3067\u3059\u3002<\/p>\n\n\n\n<pre><code class=\"language-python\">import math\n\n# --- \u30c7\u30fc\u30bf ---\nbalance = [500.00, 510.50, 505.20, 520.80, 515.00, 530.60,\n           625.30, 620.10, 635.40, 628.70, 645.20, 660.80, 655.50]\ncashflow = [0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0]\nnav_a = [10000,10180,10090,10350,10250,10500,10420,\n         10310,10550,10480,10700,10950,10850]\nnav_b = [10000,10030,10050,10080,10060,10100,10090,\n         10110,10140,10120,10160,10190,10170]\nw_a, w_b, r_ann = 0.60, 0.40, 0.005\n\n# --- \u6708\u6b21\u30ea\u30bf\u30fc\u30f3\uff08\u5165\u51fa\u91d1\u9664\u53bb\uff09 ---\nret = [(balance[t]-cashflow[t]-balance[t-1])\/balance[t-1]\n       for t in range(1, 13)]\nlog_ret = [math.log(1 + r) for r in ret]\n\n# --- \u5e74\u7387\u6307\u6a19 ---\navg_m = sum(ret) \/ 12\nstd_m = math.sqrt(sum((r - avg_m)**2 for r in ret) \/ 11)\nprint(f&quot;\u5e74\u7387\u5e73\u5747\u30ea\u30bf\u30fc\u30f3: {avg_m*12:.6f}&quot;)\nprint(f&quot;\u5e74\u7387\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3: {std_m*math.sqrt(12):.6f}&quot;)\nprint(f&quot;\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa: {(avg_m*12 - r_ann)\/(std_m*math.sqrt(12)):.4f}&quot;)\n\n# --- 2\u8cc7\u7523\u306e\u5171\u5206\u6563\u30fb\u76f8\u95a2 ---\nra = [(nav_a[t]-nav_a[t-1])\/nav_a[t-1] for t in range(1,13)]\nrb = [(nav_b[t]-nav_b[t-1])\/nav_b[t-1] for t in range(1,13)]\nma, mb = sum(ra)\/12, sum(rb)\/12\nva = sum((x-ma)**2 for x in ra)\/11\nvb = sum((x-mb)**2 for x in rb)\/11\ncab = sum((a-ma)*(b-mb) for a, b in zip(ra, rb))\/11\nprint(f&quot;\u5171\u5206\u6563\u884c\u5217: [[{va:.6f}, {cab:.6f}], [{cab:.6f}, {vb:.6f}]]&quot;)\nprint(f&quot;\u76f8\u95a2\u4fc2\u6570: {cab\/(va**0.5 * vb**0.5):.4f}&quot;)\n\n# --- \u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u5206\u6563 ---\nvp = w_a**2*va + 2*w_a*w_b*cab + w_b**2*vb\nprint(f&quot;\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u6708\u6b21\u6a19\u6e96\u504f\u5dee: {vp**0.5:.6f}&quot;)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u30b3\u30fc\u30c9\u306f <code>compute_practice.py<\/code> \u3068\u540c\u3058\u6570\u5024\u3092\u51fa\u3057\u307e\u3059\u3002\u51fa\u529b\u306f\u6b21\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<pre><code>\u5e74\u7387\u5e73\u5747\u30ea\u30bf\u30fc\u30f3: 0.098878\n\u5e74\u7387\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3: 0.065691\n\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa: 1.4291\n\u5171\u5206\u6563\u884c\u5217: [[0.000273, 0.000032], [0.000032, 0.000006]]\n\u76f8\u95a2\u4fc2\u6570: 0.8026\n\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u6708\u6b21\u6a19\u6e96\u504f\u5dee: 0.010698\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u7d50\u679c\u306e\u8aad\u307f\u65b9<\/h3>\n\n\n\n<p>\u5e74\u7387\u5e73\u5747\u30ea\u30bf\u30fc\u30f3 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.098878<\/span><\/span><\/span><\/span><\/eq>\u3001\u5e74\u7387\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.065691<\/span><\/span><\/span><\/span><\/eq>\u3001\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">1.4291<\/span><\/span><\/span><\/span><\/eq> \u304c\u6b63\u3057\u3044\u5024\u3067\u3059\u3002\u305f\u3060\u3057\u300112\u304b\u6708\u3068\u3044\u3046\u77ed\u3044\u6a19\u672c\u3067\u306f\u63a8\u5b9a\u8aa4\u5dee\u304c\u5927\u304d\u304f\u3001\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa\u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8056em;vertical-align:-0.0556em;\"><\/span><span class=\"mord\">95%<\/span><\/span><\/span><\/span><\/eq> \u4fe1\u983c\u533a\u9593\u306e\u534a\u5e45\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">2.0417<\/span><\/span><\/span><\/span><\/eq> \u3067\u3059\u3002\u533a\u9593\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">0.6126<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">3.4708<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/eq> \u3068\u306a\u308a\u30bc\u30ed\u3092\u307e\u305f\u3050\u305f\u3081\u3001\u6b63\u304b\u8ca0\u304b\u3059\u3089\u5224\u5b9a\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">CEX-PR42-1: \u5165\u51fa\u91d1\u3092\u9664\u304b\u306a\u3044\u3068\u5168\u6307\u6a19\u304c\u6b6a\u3080<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5165\u51fa\u91d1\u3092\u9664\u3044\u305f\u5834\u5408\u3068\u9664\u304b\u306a\u3044\u5834\u5408\u3092\u4e26\u3079\u307e\u3059\u3002<\/p>\n\n\n\n<table>\n<thead>\n<tr>\n<th>\u6307\u6a19<\/th>\n<th>\u5165\u51fa\u91d1\u9664\u53bb\u3042\u308a<\/th>\n<th>\u5165\u51fa\u91d1\u9664\u53bb\u306a\u3057<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5e74\u7387\u5e73\u5747\u30ea\u30bf\u30fc\u30f3<\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.098878<\/span><\/span><\/span><\/span><\/eq><\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.287344<\/span><\/span><\/span><\/span><\/eq><\/td>\n<\/tr>\n<tr>\n<td>\u5e74\u7387\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3<\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.065691<\/span><\/span><\/span><\/span><\/eq><\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.179831<\/span><\/span><\/span><\/span><\/eq><\/td>\n<\/tr>\n<tr>\n<td>\u30b7\u30e3\u30fc\u30d7\u30ec\u30b7\u30aa<\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">1.4291<\/span><\/span><\/span><\/span><\/eq><\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">1.5701<\/span><\/span><\/span><\/span><\/eq><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<p>\u5165\u51fa\u91d1\u3092\u9664\u304b\u306a\u3044\u3068\u3001\u67086\u306e\u30ea\u30bf\u30fc\u30f3\u304c <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.178477<\/span><\/span><\/span><\/span><\/eq> \u306b\u8df3\u306d\u4e0a\u304c\u308a\u3001\u5e74\u7387\u5e73\u5747\u30ea\u30bf\u30fc\u30f3\u306f\u7d043\u500d\u306b\u81a8\u3089\u307f\u307e\u3059\u3002\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u3082\u7d043\u500d\u3067\u3059\u3002\u5165\u51fa\u91d1\u3092\u9664\u304b\u306a\u3044\u6307\u6a19\u306f\u3001\u904b\u7528\u306e\u8155\u3067\u306f\u306a\u304f\u5165\u91d1\u306e\u5927\u304d\u3055\u3092\u6e2c\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">CEX-PR42-2: \u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u306e\u5e74\u7387\u63db\u7b97\u3092\u9593\u9055\u3048\u308b<\/h4>\n\n\n\n<p>\u6708\u6b21\u6a19\u6e96\u504f\u5dee <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.018963<\/span><\/span><\/span><\/span><\/eq> \u3092\u5e74\u7387\u306b\u76f4\u3059\u65b9\u6cd5\u3092\u6bd4\u3079\u307e\u3059\u3002<\/p>\n\n\n\n<table>\n<thead>\n<tr>\n<th>\u65b9\u6cd5<\/th>\n<th>\u5e74\u7387\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u6b63\u3057\u3044\uff08<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.04em;vertical-align:-0.1328em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9072em;\"><span class=\"svg-align\" style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\" style=\"padding-left:0.833em;\"><span class=\"mord\">12<\/span><\/span><\/span><span style=\"top:-2.8672em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1328em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq>\uff09<\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.065691<\/span><\/span><\/span><\/span><\/eq><\/td>\n<\/tr>\n<tr>\n<td>\u9593\u9055\u3044\uff08<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">12<\/span><\/span><\/span><\/span><\/eq>\uff09<\/td>\n<td><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">0.227562<\/span><\/span><\/span><\/span><\/eq><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n<p><eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">12<\/span><\/span><\/span><\/span><\/eq> \u500d\u306f <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.04em;vertical-align:-0.1328em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9072em;\"><span class=\"svg-align\" style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\" style=\"padding-left:0.833em;\"><span class=\"mord\">12<\/span><\/span><\/span><span style=\"top:-2.8672em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1328em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/eq> \u500d\u306e <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.04em;vertical-align:-0.1328em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9072em;\"><span class=\"svg-align\" style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\" style=\"padding-left:0.833em;\"><span class=\"mord\">12<\/span><\/span><\/span><span style=\"top:-2.8672em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1328em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">3.4641<\/span><\/span><\/span><\/span><\/eq> \u500d\u3067\u3001\u5e74\u7387\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u3092\u7d04 <eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">3.5<\/span><\/span><\/span><\/span><\/eq> \u500d\u306b\u904e\u5927\u8a55\u4fa1\u3057\u307e\u3059\u3002\u5e73\u5747\u30ea\u30bf\u30fc\u30f3\u306f\uff08\u5bfe\u6570\u30ea\u30bf\u30fc\u30f3\u304c\u72ec\u7acb\u306a\u5834\u5408\uff09<eq><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">12<\/span><\/span><\/span><\/span><\/eq> \u500d\u3067\u3088\u3044\u306e\u3067\u3001\u5e73\u5747\u3068\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u306e\u5e74\u7387\u63db\u7b97\u306e\u30eb\u30fc\u30eb\u304c\u9055\u3046\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">8. \u6b21\u56de\u3078 \u2015 \u7121\u88c1\u5b9a\u3060\u3051\u3067\u4fa1\u683c\u3092\u6c7a\u3081\u308b\u4e16\u754c<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">VaR \u3082 ES \u3082\u300c\u30ea\u30b9\u30af\u3092\u6e2c\u308b\u300d\u9053\u5177\u3067\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30ea\u30b9\u30af\u306e\u5927\u304d\u3055\u3092\u77e5\u308b\u3053\u3068\u3068\u3001\u9069\u6b63\u306a\u4fa1\u683c\u3092\u77e5\u308b\u3053\u3068\u306f\u5225\u306e\u554f\u984c\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b21\u56de\u304b\u3089\u306f\u7b2c5\u90e8\u306b\u5165\u308a\u3001\u3053\u3053\u307e\u3067\u7a4d\u307f\u4e0a\u3052\u3066\u304d\u305f\u78ba\u7387\u3068\u671f\u5f85\u5024\u306e\u9053\u5177\u3092\u3044\u3063\u305f\u3093\u8107\u306b\u7f6e\u304d\u307e\u3059\u3002\u7121\u88c1\u5b9a\u3068\u3044\u3046\u4eee\u5b9a\u3060\u3051\u3067\u3001\u30c7\u30ea\u30d0\u30c6\u30a3\u30d6\u306e\u4fa1\u683c\u304c\u3069\u3053\u307e\u3067\u6c7a\u307e\u308b\u306e\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u56de\u3067\u30012\u3064\u76ee\u306e\u30de\u30a4\u30eb\u30b9\u30c8\u30fc\u30f3\u306b\u5230\u9054\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u3088\u304f\u3042\u308b\u8cea\u554f<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>VaR \u3068 ES \u306f\u3069\u3061\u3089\u3092\u4f7f\u3046\u3079\u304d\u3067\u3059\u304b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5206\u6563\u6295\u8cc7\u306e\u52b9\u679c\u3092\u6b63\u3057\u304f\u53cd\u6620\u3057\u305f\u3044\u306a\u3089 ES \u3067\u3059\u3002\u898f\u5236\u3067\u3082 ES \u3078\u306e\u79fb\u884c\u304c\u9032\u3093\u3067\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>99\u30d1\u30fc\u30bb\u30f3\u30c8 VaR \u306a\u3089\u5b89\u5168\u3067\u3059\u304b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">100\u56de\u306b1\u56de\u306f\u8d85\u3048\u307e\u3059\u3002\u8d85\u3048\u305f\u3068\u304d\u306b\u3069\u308c\u3060\u3051\u640d\u3059\u308b\u304b\u306f VaR \u304b\u3089\u306f\u5206\u304b\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6570\u5b571\u3064\u306b\u307e\u3068\u3081\u308b\u306e\u306f\u5371\u967a\u3067\u3059\u304b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4fbf\u5229\u3067\u3059\u304c\u3001\u5fc5\u305a\u4f55\u304b\u3092\u6368\u3066\u3066\u3044\u307e\u3059\u3002\u4f55\u3092\u6368\u3066\u305f\u304b\u3092\u77e5\u3063\u3066\u4f7f\u3046\u3053\u3068\u304c\u5927\u4e8b\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n\n<li>Artzner P.\u3001Delbaen F.\u3001Eber J. M. and Heath D.\u3001Coherent Measures of Risk\u3001Mathematical Finance\u30011999\u5e74\u3001DOI 10.1111\/1467-9965.00068<\/li>\n\n\n<li>McNeil A. J.\u3001Frey R. and Embrechts P.\u3001Quantitative Risk Management\u3001\u6539\u8a02\u7248\u3001Princeton University Press\u30012015\u5e74<\/li>\n\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u6570\u5024\u4f8b\u306f <code>compute.py<\/code> \u306b\u3088\u308a\u8a08\u7b97\u6e08\u307f\uff08\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306f\u4e71\u6570\u30b7\u30fc\u30c9\u56fa\u5b9a\u3067\u691c\u7b97\uff09\u3002\u672c\u6587\u4e2d\u306e\u5c0f\u6570\u306f4\u6841\u3067\u4e38\u3081\u3066\u3044\u308b\u3002<\/em><\/p>\n\n","protected":false},"excerpt":{"rendered":"<p>\u4f4d\u7f6e: \u7b2c4\u90e8 \u7b2c42\u56de \/ \u524d\u63d0: \u7b2c20\u56de\u3001\u7b2c35\u56de \/ \u6570\u5b66\u7de8: M29 \/ \u3053\u306e\u56de\u3067\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068: \u640d\u5931\u5206\u5e03\u304b\u3089 VaR \u3068 Expected Shortfall \u3092\u8a08\u7b97\u3057\u3001VaR \u304c\u5206\u6563\u6295\u8cc7\u306e\u52b9\u679c\u3092\u6b63\u3057 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":209140,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[159],"tags":[163],"class_list":["post-208449","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-financial-engineering","tag-fe-part3-portfolio"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.4 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u4f4d\u7f6e: \u7b2c4\u90e8 \u7b2c42\u56de \/ \u524d\u63d0: \u7b2c20\u56de\u3001\u7b2c35\u56de \/ \u6570\u5b66\u7de8: M29 \/ \u3053\u306e\u56de\u3067\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"\u6c34\u91ce\u502b\u592a\u90ce\"\/>\n\t<link rel=\"canonical\" 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