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\u4f5c \u8005\uff1a\u8001\u4f59\u635e\u9c7c<\/a><\/p>\n\n\n\n

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\u00b7 \u00b7 \u00b7<\/p>\n\n\n\n

\u6bcf\u4e2a\u8003\u8fc7CFA\u7684\u91cf\u5316\u4eba\u90fd\u80fd\u80cc\u8fd9\u6bb5\u8bdd\uff1a\u5747\u503c\u65b9\u5dee\u4f18\u5316\uff08MVO\uff09\u8106\u5f31\uff0c\u9884\u671f\u56de\u62a5\u8f93\u5165\u4e0d\u53ef\u9760\uff0c\u5410\u51fa\u6765\u7684\u7ec4\u5408\u5bf9\u4f30\u8ba1\u566a\u97f3\u6781\u5ea6\u654f\u611f\u30021989\u5e74\uff0cRichard Michaud\u7ed9\u5b83\u8d77\u4e86\u4e2a\u5916\u53f7\u53eb”\u8bef\u5dee\u653e\u5927\u5668”\uff0c\u8fd9\u4e2a\u6807\u7b7e\u4e00\u8d34\u5c31\u662f\u4e09\u5341\u591a\u5e74\u30022009\u5e74\u6709\u7bc7\u7814\u7a76\u66f4\u624e\u5fc3\uff1a\u5728\u5b9e\u6d4b\u4e2d\uff0c\u6700\u7b80\u5355\u7c97\u66b4\u7684”\u7b49\u6743\u91cd\u7b56\u7565”\uff08\u5c31\u662f\u628a\u94b1\u5e73\u5747\u5206\u7ed9\u6bcf\u53ea\u80a1\u7968\uff09\u5c45\u7136\u8dd1\u8d62\u4e8614\u79cdMVO\u7684\u53d8\u79cd\u3002<\/p>\n\n\n\n

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\u4f46\u5728\u771f\u6b63\u505a\u91cf\u5316\u4ea4\u6613\u7684\u4eba\u773c\u91cc\uff0c\u90a3\u4e9b\u5929\u5929\u8dd1Barra\u6216\u8005Aladdin\u7cfb\u7edf\u7684\uff0c\u8fd9\u5b8c\u5168\u4e0d\u662f\u4e8b\u5b9e\u3002\u6709\u610f\u601d\u7684\u4e0d\u662fMVO\u8fd8\u5728\u7528\uff0c\u800c\u662f\u5b83\u5230\u5e95\u600e\u4e48\u88ab”\u6551\u6d3b”\u7684\u3001\u4e3a\u4ec0\u4e48\u8fd9\u5957\u4fee\u590d\u65b9\u6848\u4e00\u76f4\u6ca1\u53d8\u4fbf\u5b9c\uff0c\u4ee5\u53ca\u8fd9\u5bf9\u4f60\u6311\u9009\u57fa\u91d1\u7ecf\u7406\u610f\u5473\u7740\u4ec0\u4e48\u3002\u4e49\u3002<\/p>\n\n\n\n

\u4e00\u3001\u95ee\u9898<\/strong>\u5230\u5e95\u51fa\u5728\u54ea\u513f\uff0c\u5176\u5b9e\u65e9\u5c31\u88ab\u7b97\u6e05\u695a\u4e86<\/strong><\/h2>\n\n\n\n

Michaud 1989\u5e74\u90a3\u7bc7\u8bba\u6587\u88ab\u5f15\u7528\u4e86\u65e0\u6570\u6b21\uff0c\u4f46\u5f88\u5c11\u6709\u4eba\u51c6\u786e\u8bf4\u6e05\u695a\u4ed6\u53d1\u73b0\u4e86\u4ec0\u4e48\u3002\u6838\u5fc3\u95ee\u9898\u5c31\u4e00\u53e5\u8bdd\uff1aMVO\u603b\u662f\u503e\u5411\u4e8e\u91cd\u4ed3\u90a3\u4e9b”\u8f93\u5165\u6570\u636e\u6700\u4e0d\u9760\u8c31”\u7684\u8d44\u4ea7\u3002\u56e0\u4e3a\u4f18\u5316\u5668\u5206\u4e0d\u6e05”\u8fd9\u4e2a\u8d44\u4ea7\u771f\u7684\u56de\u62a5\u9ad8”\u548c”\u6570\u636e\u8bef\u5dee\u770b\u8d77\u6765\u50cf\u56de\u62a5\u9ad8”\u7684\u533a\u522b\uff0c\u6240\u4ee5\u5b83\u4f1a\u628a\u94b1\u731b\u7838\u5230\u90a3\u4e9b\u6570\u636e\u566a\u97f3\u6700\u5927\u7684\u5730\u65b9\u3002\u8fd9\u4e0d\u662f\u6570\u5b66\u7684\u9519\uff0c\u6570\u5b66\u53ea\u662f\u8001\u5b9e\u6267\u884c\u4e86\u6307\u4ee4\u3002\u9519\u7684\u662f\u628a\u4e00\u5806\u5145\u6ee1\u566a\u58f0\u7684\u5386\u53f2\u6570\u636e\u5582\u7ed9\u4e86\u4e00\u53f0\u6839\u672c\u6ca1\u6709”\u8bef\u5dee”\u6982\u5ff5\u7684\u7ebf\u6027\u4ee3\u6570\u673a\u5668\u3002<\/p>\n\n\n\n

\u56db\u5e74\u540e\uff0cChopra\u548cZiemba\u66f4\u72e0\uff0c\u76f4\u63a5\u628a\u54ea\u79cd\u8f93\u5165\u6700\u81f4\u547d\u7ed9\u91cf\u5316\u4e86\u3002\u4ed6\u4eec\u6a21\u62df\u4e86\u4e00\u4e2a\u5927\u578b\u673a\u6784\u6295\u8d44\u8005\u7684\u98ce\u9669\u627f\u53d7\u80fd\u529b\uff0c\u7136\u540e\u53d1\u73b0\uff1a\u9884\u671f\u56de\u62a5\u7684\u4f30\u8ba1\u8bef\u5dee\u5bf9\u6700\u7ec8\u7ec4\u5408\u7684\u7834\u574f\u529b\uff0c\u662f\u65b9\u5dee\u8bef\u5dee\u768411\u500d\uff0c\u800c\u65b9\u5dee\u8bef\u5dee\u53c8\u662f\u534f\u65b9\u5dee\u8bef\u5dee\u76842\u500d\u3002\u6362\u7b97\u4e0b\u6765\uff0c\u56de\u62a5\u8bef\u5dee\u7684\u603b\u6740\u4f24\u529b\u662f\u534f\u65b9\u5dee\u8bef\u5dee\u768422\u500d\u3002\u628a\u4e09\u4e2a\u8bef\u5dee\u653e\u540c\u4e00\u628a\u5c3a\u5b50\u4e0a\u770b\uff1a\u534f\u65b9\u5dee\u7b971\uff0c\u65b9\u5dee\u7b972\uff0c\u56de\u62a5\u7b9722\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u6240\u6709\u4f30\u8ba1\u8bef\u5dee\u91cc\uff0c\u56de\u62a5\u9884\u6d4b\u4e0d\u51c6\u5360\u4e86\u6574\u657488%\u7684\u9505\u3002<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

\u25b2 MVO\u4f30\u8ba1\u8bef\u5dee\u8d21\u732e\u5360\u6bd4\uff1a\u56de\u62a588%\uff0c\u65b9\u5dee8%\uff0c\u534f\u65b9\u5dee4%\uff08Chopra & Ziemba, 1993\uff09<\/p>\n\n\n\n

88%\uff0c<\/strong>\u8fd9\u4e0d\u662f\u56db\u820d\u4e94\u5165\u80fd\u7cca\u5f04\u8fc7\u53bb\u7684\uff0c\u8fd9\u662f\u4e00\u4e2a\u6570\u91cf\u7ea7\u7684\u78be\u538b\u3002\u7edd\u5927\u591a\u6570\u79d1\u666e\u6587\u7ae0\u8df3\u8fc7\u8fd9\u4e2a\u6570\u5b57\uff0c\u56e0\u4e3a\u5b83\u628a\u4e00\u4e2a\u6a21\u7cca\u7684”MVO\u4e0d\u884c”\u53d8\u6210\u4e86\u4e00\u53e5\u5177\u4f53\u7684\u5de5\u7a0b\u6307\u4ee4\uff1a\u53ea\u8981\u628a\u56de\u62a5\u4f30\u8ba1\u4fee\u597d\u4e86\uff0c\u5927\u90e8\u5206\u95ee\u9898\u5c31\u89e3\u51b3\u4e86\u3002<\/p>\n\n\n\n

2009\u5e74\uff0cDeMiguel\u3001Garlappi\u548cUppal\u7ed9\u51fa\u4e86\u5b9e\u8bc1”\u5224\u51b3\u4e66”\u3002\u4ed6\u4eec\u57287\u7ec4\u771f\u5b9e\u6570\u636e\u4e0a\u6d4b\u8bd5\u4e8614\u79cdMVO\u53d8\u79cd\uff0c\u6ca1\u6709\u4e00\u4e2a\u80fd\u5728\u5b9e\u9645\u4ea4\u6613\u4e2d\u7a33\u5b9a\u8dd1\u8d62\u7b49\u6743\u91cd\u7ec4\u5408\u3002\u4ed6\u4eec\u8fd8\u7b97\u4e86\u7b14\u8d26\uff1a\u5982\u679c\u4f60\u670925\u53ea\u80a1\u7968\uff0c\u9700\u8981\u5927\u7ea63000\u4e2a\u6708\uff08\u4e5f\u5c31\u662f250\u5e74\uff09\u7684\u5386\u53f2\u6570\u636e\uff0cMVO\u624d\u80fd\u5728\u7edf\u8ba1\u4e0a”\u53ef\u9760\u5730”\u51fb\u8d25\u5e73\u5747\u5206\u914d\uff1b50\u53ea\u80a1\u7968\u7684\u8bdd\uff0c\u9700\u89816000\u4e2a\u6708\uff08500\u5e74\uff09\u3002\u73b0\u5b9e\u4e2d\u6ca1\u6709\u54ea\u4e2a\u57fa\u91d1\u6709250\u5e74\u5e72\u51c0\u7684\u6570\u636e\u30022024\u5e74\u6709\u4eba\u628a\u6d4b\u8bd5\u7a97\u53e3\u53c8\u5ef6\u957f\u4e8620\u5e74\u91cd\u65b0\u9a8c\u8bc1\uff0c\u7ed3\u8bba\u7eb9\u4e1d\u4e0d\u52a8\u3002<\/p>\n\n\n\n

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\u4f46\u5b83\u4ece\u6ca1\u8bf4\u8fc7MVO\u6846\u67b6\u672c\u8eab\u8be5\u6b7b\u3002\u5b83\u8bf4\u7684\u662f\u90a3\u4e24\u4e2a\u8f93\u5165\u4e0d\u80fd\u76f4\u63a5\u4ece\u539f\u59cb\u5386\u53f2\u6570\u636e\u91cc\u751f\u642c\u786c\u5957\u3002\u8fd9\u662f\u4e24\u4e2a\u72ec\u7acb\u7684\u5de5\u7a0b\u95ee\u9898\uff0c\u4e1a\u754c\u51e0\u5341\u5e74\u524d\u5c31\u5206\u522b\u89e3\u51b3\u4e86\u30022009\u5e74\u90a3\u7bc7\u8bba\u6587\u5f97\u51fa”\u7b49\u6743\u8dd1\u8d62MVO”\u7684\u7ed3\u8bba\uff0c\u6070\u6070\u662f\u56e0\u4e3a\u4ed6\u4eec\u6545\u610f\u6d4b\u7684\u662f\u6ca1\u4fee\u8fc7\u7684”\u539f\u5382\u7248”\uff0c\u4eba\u5bb6\u5c31\u662f\u8981\u6d4b\u90a3\u4e2a\u7248\u672c\u3002<\/p>\n\n\n\n

\u4e8c\u3001\u4fee<\/strong>\u590d\u7b2c\u4e00\u5757\u77ed\u677f\uff1a\u628a”\u731c\u56de\u62a5”\u53d8\u6210”\u53cd\u63a8\u56de\u62a5”<\/strong><\/h2>\n\n\n\n

1992\u5e74\uff0cFischer Black\u548cRobert Litterman\u5728\u9ad8\u76db\u5de5\u4f5c\u65f6\u53d1\u8868\u4e86\u4ed6\u4eec\u6700\u77e5\u540d\u7684\u6a21\u578b\u3002\u521d\u8877\u5f88\u5b9e\u9645\uff1a\u5e2e\u5ba2\u6237\u6784\u5efa\u5168\u7403\u503a\u5238\u7ec4\u5408\uff0c\u4f46\u5ba2\u6237\u4e0d\u53ef\u80fd\u5bf9\u6bcf\u4e2a\u5e02\u573a\u7684\u9884\u671f\u56de\u62a5\u90fd\u6709\u72ec\u7acb\u3001\u81ea\u4fe1\u7684\u5224\u65ad\u3002<\/p>\n\n\n\n

\u4ed6\u4eec\u7684\u521b\u65b0\u53eb\u53cd\u5411\u4f18\u5316\u3002\u4e0d\u8ba9\u5206\u6790\u5e08\u4f30\u56de\u62a5\u518d\u5582\u8fdb\u4f18\u5316\u5668\uff0c\u800c\u662f\u53cd\u8fc7\u6765\uff1a\u62ff\u5e02\u573a\u5b9e\u9645\u7684\u5e02\u503c\u52a0\u6743\u7ec4\u5408\u4f5c\u4e3a\u7ed9\u5b9a\u8f93\u5165\uff08\u8fd9\u662f\u6574\u4e2a\u5e02\u573a\u5df2\u7ecf\u96c6\u4f53\u613f\u610f\u6301\u6709\u7684\u90a3\u4e2a\u7ec4\u5408\uff09\uff0c\u53cd\u89e3\u51fa\u8ba9\u8fd9\u4e2a\u7ec4\u5408\u6700\u4f18\u7684\u9884\u671f\u56de\u62a5\u3002\u8fd9\u4e9b”\u9690\u542b\u5747\u8861\u56de\u62a5”\u6210\u4e86\u4e00\u4e2a\u6709\u7eaa\u5f8b\u7684\u3001\u5e02\u573a\u884d\u751f\u51fa\u6765\u7684\u5148\u9a8c\u3002\u6295\u8d44\u8005\u7684\u5b9e\u9645\u89c2\u70b9\u53ea\u5728\u6709\u5177\u4f53\u91cf\u5316\u5224\u65ad\u65f6\u624d\u53e0\u52a0\u8fdb\u53bb\uff0c\u6309\u4fe1\u5fc3\u7a0b\u5ea6\u52a0\u6743\u3002<\/p>\n\n\n\n

Black-Litterman\u6ca1\u6709\u628aMVO\u8e22\u51fa\u6d41\u6c34\u7ebf\u3002\u5b83\u672c\u8eab\u5c31\u662fMVO\u3002\u53ea\u662f\u628a”\u4ece\u5386\u53f2\u731c\u56de\u62a5\u5411\u91cf”\u66ff\u6362\u6210”\u4ece\u65e0\u5957\u5229\u5e02\u573a\u4ef7\u683c\u5012\u63a8\u56de\u62a5\uff0c\u518d\u5728\u6709\u89c2\u70b9\u7684\u5730\u65b9\u8c03\u6574”\u3002\u5b83\u5927\u5e45\u7f13\u89e3\u4e86Chopra\u548cZiemba 1993\u5e74\u91cf\u5316\u51fa\u6765\u7684\u90a3\u4e2a\u4e3b\u8981\u8bef\u5dee\u6e90\uff0c\u800c\u975e\u5b8c\u5168\u6d88\u9664\u3002\u6b8b\u7559\u901a\u9053\u662f\u6295\u8d44\u8005\u81ea\u5df1\u8f93\u5165\u7684\u89c2\u70b9\uff0c\u4ecd\u7136\u662f\u4e0d\u786e\u5b9a\u7684\u4eba\u4e3a\u8f93\u5165\uff0c\u4f46\u6bd4”\u5bf9\u6574\u4e2a\u8d44\u4ea7\u7a7a\u95f4\u505a\u65e0\u7ea6\u675f\u7684\u5386\u53f2\u5747\u503c\u4f30\u8ba1”\u5c0f\u5f97\u591a\u3001\u6709\u7eaa\u5f8b\u5f97\u591a\u3002<\/p>\n\n\n\n

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\u4e09\u3001\u4fee<\/strong>\u590d\u7b2c\u4e8c\u5757\u77ed\u677f\uff1a\u628a\u534f\u65b9\u5dee\u77e9\u9635”\u538b\u7f29”\u4e00\u4e0b<\/strong><\/h2>\n\n\n\n

\u534f\u65b9\u5dee\u77e9\u9635\u7684\u95ee\u9898\u6709\u81ea\u5df1\u7684\u89e3\u6cd5\uff0c\u751a\u81f3\u6bd4\u7b2c\u4e00\u4e2a\u8f93\u5165\u4fee\u5f97\u66f4\u65e9\u3002<\/p>\n\n\n\n

N\u53ea\u80a1\u7968\u7684\u534f\u65b9\u5dee\u77e9\u9635\u6709\u591a\u5c11\u4e2a\u72ec\u7acb\u53c2\u6570\u5462\uff1fN\u00d7(N+1)\/2\u4e2a\u3002500\u53ea\u80a1\u7968\u7684\u8bdd\uff0c\u5c31\u662f125,250\u4e2a\u65b9\u5dee\u548c\u534f\u65b9\u5dee\u9879\u3002\u53ef\u73b0\u5b9e\u4e2d\u4f60\u80fd\u7528\u7684\u6570\u636e\u5927\u6982\u53ea\u67095\u523010\u5e74\u7684\u6708\u5ea6\u56de\u62a5\uff0c\u6bcf\u53ea\u80a1\u7968\u9876\u591a60\u5230120\u4e2a\u6570\u636e\u70b9\u3002\u7528\u8fd9\u4e48\u5c11\u7684\u6570\u636e\u53bb\u4f30\u7b97125,250\u4e2a\u53c2\u6570\uff0c\u600e\u4e48\u7b97\u90fd\u4e0d\u9760\u8c31\u3002\u8fd9\u4e2a\u89c4\u6a21\u4e0b\u7684\u6837\u672c\u534f\u65b9\u5dee\u77e9\u9635\u57fa\u672c\u88ab\u566a\u97f3\u6df9\u6ca1\u4e86\uff0c\u6b63\u597d\u5c31\u662fMichaud\u8bf4\u7684\u90a3\u79cd\u4f18\u5316\u5668\u4f1a\u653e\u5927\u4e0d\u7a33\u5b9a\u7684\u6e90\u5934\u3002<\/p>\n\n\n\n

Barr Rosenberg 1974\u5e74\u7684\u8bba\u6587\u7ed9\u4e86\u884c\u4e1a\u6cbf\u7528\u81f3\u4eca\u7684\u601d\u8def\uff1a\u591a\u56e0\u5b50\u534f\u65b9\u5dee\u6a21\u578b\u3002\u7b80\u5355\u8bf4\uff0c\u5c31\u662f\u6bcf\u53ea\u80a1\u7968\u7684\u56de\u62a5\u4e0d\u662f\u5b64\u7acb\u7684\uff0c\u800c\u662f\u7531\u5b83\u5bf9\u5c11\u6570\u51e0\u4e2a”\u516c\u5171\u56e0\u5b50”\u7684\u66b4\u9732\u7a0b\u5ea6\u51b3\u5b9a\u7684\uff08\u8fd9\u4e9b\u56e0\u5b50\u6765\u81ea\u8d22\u62a5\u3001\u884c\u4e1a\u5c5e\u6027\u3001\u5386\u53f2\u8d70\u52bf\u7b49\uff09\uff0c\u5269\u4e0b\u7684\u90a3\u70b9\u7279\u6709\u98ce\u9669\u5047\u8bbe\u5404\u53ea\u80a1\u7968\u4e92\u4e0d\u76f8\u5173\u3002<\/p>\n\n\n\n

\u7ef4\u5ea6\u538b\u7f29\u7684\u903b\u8f91\u5f88\u76f4\u89c2\u3002\u5546\u4e1a\u80a1\u7968\u98ce\u9669\u6a21\u578b\u4e00\u822c\u752840\u5230100\u4e2a\u56e0\u5b50\u3002\u630970\u4e2a\u56e0\u5b50\u7b97\uff0c\u9700\u8981\u4f30\u7b97\u7684\u56e0\u5b50\u534f\u65b9\u5dee\u77e9\u9635\u53ea\u670970\u00d771\u00f72=2,485\u9879\uff1a\u6bd4125,250\u5c11\u4e8698%\u3002\u800c\u4e14\u8fd92,485\u9879\u53ef\u4ee5\u7528\u51e0\u5341\u5e74\u7684\u56e0\u5b50\u56de\u62a5\u5386\u53f2\u6765\u7a33\u5b9a\u4f30\u7b97\u3002<\/p>\n\n\n\n

Rosenberg\u521b\u7acb\u7684Barra\u516c\u53f8\u5c31\u9760\u8fd9\u5957\u6a21\u578b\u505a\u6210\u4e86\u5546\u4e1a\u4e1a\u52a1\u30022004\u5e74\u6469\u6839\u58eb\u4e39\u5229\u82b1\u4e86\u7ea68.16\u4ebf\u7f8e\u5143\u628aBarra\u4e70\u4e0b\u6765\uff0c\u5e76\u5165\u4e86MSCI\u3002Ledoit-Wolf\u6536\u7f29\u4f30\u8ba1\u6cd5\u662f\u53e6\u4e00\u4e2a\u8865\u5145\u6280\u672f\uff0c\u5b83\u628a\u6837\u672c\u534f\u65b9\u5dee\u77e9\u9635\u5f80\u4e00\u4e2a\u66f4\u7a33\u5b9a\u7684”\u76ee\u6807\u7ed3\u6784”\u62c9\u3002\u4e24\u4f4d\u4f5c\u8005\u7684\u539f\u8bdd\u5f88\u76f4\u767d\uff1a”\u8fd9\u7bc7\u8bba\u6587\u7684\u6838\u5fc3\u4fe1\u606f\u5c31\u662f\uff0c\u4efb\u4f55\u4eba\u90fd\u4e0d\u8be5\u7528\u539f\u59cb\u6837\u672c\u534f\u65b9\u5dee\u77e9\u9635\u505a\u7ec4\u5408\u4f18\u5316”\u3002<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

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\u56db\u3001<\/strong>\u660e\u660e\u516c\u5f0f\u90fd\u516c\u5f00\u4e86\uff0c\u4e3a\u4ec0\u4e48\u8fd8\u662f\u90a3\u4e48\u8d35\uff1f<\/strong><\/h2>\n\n\n\n

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