经济学 1952

投资组合选择

哈里·马科维茨

组合的风险，不在每只股票自身，而在它们如何一同起伏。

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In depth · the introduction

人人都说「别把鸡蛋放进同一个篮子」。1952 年，一位 25 岁的研究生，把这句谚语变成了数学——并指出：保护你的，不是篮子的数目，而是它们会不会一起翻。

核心想法

在马科维茨之前，挑选投资意味着去搜寻最好的个股——那些被预期回报最高的。他认为这没抓住要点。要紧的，不是每项持仓单独如何表现，而是整个组合一起如何表现。一个组合有两个数字：它的预期回报，以及它的风险——也就是这份回报有多容易上下摆动。他决定性的一步，是用「各项持仓彼此同步的程度」来度量风险。

如果两项投资总是一同涨、一同跌，那同时持有它们几乎给不了你什么保护——一个跌的时候，另一个也跌。可如果它们步调不一致，那么一项的坏月份，往往正是另一项的好月份，颠簸便部分地相互抵消。于是你有时能把两项有风险的资产组合起来，最后得到一个比其中任何一个都更不冒险的混合——还不必牺牲回报。这，就是分散化那个出人意料、又精确无比的内核。

它是如何诞生的

哈里·马科维茨是芝加哥大学的博士生，正在找论文题目。据说，他在一位教授办公室外等候时，与一位股票经纪人攀谈起来，对方建议他去研究股市。读着当时标准的投资价值理论，他惊讶地发现：它只盯着预期回报，对风险、对「持有不止一样东西」却只字未提。在纸上画下一条曲线，他看出：如果投资者既在意回报又在意风险，那些明智的选择，就会构成一条前沿。1952 年，他发表了这份九页的成果。

多年后，他自己的论文答辩险些出岔子：据说米尔顿·弗里德曼打趣道，这工作算不上经济学。可它后来却重塑了这门学科。1990 年，马科维茨与威廉·夏普、默顿·米勒分享了诺贝尔经济学纪念奖——表彰的，正是从那九页里长出来的理论。

它为何重要

它把问题从「哪只股票会涨？」换成了「我该如何组合，才能让整个组合按我想要的方式表现？」正是这一转变，建起了现代投资业。这就是为什么你的退休基金持有的是一篮子股票与债券，而非单独一注押宝；为什么「分散」是每一位诚实的顾问开口的第一句建议；也是为什么指数基金——每样都持有一点点——成了普通人投资的默认方式。风险，不再是一团模糊的忧虑，而成了一个你能管理的数字。

一个可以想象的画面

想象你同时经营一个冰淇淋摊和一个雨伞摊。单看哪一个都有风险：一下雨，冰淇淋摊就完了；一出太阳，雨伞摊就完了。可两个都开着，几乎每天总有一个生意红火。你的总收入，比任何一门生意单独来都稳得多——尽管你并没有去挑「更安全」的生意，只是挑了两个会在相反时候失手的。马科维茨的数学，正是把这个想法变得精确：把不会一起垮的东西配在一起，它们的风险便部分抵消。

它的位置

马科维茨建立在更早的「价值与风险」经济学，以及基础概率论之上——在本馆里，沿着「不确定下推理」这条故事线，贝叶斯位于它的上游。他的前沿，成了夏普等人扩展为资本资产定价模型（CAPM）的地基；它与本馆的布莱克–斯科尔斯（1973）共享同一种世界观：靠组合资产来为风险定价、管理风险，而不是去预测它们的方向。两者一起，把金融变成了一门量化科学——往好里说，是指数基金；往坏里说，是危机来临时，人人「分散好」的组合最终却一同下跌。

The original document

Original source text

H. Markowitz · The Journal of Finance 7, no. 1 (Mar. 1952): 77–91

Two stages

The process of selecting a portfolio may be divided into two stages. The first stage starts with observation and experience and ends with beliefs about the future performances of available securities. The second stage starts with the relevant beliefs about future performances and ends with the choice of portfolio. This paper is concerned with the second stage.

Taking the investor's beliefs as given, Markowitz asks which portfolio to hold. He first considers — and rejects — the rule of maximizing the discounted expected value of future returns, on the grounds that it never recommends diversification: it would tell the investor to put everything into the single security with the highest expected yield, which is neither how investors behave nor sound advice.

Return is desirable, variance is not

We next consider the rule that the investor does (or should) consider expected return a desirable thing and variance of return an undesirable thing.

A portfolio's return is the weighted average of its securities' returns, so its expected return is the weighted average of their expected returns. Its variance, however, depends on the covariances between every pair of securities — not just their individual variances. This is why risk is not the simple average of the parts, and why how securities move together becomes the central quantity.

Why diversification works

Diversification is both observed and sensible. A rule of behavior which does not imply the superiority of diversification must be rejected both as a hypothesis and as a maxim.

Among all portfolios yielding a given expected return there is one of minimum variance; the set of portfolios that are not dominated — offering the most expected return for their variance, or the least variance for their return — forms the “efficient” frontier, from which the investor should choose. Securities with low or negative covariance reduce variance far more than merely holding a large number of securities does.

Not only does the E-V (Expected returns – Variance of returns) rule imply diversification, it implies the 'right kind' of diversification for the 'right reason.'

[ … ]

The paper then develops the geometry of the efficient set explicitly for three and four securities, and indicates how the general problem is solved. The full article — including the geometric exposition and a closing discussion of expected utility — is available at the source below.

The Journal of Finance · March 1952