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马克维茨投资组合选择

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Portfolio Selection Harry Markowitz

The Journal of Finance, Vol. 7, No. 1.(Mar., 1952), pp.

77-91. Stable URL:

http://links.jstor.org/sici?sici=0022-1082(195203)7:1<77:PS>2.0.CO;2-1

The Journal of Finance is currently published by

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advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Sun Oct 21 07:53:25 2007 PORTFOLIO SELECTION* HARRYMARKOWITZ

The Rand Corporation THEPROCESS 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. We first consider the rule that the investor does (or should)

maximize discounted expected, or anticipated, returns. This rule is rejected

both as a hypothesis to explain, and as a maximum to guide investment

behavior. We next consider the rule that the investor does (or

should) consider expected return a desirable thing and variance of return

an undesirable thing. This rule has many sound points, both as a

maxim for, and hypothesis about, investment behavior. We illustrate

geometrically relations between beliefs and choice of portfolio according

to the \One type of rule concerning choice of portfolio is that the investor

does (or should) maximize the discounted (or capitalized) value of

futurereturns.l Since the future is not known with certainty, it must

be \discount. Variations

of this type of rule can be suggested. Following Hicks, we could let

\Or, we could let

the rate at which we capitalize the returns from particular securities vary with risk.

The hypothesis (or maxim) that the investor does (or should)

maximize discounted return must be rejected. If we ignore market imperfections

the foregoing rule never implies that there is a diversified

portfolio which is preferable to all non-diversified portfolios. 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.

* This paper is based on work done by the author while at the Cowles Commission for

Research in Economics and with the financial assistance of the Social Science Research

Council. I t will be reprinted as Cowles Commission Paper, New Series, No. 60.

1. See, for example, J.B. Williams, The Theory of Investment Value (Cambridge, Mass.:

Harvard University Press, 1938), pp. 55-75.

2. J. R. Hicks, V a l ~ eand Capital (New York: Oxford University Press, 1939), p. 126.

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