Portfolio selection

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American Finance Association
Portfolio Selection
Author(s): Harry Markowitz
Reviewed work(s):
Source: The Journal of Finance, Vol. 7, No. 1 (Mar., 1952), pp. 77-91 Published by: Blackwell Publishing for the American Finance Association Stable URL: http://www.jstor.org/stable/2975974
Accessed: 19/02/2012 16:49
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77
PORTFOLIO SELECTION*
HARRY MARKOWITZ
The Rand Corporation
THE PROCESS OF SELECTING a portfolio may be divided into two stages. The first stage starts with observation and experience andends 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 toexplain, 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"expected returns—variance of returns" rule.
One type of rule concerning choice of portfolio is that the investor does (or should) maximize the discounted (or capitalized) value of future returns.' Since the future is not known with certainty, it must be "expected" or "anticipated" returns which we discount. Variations of this type of rule can be suggested. Following Hicks, we could let "anticipated"returns include an allowance for risk.2 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-diversifiedportfolios. 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. It will be reprinted as CowlesCommission 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, Value and Capital (New York: Oxford University Press, 1939), p. 126. Hicks applies the rule to a firm rather than a portfolio.

78 The Journal of Finance
The foregoing rule fails to implydiversification no matter how the anticipated returns are formed; whether the same or different discount rates are used for different securities; no matter how these discount rates are decided upon or how they vary over time.3 The hypothesis implies that the investor places all his funds in the security with the greatest discounted value. If two or more securities have the same value, then any of these or any...