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
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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.