Portfolio Selection Author(s): Harry Markowitz 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: 23/06/2011 20:52 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=black. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact email@example.com.
Blackwell Publishing and American Finance Association are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Finance.
PORTFOLIO SELECTION* MARKOWITZ HARRY
The Rand Corporation
a portfoliomay be divided into two stages. OF THEPROCESS SELECTING The first stage starts with observation and experienceand 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 concernedwith the secondstage. We firstconsiderthe rule that the investordoes (or should) maximize discountedexpected, or anticipated, returns.This rule is rejected both as a hypothesis to explain, and as a maximumto guide investment behavior.We next considerthe rule that the investor does (or should) considerexpected return a desirablething and variance of return an undesirablething. This rule has many sound points, both as a maxim for, and hypothesis about, investment behavior. We illustrate geometricallyrelations between beliefs and choice of portfolio according to the "expected returns-variance of returns"rule. One type of rule concerningchoice of portfolio is that the investor does (or should) maximize the discounted (or capitalized) value of future returns.1Since the future is not known with certainty, it must be "expected"or "anticipated"returnswhich we discount. Variations of this type of rule can be suggested. Following Hicks, we could let "anticipated"returns include an allowance for risk.2Or, 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) discountedreturnmust be rejected. If we ignore market imnmaximize perfections the foregoingrule never implies that there is a diversified portfolio which is preferableto all non-diversifiedportfolios. Diversification is both observed and sensible; a rule of behavior which does not imply the superiorityof diversificationmust be rejected both as a hypothesis and as a maxim. * This paperis basedon work done by the authorwhile at the CowlesCommission for Researchin Economicsand with the financialassistanceof the Social Science Research Paper,New Series,No. 60. as Council.It will be reprinted CowlesCommission Mass.: Value(Cambridge, of 1. See,for example,J. B. Williams,TheTheory Investment HarvardUniversityPress, 1938),pp. 55-75. 2. J. R. Hicks, Valueand Capital(New York:OxfordUniversityPress, 1939),p. 126. Hicks appliesthe...