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An Analytic Derivation of the Efficient Portfolio Frontier

Published online by Cambridge University Press:  19 October 2009

Robert C. Merton
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Extract

The characteristics of the mean-variance, efficient portfolio frontier have been discussed at length in the literature. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs. In this paper, the efficient portfolio frontiers are derived explicitly, and the characteristics claimed for these frontiers are verified. The most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem. It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 7 , Issue 4 , September 1972 , pp. 1851 - 1872
Copyright
Copyright © School of Business Administration, University of Washington 1972

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References

[1]Black, F. “Capital Market Equilibrium with Restricted Borrowing.” Forthcoming in Journal of Business.Google Scholar
[2]Borch, K. “A Note on Uncertainty and Indifference Curves.” Review of Economic Studies, 36, January 1969.CrossRefGoogle Scholar
[3]Cass, D., and Stiglitz, J.. “The Structure of Investor Preferences and Asset Returns, and Separability in Portfolio Allocation: A Contribution to the Pure Theory of Mutual Funds.” Journal of Economic Theory, 2, June 1970.CrossRefGoogle Scholar
[4]Fama, E. “Risk, Return, and Equilibrium.” Journal of Political Economy, 79, January–February 1971.CrossRefGoogle Scholar
[5]Feldstein, M. S. “Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection.” Review of Economic Studies, 36, January 1969.CrossRefGoogle Scholar
[6]Hakansson, N. H. “Capital Growth and the Mean-Variance Approach to Portfolio Selection.” Journal of Financial and Quantitative Analysis, January 1971CrossRefGoogle Scholar
[7]Jensen, M. “Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios.” Journal of Business, Vol. 42, April 1969.Google Scholar
[8]Lintner, J. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, XLVIII, February 1965.Google Scholar
[9]Lintner, J. “Security Prices, Risk, and Maximal Gains from Diversification.” Journal of Finance, March 1968.Google Scholar
[10]Markowitz, H.bPortfolio Selection: Efficient Diversification of Investment. New York: John Wiley and Sons, 1959.Google Scholar
[11]Merton, R.C. “Optimum Consumption and Portfolio Rules in a Continuous-Time Model.” Journal of Economic Theory, Vol. 3, December 1971.CrossRefGoogle Scholar
[12]Merton, R.C. “An Intertemporal Capital Asset Pricing Model.” Forthcoming in Econometrica.Google Scholar
[13]Mossin, J. “Equilibrium in a Capital Asset Market.” Econometrica, October 1966.CrossRefGoogle Scholar
[14]Samuelson, P.A. “General Proof that Diversification Pays.” Journal of Financial and Quantitative Analysis, Vol. II, March 1967.Google Scholar
[15]Samuelson, P.A. “The Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances, and Higher Moments.” Review of Economic Studies, 37, October 1970.CrossRefGoogle Scholar
[16]Sharpe, W.Portfolio Theory and Capital Markets. New York: McGraw-Hill Book Company, 1970.Google Scholar
[17]Tobin, J. “Liquidity Preference as Behavior Toward Risk.” Review of Economic Studies, Vol. 25, February 1958.CrossRefGoogle Scholar
[18]Tobin, J.. “The Theory of Portfolio Selection.” The Theory of Interest Rates. Edited by Hahn, F.H. and Brechling, F.P.R.. New York: Macmillan, 1965.Google Scholar