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Necessary and Sufficient Conditions for the Mean-Variance Portfolio Model With Constant Risk Aversion

Published online by Cambridge University Press:  06 April 2009

Extract

The familiar two-parameter model for portfolio decisions, attributed to Markowitz [11], has individuals maximizing an objective function, ϕ [E(Y), V(Y)], of mean and variance of end-of-period wealth, subject to a constraint imposed by initial wealth. In the usual version there is an arbitrary number, n, of risky assets with stochastic end-of-period values (price plus dividend) represented by the vector X with exogenously given mean vector μ and nonsingular variance matrix σ. There is also one riskless asset, whose certain end-of-period value per dollar invested is p. Final wealth, as constrained by initial wealth, W, is given by Y = WP + a' (X – OP), where a and P are vectors of risky asset quantities and prices. Assuming ϕE > 0 (wealth preference), ϕV < 0 (risk aversion), and that the Hessian of $ is negative and semidefinite, portfolio optimum calls for ϕE(μ − OP) + 2ϕVσa = 0, or

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 1981

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References

REFERENCES

[1]Arrow, Kenneth J.Aspects of the Theory of Risk Bearing. Helsinki: Yrjo Jahnsson Foundation (1965).Google Scholar
[2]Black, Fisher. “Capital Market Equilibrium with Restricted Borrowing.” Journal of Business, Vol. 45 (1972), pp. 444454.CrossRefGoogle Scholar
[3]Copeland, Thomas E.A Model of Asset Trading under the Assumption of Sequential Information Arrival.” Journal of Finance, Vol. 31 (1976), pp. 11491168.CrossRefGoogle Scholar
[4]Epps, Thomas W.Security Price Changes and Transaction Volumes: Theory and Evidence.” American Economic Review, Vol. 65 (1975), pp. 586597.Google Scholar
[5]Epps, Thomas W.. “The Demand for Brokers' Services: The Relation between Security Trading Volume and Transaction Cost.” Bell Journal of Economics, Vol. 7 (1976), pp. 163194.CrossRefGoogle Scholar
[6]Epps, Thomas W.. “Efficient Markets and Martingale Price Processes.” Manuscript (1978).Google Scholar
[7]Epps, Thomas W., and Epps, Mary Lee. “The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of- Distributions Hypothesis.” Econometrica, Vol. 44 (1976), pp. 305321.CrossRefGoogle Scholar
[8]Feldstein, M. S.Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection.” The Review of Economic Studies, Vol. 36 (1969), pp. 512.CrossRefGoogle Scholar
[9]LeRoy, Stephen F.Risk Aversion and the Martingale Property of Stock Prices.” International Economic Review, Vol. 14 (1973), pp. 436446.CrossRefGoogle Scholar
[10]Lintner, John.The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, Vol. 47 (1965), pp. 1337.CrossRefGoogle Scholar
[11]Markowitz, Harry. Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley & Sons (1959).Google Scholar
[12]Mossin, Jan. “Equilibrium in a Capital Asset Market.” Econometrica, Vol. 34 (1966), pp. 768783.CrossRefGoogle Scholar
[13]Pratt, John W.Risk Aversion in the Small and in the Large.” Econometrica, Vol. 32 (1964), pp. 122136.CrossRefGoogle Scholar
[14]Rabinovitch, Ramon, and Owen, Joel. “Non-Homogeneous Expectations and Information in the Capital Asset Market.” Journal of Finance, Vol. 33 (1978), pp. 575587.CrossRefGoogle Scholar
[15]Richter, M. K.Cardinal Utility, Portfolio Selection, and Taxation.” The Review of Economic Studies, Vol. 27 (1960), pp. 152166.CrossRefGoogle Scholar
[16]Ross, Stephen A.Mutual Fund Separation in Financial Theory—The Separating Distributions.” Journal of Economic Theory, Vol. 17 (1978), pp. 254286.CrossRefGoogle Scholar
[17]Savage, Leonard J.The Foundations of Statistics. New York: John Wiley & Sons (1954).Google Scholar
[18]Sharpe, William F.Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, Vol. 19 (1964), pp. 425442.Google Scholar
[19]Tobin, J. E.Liquidity Preference as Behavior towards Risk.” The Review of Economic Studies, Vol. 25 (1958), pp. 6586.CrossRefGoogle Scholar
[20]vonNeumann, John, and Morgenstern, Oskar. Theory of Games and Economic Behavior. Princeton: Princeton University Press (1944).Google Scholar