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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

Thomas W. Epps
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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
Information
Journal of Financial and Quantitative Analysis , Volume 16 , Issue 2 , June 1981 , pp. 169 - 176
Copyright
Copyright © School of Business Administration, University of Washington 1981

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