THE STRUCTURE OF SKEWNESS PREFERENCES IN ASSET PRICING MODELS WITH HIGHER MOMENTS: AN EMPIRICAL TEST

R. Stephen Sears · K.C. John Wei

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Financial Markets and Investment Strategies Financial Risk and Volatility Modeling Risk and Portfolio Optimization

Abstract

ABSTRACT In this paper, the authors employ a nonlinear formulation to examine empirically the structural content of the three moment capital asset pricing model (CAPM). Whereas previous research focused on the coefficients of beta and co‐skewness, this paper presents empirical results on the market risk premium and elasticity coefficient components of these two coefficients. The results indicate that although the estimated coefficient of coskewness gives important information on the marginal rate of substitution between skewness and expected return, the elasticity coefficient can provide additional (albeit different) information on skewness preference that is independent of the effects of the market risk premium. This research also shows how the non‐linear formulation provides a direct linkage between the twomoment and three‐moment CAPM versions and thus provides an empirical test of the theoretical conditions under which skewness preference is consistent with the two‐moment CAPM empiricial results.

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1964CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*1973Risk, Return, and Equilibrium: Empirical Tests 1965The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets 1975THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]1966Equilibrium in a Capital Asset Market 1962Portfolio Selection: Efficient Diversification of Investments.1972Capital Market Equilibrium with Restricted Borrowing 1976

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