Risk, Return, and Equilibrium

Abstract

Sharpe (1964) and Lintner (11965a, 1965b) have presented a model directed at the following questions. (a) What is the appropriate measure of the risk of an investment asset? And (b) what is the relationship in equilibrium between this measure of the asset's risk and its one-period expected return? The Sharpe-Lintner asset pricing model is a natural extension of the one-period portfolio models of Markowitz (1959) and Tobin (1958), which in turn are built on the expected utility model of von Neumann and Morgenstern (1953) and others. The portfolio models are concerned with how the consumer (investor) should allocate his wealth among the various assets available in the market, given that he is a oneperiod expected utility maximizer. The asset pricing model then uses the characteristics of consumer wealth allocation decisions to derive the market equilibrium relationship between risk and expected return for assets and portfolios. Like the portfolio models of Markowitz and Tobin, the Sharpe-Lintner asset pricing model assumes a market of risk-averse consumers who can make portfolio decisions on the basis of the means and standard deviations of one-period portfolio returns, implicitly assuming that these standard deviations exist. But the empirical work of Blume (1968), Fama (1965a), Mandelbrot (1963), and Roll (1968) suggests that this assumption may be inappropriate; distributions of returns on common stocks and government bonds conform well to nonnormal members of the stable or stable Paretian class of distributions, and the standard deviations of these distributions do not exist.