Asset Pricing Under a Subset of Linear Risk Tolerance Functions and Log-Normal Market Returns

Abstract

The Capital Asset Pricing Model (CAPM) developed and popularized by Treynor [27], Sharpe [26], Lintner [16], Mossin [19], and Fama [6] is of the formwhereE is the expected return at time t for firm i (conditional on information available at time t); the subscript m denotes the analogous market variable; rf is the risk-free rate; and . Black [2] has developed a similar form with expected returns from a zero beta portfolio, , assuming the role of the risk-free rate.