Two-Fund separation and positive marginal utility - Wolfgang Breuer; Marc Gürtler (Technische Universität Braunschweig, Institut für Finanzwirtschaft, 2004)
The requirement of positive marginal utility only makes it possible to derive a restricted twofund separation theorem for portfolio selection problems replacing the original separation theorem of Cass and Stiglitz (1970). We use our findings for a re-examination of the bias-in-beta problem in mutual funds performance evaluation and of the relevance of the standard CAPM without borrowing restrictions. We also present empirical evidence for the only limited validity of the separation theorem when explicitly recognizing positive marginal utility. Moreover, quadratic utility functions are not apt to approximate the admissible range of risk preferences in the case of higher-order utility functions.
Keywords: G11; 330; two-fund separation; HARA utility; positive marginal utility; borrowing restrictions; Capital Asset Pricing Model; bias in beta; performance evaluation