Revisiting Static Portfolio Theory for Hara Investors

Abstract

The implications of the two-fund separation theorem have been carefully examined in the literature for the case of mean-variance preferences. However, even though the two-fund theorem applies to the whole class of HARA utility functions, its implications for the e¢ ciency sets spanned by these preferences are much less known. Without dealing with general equilibrium issues, the goal of this paper is to show how most of the wellknown constructions which arise in connection with the former subclass, extend in a relatively natural way to the whole latter set of preferences. Furthermore, graphical illustrations of the HARA portfolio problem that parallel mean-variance geometry are also provided. Along the same lines, It is also shown how the general problem can be seen as a choice between two parameters, one measuring reward and the other one measuring risk. The youth years of …nancial economics are clearly dominated by the early results of portfolio choice theory. Among other things, the contributions of Markowitz (1957) together with the derivation by Tobin (1958) of the two-fund theorem, always in the context of mean-variance preferences, play a crucial role in developing the …rst general equilibrium model of asset pricing, i.e. the CAPM. These two …elds of …nance marched closely together until the seminal work of Lucas (1978) which implies a radical change of perspective. From this point onwards, it becomes clear that it is not necessary to solve a portfolio choice problem in order to model the behavior of asset prices. The consumption-based approach allows asset pricing to (partially) abandon its early companion and walk its way mostly alone. The GMM technology of Hansen (1982) pushes further in this direction and it helps creating a new approach where the stochastic discount factor (SDF) is to be the main focus.