Markowitz Models of Portfolio Selection: The Inverse Problem

Predictions about investor portfolio holdings can provide powerful tests of asset pricing theories. In the context of Markowitz portfolio selection problem, this paper develops an algorithm which determines the structural parameters in both the investor's return-generating process and the utility function based upon the actual portfolio choices made by each investor. We refer to this problem as the inverse of portfolio selection. Furthermore, through the introduction of a set of investor-speci c characteristics, the methodology accommodates either homogeneous or heterogeneous anticipated rates of return{a contribution over the existing returns{generating models. Generalization of the algorithm to Black (1972) and Tobin (1965) models where the e ciency frontier is known in closed form is direct and immediate. The methodology is useful for understanding the investor risk-return tradeo s and, in particular, can be considered as the micro-level counterpart of the determination of the "taste parameters" in Hansen-Singleton (1982) and the simultaneous determination of the parameters driving the forcing process and the "taste parameters" in Du e-Singleton (1993).