Making Parametric Portfolio Policies Work

The implementation of parametric portfolio policies as introduced by Brandt, Santa Clara and Valkanov (RFS 2009) may run into empirical problems. For example, expected utility based on monthly returns of S&P-500 data from 1995-2013 turns non-monotonic for moderate levels of (constant) risk aversion. We establish that in the leading case of constant relative risk aversion (CRRA) strong assumptions on the properties of the returns, the variables used to implement the parametric portfolio policy and the parameter space are necessary to obtain a well defined optimization problem. Without such refinements an interior maximum of the expected utility functional may not exist. We provide economic conditions on the domain and/or the utility functions that overcome such empirical problems and that guarantee the effectiveness of the approach. We illustrate the implications of our improvements by applying parametric portfolio policies to a large universe of stocks.