Online-Appendix to: Making Parametric Portfolio Policies Work: Comments on Brandt, Santa-Clara and Valkanov (2009)

Abstract

We provide examples of pitfalls for parametric portfolio policies as introduced by Brandt, Santa Clara and Valkanov. For 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. As possible remedies for practical work various extensions of CRRA Bernoulli utility to the real line are discussed. Also prospect theory is suggested as an alternative approach. We observe that for low levels of relative risk aversion expected utility turns non-monotonic and an interior maximum need not exist. We provide economic conditions that overcome such empirical problems and that guarantee the effectiveness of the approach more broadly. We illustrate our concerns by applying parametric portfolio policies to a large universe of stocks. Full paper is available at: https://ssrn.com/abstract=3081100