A Discretionary Wealth Approach to Investment Policy

Abstract

Despite portfolio construction based on expected utility theory and Markowitz mean-variance optimization having been the foundation of financial economic theory for more than 50 years, its practical application by financial advisors has been limited. Particularly troubling are the lack of a normative risk-aversion parameter customized to individual investor circumstances and the need for extensive constraints to produce practically acceptable results. We propose a comprehensive conceptual framework for better investment policy. To begin, we develop investor circumstance-contingent risk aversion for use in portfolio construction, taking into account higher moments of return only as needed. We recursively maximize expected logarithmic return on what we define as "discretionary wealth" to generate many-period maximization of median wealth without violating interim shortfall points. Then we extend this basic framework based on point estimates to fully Bayesian logic. This offers not only improved decision inputs but the advantage of deriving the probability distribution of the objective as a function of portfolio weights before selecting the best portfolio. Implications are discussed for a wide array of practical issues: investor leverage, longevity risk, higher return moments, dynamic hedging, life-cycle investing, performance measures, and robust portfolio construction. Hypotheses for implied market structure and pricing are also generated.

Keywords: investment policy, discretionary wealth, Markowitz optimization, higher moments, implied leverage, Bayesian investing, robust optimization

JEL Classification: D81, G11