Solving the Net Worth Optimization Problem

ABSTRACT The mean–variance optimization (MVO) model of Harry M. Markowitz is the foundation of quantitative portfolio construction and asset allocation. While Markowitz originally developed MVO for forming portfolios of tradable assets in isolation, it has been adapted for creating portfolios of tradable assets in the presence of non‐tradable assets and liabilities. In a series of publications, Paul D. Kaplan and Thomas M. Idzorek further extend MVO to the household economic balance sheet. The extended MVO model is the net worth optimization (NWO) model. In NWO, human capital is modeled as an asset mix held long, and, as in surplus optimization, liabilities are modeled as an asset mix held short. NWO operates in terms of net worth returns rather than in the returns on the financial assets. Kaplan and Idzorek maximize an approximation for expected utility developed by Haim Levy and Harry M. Markowitz. In this article, I show how to achieve this by combining existing quadratic programming techniques with nonlinear equation solution techniques in a novel way. I also discuss and demonstrate how NWO differs from the discretionary wealth approach (DWA) introduced by Jarrod Wilcox.