Portfolio Optimization in a Multidimensional Structural-Default Model with a Focus on Private Equity

Abstract

Investments in various asset classes, such as private equity or hedge funds, are prone to default risk, which needs to be accounted for when calculating individual investment opportunities and optimal portfolio selection. The correspondent literature on portfolio optimization, however, mostly disregards default risk and accordingly skewed return distributions. This article presents a realistic and tractable framework for a portfolio optimization, including default risk, with a specific focus on private equity investments. Default events are modeled by means of a Merton- or Black–Cox structural model. On a portfolio level, the mean and covariance of the resulting return distribution can be derived analytically, allowing for a classical mean-variance optimization. To include tail risk, we additionally present a Monte-Carlo simulation for a mean conditional value-at-risk optimization. The article concludes with an application to unlisted private equity and compares the results with a model proposed by Hamada [1972], which does not explicitly consider default risk. <b>TOPICS:</b>Private equity, portfolio construction, VAR and use of alternative risk measures of trading risk, simulations