Utility-Based Approach to Solve Discrete Asset Optimization Problem under Non-Delta Property

Wang Junzhe

Abstract

This research topic is proposed based on a real world problem – to make private equity fund investment decisions from a fund of funds manager’s prospective. Private equity fund investment has the characteristics of high risk, high return and high illiquidity. Unlike traditional asset (eg. stocks and bonds), private equity investors has less flexibility of investment amount, which is constrained by the target fund’s requirement, as well as the fund of fund’s own investment strategy. Hence the investment decision is simplified to a binary (discrete) problem (“yes” or “no”) that can be readily solved with decision analysis tools. However the difficulty comes in when the investment opportunities are correlated with each other and also with the initial portfolio. The complexity of decision analysis approach grows exponentially due to the inter-correlation nature. This research paper focus on integrating the portfolio diversification tools into decision analysis and proposes a heuristic approach to find the optimal private equity asset allocation strategy.