Portfolio Optimization with Private Equity Funds

Abstract

This paper extends the standard Merton portfolio choice model to include illiquid private equity funds. This is done in a realistic modeling framework where private equity funds cannot be traded during their entire bounded lifecycle and involve capital commitments and intermediate capital distributions that cannot be reinvested immediately. Assuming an investor that derives CRRA power utility from terminal portfolio wealth, the paper solves for a dynamic commitment and portfolio strategy that shows investors how to optimally commit capital to private equity funds and how to optimally rebalance between liquid stocks and bonds over time. The framework also allows directly studying the effects of illiquidity on optimal portfolio allocations and on investors' utilities. These results provide a number of important insights about the effects of illiquidity of private equity funds. Most importantly, the paper shows that liquidity associated welfare losses are negligible in case that private equity funds and traded stocks are relatively close substitutes, i.e. both have similar risk-return characteristics and a medium or high return correlation. This finding sheds new light on the discussion why many recent papers document that private equity funds only generate returns that are comparable to traded stocks despite being highly illiquid investments.