Valuing a Private Equity Carried Interest as a Call Option on Fund Performance

Abstract

A private equity fund manager’s carried interest is a valuable call option on the value of the fund’s investment portfolio. The authors model three alternative structures for the carried interest and obtain explicit valuation formulas, which are analogous to the familiar Black–Scholes–Merton option pricing model. The carried interest delta is calculated for each structure to quantify the sensitivity of the value of the carried interest to increases in portfolio value and to show that the three structures have different fund manager incentive effects. The authors also quantify the sensitivity of the value of the carried interest to the investors’ preferred rate of return, the investment portfolio’s expected return and volatility, the fraction of monitoring and transaction fees rebated to investors, and the cost of the carried interest’s illiquidity. The conclusion is that the carried interest typically accounts for about one-third to one-half of fund manager compensation.