Valuing private equity∗

To understand the pricing and performance of private equity (PE), we analyze the incomplete-markets portfolio choice problem facing a risk-averse limited partner (LP) investing in liquid stocks and bonds along with an illiquid PE investment. A general partner (GP) manages the PE asset and generates alpha on it and charges management and performance fees via carried interest in return. Our complete-markets benchmark extends the Black-Scholes option pricing framework to allow for positive alpha, which is necessary to justify managerial fees. For our incomplete-markets framework, we derive tractable formulas for the LP’s portfolio weights and certainty equivalent valuation for the PE asset. The key term that accounts for the discount due to illiquidity and idiosyncratic risk reflects the fundamental difference between our valuation framework and the standard Black-Scholes framework. We find that the typically observed 2-20 compensation contract implies a large alpha for the LP to break even, but leveraging the PE asset substantially reduces this break-even alpha. Our model also allows us to quantify the increase in performance measures, break-even alpha being a natural one, as the GP increases fees. For our baseline calibration, our model implied performance measures are in line with empirical measures. We also evaluate the limitations of standard PE performance measures from a certainty equivalent perspective, and propose a new Adjusted Public-Market-Equivalent (PME) measure.