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We develop a continuous-time model of the cash flow dynamics and equilibrium values of private equity funds. Intertemporal asset pricing considerations yield the dynamics of the value, of expected returns and of the systematic risk of funds under liquidity and illiquidity. Our closed-form solutions allow us to calibrate the model to a broad sample of European private equity funds. We find that (i) private equity funds have an average risk-adjusted excess value of 25 percent relative to committed capital, (ii) upper boundary illiquidity costs amount to around 2.5 percent of committed capital annually, (iii) illiquidity discounts are increasing functions of the remaining fund lifetime and that (iv) expected fund returns show distinct patterns in which they vary with systematic fund risk as well as illiquidity premiums.
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