How much can lack of marketability affect private equity fund values?

This paper derives an upper bound on the discounts for lack of marketability of private equity funds using option-pricing theory. The upper bound is a function of the volatility of the fund returns, of the (remaining) lifetime of the fund, of two parameters governing the speed of capital drawdowns and distributions, of the volatility of the stock market returns, and of the return correlation between the fund and the stock market. The model calibration and numerical analysis deliver several novel insights about how non-marketability affects the value: (i) upper boundary discounts are increasing functions of the return volatility of the fund, of the return volatility of the stock market, and of the average time over which a dollar committed remains invested in the fund; (ii) upper boundary discounts decrease non-linearly over the finite lifetime of a fund; (iii) estimated upper boundary discounts at the start of an average private equity fund equal $35.3 relative to $100 committed, which corresponds to an annual upper boundary return premium demanded for lack of marketability of around 7%; and (iv) estimated upper boundary discounts of venture and buyout funds are around the same magnitude, though, discounts of venture capital funds are slightly higher.