This paper shows the importance of correcting for sample selection when investing in illiquid assets that trade endogenously. Using a sample of 32,928 paintings that sold repeatedly between 1960 and 2013, we find an asymmetric V-shaped relation between sale probabilities and returns. Adjusting for the resulting selection bias reduces average annual index returns from 8.7% to 6.3%, lowers Sharpe ratios from 0.27 to 0.11, and materially impacts portfolio allocations. Investing in a broad portfolio of paintings is not attractive, but targeting specific styles or top-selling artists may add value. The methodology naturally extends to other asset classes.

ABSTRACT We adapt stochastic discount factor (SDF) valuation methods for venture capital (VC) performance evaluation. Our approach generalizes the popular Public Market Equivalent (PME) method and allows statistical inference in the presence of cross‐sectionally dependent, skewed VC payoffs. We relax SDF restrictions implicit in the PME so that the SDF can accurately reflect risk‐free rates and returns of public equity markets during the sample period. This generalized PME yields substantially different abnormal performance estimates for VC funds and start‐up investments, especially in times of strongly rising public equity markets and for investments with betas far from one.