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.