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__ This paper shows the importance of correcting for sample selection when investing in illiquid assets with endogenous trading. Using a large sample of 20,538 paintings that were sold repeatedly at auction between 1972 and 2010, we find that paintings with higher price appreciation are more likely to trade. This strongly biases estimates of returns. The selection-corrected average annual index return is 7 percent, down from 11 percent for traditional uncorrected repeat-sales regressions, and Sharpe Ratios drop from 0.4 to 0.1. From a pure financial perspective, passive index investing in paintings is not a viable investment strategy, once selection bias is accounted for. Our results have important implications for other illiquid asset classes that trade endogenously.