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 cuts 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. (JEL D44, G11, Z11) 2 Over the last three decades investors have started allocating increasingly larger shares of their portfolios to alternative assets. Many of these alternative asset classes, such as private equity and real estate, and even certain traditional assets, such as corporate bonds, are highly illiquid, complicating return evaluation. In particular, when sales are endogenously related to the performance of the asset, a sample selection problem arises that is pervasive across asset classes. This paper develops a methodology to quantify the magnitude of the selection bias and demonstrates its empirical first-order importance when evaluating investment performance and constructing optimal portfolios that include alternative assets. 6% to 18% of their total wealth to art and collectibles (depending on the region), and the majority 1 Following the literature, we use the terms "art" and "paintings" interchangeably throughout the paper.