[Valuations of entrepreneurial companies are only observed occasionally, albeit more frequently for well-performing companies. Consequently, estimators of risk and return must correct for sample selection to obtain consistent estimates. We develop a general model of dynamic sample selection and estimate it using data from venture capital investments in entrepreneurial companies. Our selection correction leads to markedly lower intercepts and higher estimates of risks compared to previous studies. The methodology is generally applicable to estimating risk and return in illiquid markets with endogenous trading.]

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.

Valuations of entrepreneurial companies are only observed occasionally, albeit more frequently for well-performing companies. Consequently, estimators of risk and return must correct for sample selection to obtain consistent estimates. We develop a general model of dynamic sample selection and estimate it using data from venture capital investments in entrepreneurial companies. Our selection correction leads to markedly lower intercepts and higher estimates of risks compared to previous studies. The methodology is generally applicable to estimating risk and return in illiquid markets with endogenous trading.

This paper introduces a new metric, α, to benchmark the performance of individual private equity funds. Our metric is substantially less sensitive to noise in fund cash flows compared to the popular public market equivalent (PME) and its generalization (GPME), while having the same aggregate pricing implications as GPME. For a large data set of fund cash flows, α estimates have much lower standard deviation across funds than does (G)PME. For buyout funds, PME and α are close, but deviate in certain subsamples. Using α increases power in regressions involving fund performance and improves performance predictability of future funds.

__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.