with Raymond Kan and Xiaolu Wang, 2026, working paper.
[Paper] [Internet Appendix] Following Barillas and Shanken (2017), traded factor asset pricing models are increasingly compared on the basis of the squared Sharpe ratios of the tangency portfolios of their factors. Inference typically relies on the asymptotic normal distribution of the difference of the two sample squared Sharpe ratios. We show that this asymptotic approximation can be very poor in the sample sizes and Sharpe ratio configurations that are typical in applications. The limiting distribution is nonstandard precisely on the boundary of the null hypothesis that matters for model comparison, the sample difference is biased, its exact density can be unbounded at zero, and the usual t-ratio is not asymptotically standard normal for nested models or when the two models are close in explanatory power. Under multivariate normality, we derive the exact finite-sample joint distribution of the two sample squared Sharpe ratios for nested, non-overlapping, and overlapping models. We obtain explicit expressions for the exact moments in terms of hypergeometric functions and develop stochastic representations that permit extremely fast simulation of the exact distribution using only low-dimensional random variables. A Pearson curve approximation based on the first four exact moments is shown to be nearly indistinguishable from the exact distribution.