We propose and estimate a quantitative model of exchange rates in which participants in the foreign exchange market are intermediaries subject to value-at-risk (VaR) constraints. Higher volatility translates into tighter VaR constraints, and intermediaries require higher returns to hold foreign assets. Therefore, the foreign currency is expected to appreciate. The model quantitatively resolves the Backus–Smith puzzle, the forward premium puzzle, and the exchange rate volatility puzzle and explains deviations from the covered interest rate parity. Moreover, the model implies both contemporaneous and predictive relations between proxies of leverage constraint tightness and exchange rates. These implications are supported in the data.

Traditional performance evaluation measures do not account for tail events and rare disasters. To address this issue, we reinterpret the riskiness measures of Aumann and Serrano (2008) and Foster and Hart (2009) as performance indices. We derive the moment properties of these indices and their sensitivity to rare disasters and show that they are consistent with the asset pricing literature. As applications, we show that “anomalous” investment strategies such as “momentum” or investment in private equity lose much of their glamour when accounting for high moments and rare events. Furthermore, using the indices to select mutual funds results in desirable high-moment properties out of sample.