Probability Weighting of Rare Events and Currency Returns

We show that the probability weighting of rare events, accounting for investors' attitudes toward extreme downside losses versus upside gains in non-expected utility models, provides a unified explanation for both time-series and cross-sectional variations of currency portfolio returns. We use a simple structural model to show the link between the probability weighting function and pricing kernel, and then estimate them by non-parametric methods using currency options data from 1996 to 2012. The estimates show that a domestic investor over-weights the likelihood of a substantial depreciation or appreciation of foreign currencies, consistent with experimental studies. A global probability weighting measure of left (right) tail events is highly significant in positively (negatively) predicting future currency returns over time series at both individual and portfolios levels. Furthermore, asset pricing tests show that differences in exposure to our global tail weighting measures, of high versus low interest rate currencies and of high versus low past return currencies, can explain the cross-sectional variation in average excess returns across both carry and momentum portfolios. Moreover, our global tail weighting measures remain significant after controlling for existing currency risk factors in the literature, and frequently drive their significance out, in both time-series and cross-sectional return predictability regressions.