Term-structure of consumption risk premia in the cross-section of currency returns

I quantify the risk-return relationship in the foreign exchange market in the cross-section and across investment horizons by focusing on the role of multiple sources of US consumption risk. To this end, I estimate a flexible structural model of the joint dynamics of aggregate consumption, inflation, nominal interest rate, and stochastic variance with cross-equation restrictions implied by recursive preferences. I identify the following four structural shocks: inflation, short-run, long-run and variance consumption risks. To measure their relative importance, I compute marginal quantities and prices of risk (marginal Sharpe ratios) in the cross-section of currency baskets for alternative investment horizons. I find that the long-run consumption risk plays a prominent role: it carries an average quarterly Sharpe ratio of 0.28 and contributes to the spread in excess returns between baskets of high and low interest rate currencies across investment horizons from one to five quarters. The short-run consumption risk has an effect on currencies at the horizon of one quarter only, where it explains at least 40% of the corresponding spread in excess returns. The carry trade profitability disappears at horizons longer than four quarters.