Multihorizon Currency Returns and Purchasing Power Parity

Exposures of expected future depreciation rates to the current interest rate differential violate the UIP hypothesis in a distinctive pattern that is a non-monotonic function of horizon. Conversely, forward, or risk-adjusted expected depreciation rates are monotonic. We explain the two patterns jointly by incorporating the weak form of PPP, aka stationarity of the real exchange rate, into a joint model of the stochastic discount factor, the nominal exchange rate, inflation differential, domestic and foreign yield curves. Short-term departures from PPP generate the first pattern. The risk premiums for these departures generate the second pattern. Thus, the variance of the stochastic discount factor must be related to the real exchange rate deepening the exchange rate disconnect.