Risk-based explanations of the returns to the carry trade begin from the premise that there is an SDF that prices these returns. In particular, since the carry trade is a zero net-investment strategy, the payoff, zt, must satisfy
Here Mt+1 denotes the SDF that prices payoffs denominated in dollars, while Et is the mathematical expectations operator given information available at time t. Equation (10.9) implies that
The variable pt is referred to as the conditional risk premium and corresponds to the conditional expectation of the payoff. As Equation (10.10) suggests, one approach to learning about risk premia is to build a forecasting model for the payoffs to the carry trade. An approximation to the mathematical expectation in Equation (10.10) is implicit in any forecasting model. Therefore, model forecasts correspond to estimates of the risk premium (Fama, 1984).
Consider an example of an individual-currency carry trade in which the domestic interest rate exceeds the foreign interest rate, that is, , or, equivalently that the foreign currency is at a forward premium: Ft > St. Assume that the carry trader sells units, rather than ...