In the carry trade, an investor borrows funds in a low interest rate currency and lends in a high interest rate currency. Here, I let the domestic currency be the US dollar (USD) and denote the rate of interest on riskless USD denominated securities as it. I denote the interest rate on riskless foreign denominated securities as . Abstracting from transactions costs, the payoff to borrowing one USD in order to lend the foreign currency is
where St denotes the spot exchange rate expressed as USD per foreign currency unit (FCU). The payoff to the carry-trade strategy is, therefore:
The carry-trade strategy can also be implemented by selling the foreign currency forward when it is at a forward premium (Ft ≥ St) and buying the foreign currency forward when it is at a forward discount (Ft < St). If the number of FCUs transacted forward is normalized to be (1 + it)/Ft, then the payoff to this version of the strategy, denoted zt+1, is
Covered interest rate parity (CIP) implies that
When CIP holds, the expressions ...