Uncovered interest parity
Set the two deposit rates. Interest parity says capital moves until both deposits offer the same expected return: i = i* − (expected appreciation of the domestic currency). So the market-implied expected currency move is just i* − i. If the foreign rate is higher, the domestic currency must be expected to appreciate by that gap to leave an investor indifferent — exactly the carry-trade break-even.
Implied expected move of the domestic currency (i* − i)
+2.0%
Domestic currency must be expected to APPRECIATE 2.0% to offset the lower domestic rate.
Domestic rate i3.0%
Foreign rate i*5.0%
Exp. return, domestic3.0%
Exp. return, foreign5.0% −2.0% FX = 3.0%
Both expected returns match. The interest-rate gap is exactly compensated by the expected currency move, so moving into the higher-yield currency offers no extra expected return — that is the carry-trade indifference.