Currency Carry Trade Structure and Payoffs

A carry trade typically borrows in a lower-interest-rate currency to hold assets denominated in a higher-interest-rate currency, often with leverage. The interest differential is only one component of return; exchange-rate moves, funding and hedging costs, collateral, and liquidity costs also matter. A fall in the target currency against the funding currency can overwhelm the interest earned.

Fix the quote direction before calculating

Illustrative one-year trade: borrow 1,000 units of currency A at 1% and invest currency B at 5%. Define S as units of A per one B; initially S0 = 2. Buy 500 B, receive 525 B at maturity and repay 1,010 A. The terminal payoff is 525×S1−1,010. At S1 = 2 it is +40; at 1.90 it is −12.50; at 2.10 it is +92.50. A 5% depreciation of B against A lowers S from 2 to 1.90 and erases the carry.

The pre-cost break-even quote is 1,010/525 ≈ 1.92381, about 3.8095% below the initial quote rather than exactly the 4% interest differential. Payoff divided by initial borrowing is (1.05×S1/S0−1.01), not return on equity. Collateral, forced liquidation and transaction costs are excluded; do not treat this as an actual leveraged equity return.

Separate UIP, forwards and the realized quote

Under these signs and simplified UIP assumptions, expected S1/S0 = 1.01/1.05. This predicts expected depreciation of high-interest B, not a guaranteed realized S1. Locking the terminal exchange rate with a forward changes the trade from this unhedged illustration. Even if ideal covered interest parity gives a forward ratio with the same form, actual quotes can include basis and costs. An interest differential alone is not risk-free profit.

Evidence scope and unwind risk

BIS's 2007 study explains the difficulty of tracking carry positions in market data. Aquilina, Lombardi, Schrimpf and Sushko's August 2024 analysis discusses deleveraging and increased margins in that episode. These observations do not establish future crashes for every pair or universal failure of UIP.