The dollar rate is 5%, the yen rate 0.5%, spot USDJPY is 150 and one year implied volatility is 10%. A carry trade long dollars against yen earns the 4.5% differential if spot is unchanged. Compute its ex-ante Sharpe ratio and say what that number misses.

The dollar rate is 5%, the yen rate 0.5%, spot USDJPY is 150 and one year implied volatility is 10%. A carry trade long dollars against yen earns the 4.5% differential if spot is unchanged. Compute its ex-ante Sharpe ratio and say what that number misses.

Approach: Divide the interest differential by the annual volatility, then ask what the realised distribution of carry returns looks like when positions unwind together.

0.45. The expected excess return with spot unchanged is the 4.5% interest differential against 10% volatility, so the ex-ante Sharpe ratio is 4.5/10. Uncovered interest parity says the yen should appreciate 4.5% and remove exactly that return, and the empirical failure of that prediction is what a carry trade sells. What the ratio misses is the shape of the distribution: carry returns are strongly negatively skewed, since unwinds cluster with volatility spikes and hit every carry pair at once, so a bad quarter produces a loss many times what a normal distribution with 10% volatility allows. Sizing on 0.45 under a normal assumption understates the drawdown badly, which is why carry positions are sized against stress scenarios or capped with option overlays.

Follow-up: How much does hedging the tail with one year 10 delta yen calls cost, and at what option price does the hedged carry trade stop being worth doing?

Key concepts: carry trade, uncovered interest parity, Sharpe ratio, negative skew.