The Optimal Currency Hedge Ratio

A US pension fund holds German equities. It has already decided, in principle, to hedge some of the euro exposure. But "some" is doing a lot of work in that sentence — hedge 100% and you have removed currency risk entirely; hedge 0% and the decision to hedge was pointless. The number in between that actually minimizes risk is the optimal hedge ratio, and it is almost never a round number.

Why 100% is not the automatic answer

If euro moves were pure noise relative to German equity returns, hedging fully would remove a source of volatility for free — no offsetting benefit lost. But currencies and local equity returns are often correlated. A weaker euro sometimes coincides with stronger German exporters (their goods get cheaper abroad), so some currency depreciation is naturally offset by better local stock performance. Hedging that portion away doesn't reduce risk — it removes a natural stabilizer.

The formula

The hedge ratio that minimizes the variance of the combined (asset + currency) return is the regression coefficient of the currency return on the local-asset return:

$$h^{*} = \rho_{a,c} \times \frac{\sigma_c}{\sigma_a}$$

In words: the optimal hedge ratio equals the correlation between the asset's local return and the currency return, scaled by how volatile the currency is relative to the asset. If currency and asset returns are uncorrelated, $\rho_{a,c}=0$ and $h^{*}=0$ — hedging currency alone would add a return stream but wouldn't reduce total variance unless you also consider the currency's own volatility in isolation (in practice, most desks still hedge a large fraction here because currency risk is usually unrewarded, even if uncorrelated).

Worked example

A US investor holds a Japanese equity position. Historically, JPY returns and Nikkei local returns have a correlation of -0.3 (yen typically strengthens when Japanese stocks fall, a classic risk-off pattern). Currency volatility is 9% annualized, the local equity return volatility is 16%.

1. Plug into the formula. $h^{*} = -0.3 \times (9/16) = -0.169$.
2. Interpret the sign. A negative optimal ratio means the investor should not hedge the yen at all — they should go slightly long additional yen exposure beyond the natural 100% embedded in owning the stock, because yen strength has tended to cushion equity losses.
3. Contrast with intuition. A US investor with no view on this correlation might have defaulted to a 50% or 100% hedge. The data says a small negative hedge ratio (effectively, staying unhedged or overweighting yen) has actually reduced total portfolio variance historically.

Drag the correlation slider toward negative territory and watch the fitted slope flatten and cross zero — that slope is exactly the $h^{*}$ this page derives, just estimated from a scatter of currency versus asset returns instead of formula inputs.

What this means in practice

Desks rarely compute $h^{*}$ from a single historical correlation and lock it in. Correlations between currencies and local equity markets are unstable — they can flip sign across regimes (a currency that was a safe haven in one decade can become pro-cyclical in the next). Most institutional policies instead pick a strategic hedge ratio (often 50%) as a compromise between full removal of currency risk and capturing whatever natural offset exists, then revisit it periodically rather than re-optimizing continuously.