FX Forward Hedging of a Foreign-Currency Asset

Summary

The document asks how to represent a domestic-currency portfolio holding a foreign asset when an FX forward overlays the position. It begins with the conversion of the foreign asset’s value into domestic currency using the spot exchange rate, then presents a differential return expression containing asset and FX returns, their cross term, and a discount-factor adjustment.

The stated hedge agrees to sell the foreign currency amount corresponding to the asset and receive domestic currency at a future date. The question is how this forward position changes the portfolio value and produces the displayed return. No answer or derivation is included, so the precise hedge notional, valuation convention, and interpretation of the discount-factor ratio remain unresolved. The expression serves as a setup for studying currency-hedged foreign-asset returns rather than a complete replication recipe.

Key ideas

• A foreign asset’s domestic-currency value combines its foreign-currency price with the spot exchange rate.
• The FX forward overlay is intended to offset currency exposure by selling foreign currency for domestic currency at a future date.
• The displayed return expression includes asset return, FX return, a cross term, and a discount-factor adjustment.
• The document poses the portfolio construction question but provides no derivation or answer.

Tags

# Hedge return of foreign asset


# Hedge return of foreign asset












Given that $S(T)$ is the value of an asset in a foreign currency, $X(T)$ is the spot domestic/foreign rate, $P_t$ is the value of a Portfolio in the the domestic currency (invested in $S$) and $z^{f}$ and $z^{d}$ are Discount Factors (foreign and domestic), could somebody explain me what $P_t$ is, given that $ \frac{dP_t}{P_t} =\frac{dS_t}{S_t} +\frac{dX_t}{X_t} +\frac{dX_t}{X_t} \cdot \frac{dS_t}{S_t} - \frac{dX_t}{X_t} + \frac{z^{f,t+dt}}{z^{d,t+dt}}-1$.

The porfolio is overlayed with a FX Forward contract in which one agrees to sell forward $S(t)$ of the foreign currency and buy the domestic currency at $t+dt$.

I know that it starts with $P_t^d = S_t \cdot X_t$. However, there is the part with the overlay missing. How does that look like? I hope my question is clear. Thanks a lot in advance!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.