Hedging a Foreign-Currency Fixed-Term Asset Deal
Summary
The document considers a USD-based firm that has agreed to pay a fixed EUR amount at a future date for an asset also priced in EUR. It asks how to hedge both the asset-price movement and the currency exposure. The answer first pairs the agreement with a sale of a matching asset forward, which leaves a net EUR cash flow equal to the difference between the forward asset price and the fixed purchase price, multiplied by the quantity.
That residual EUR amount can then be hedged with an FX forward in the corresponding amount, converting the combined terminal flow into USD. The central lesson is to determine the currency hedge after accounting for the asset hedge; hedging FX separately while leaving the asset exposure open means the EUR amount changes with the asset price and the FX hedge must be rebalanced. The explanation assumes perfectly matching contracts and focuses on terminal cash flows, without addressing basis risk, collateral, transaction costs, discounting conventions, or contract availability.
Key ideas
- A fixed EUR payment for an asset creates exposure to both the asset price and the EUR/USD exchange rate.
- A matching asset forward offsets the asset delivery and leaves a net EUR spread amount.
- The residual EUR amount can be hedged with an FX forward of the corresponding size.
- If the asset exposure remains unhedged, the currency hedge amount changes as the asset price moves.
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Full text
# How to effectively hedge a Fixed-Term deal in a foreign currency?
# How to effectively hedge a Fixed-Term deal in a foreign currency?
Assume my firm is based in USD and agrees with some counterparty to buy, at time $T$, some quantity $Q$ of asset $A$ for a fixed price $K$.
Assume also that $A$ prices and $K$ are denominated in EUR.
Assume also that we have forward prices:
- For $A$, denotated by $F^A(t,T)$
- For the FX rate, denotated by $F^{FX}(t,T)$, expressed in USD per EUR.
Now my mark-to-market at time $t$ for this agreement is:
$$\text{MTM}_t = DF(t,T)\cdot Q\cdot( F^A(t,T) - K ) \cdot F^{FX}(t,T)$$
I would like to hedge my position for both FX and market effects, assuming I can get perfectly matching contracts for asset and FX in order to hedge.
I would sell $Q$ "lots" of to $F^A(t,T)$ hedge the dynamics of the hedge.
However, I'm unclear how much to hedge for the FX. Indeed, my FX exposure at time $t$ is $F^A(t,T) - K$, which can vary very much from $F^A(t-1,T) - K$ and hence results in an hedge completely off. So, what should be the amount to hedge in FX? I thought about $\mathbb{E}[ F^A(t,T) - K | \mathcal{F_{t-1}}]$ but my backtest doesn't give me good results at all.
Is there a common way of hedging this king of "spread" exposure?
## Answer by q.t.f. (score 1)
https://quant.stackexchange.com/a/17927
You have already agreed to pay $QK$ EUR at $T$ to receive $Q$ units of A. If you sell $Q$ lots of $F^A(t,T)$ then you will receive $Q F^A(t,T)$ EUR and deliver $Q$ units of A. The combined flow is now just in EUR: at $T$ you receive a net of $Q(F^A(t,T)-K)$ EUR. You can hedge that by selling $Q(F^A(t,T)-K)$ of $F^{FX}(t,T).$ Then with both hedges, the net flow is just you receive $Q(F^A(t,T)-K)F^{FX}(t,T)$ USD at $T$.
You are confusing yourself by trying to calculate the FX hedge without assuming the asset hedge is in place. Indeed, if you didn't hedge the asset move but did hedge the FX move, the FX hedge has to be rebalanced every time the asset price moves, which is what you are seeing.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.