Foreign Exchange Markets and Currency Forwards › Currency Forwards for Hedging

Currency forwards are powerful tools for managing foreign exchange exposure. You must understand how to construct and value these hedges.

Organizations face several types of currency risk:

• transaction exposure: Risk from known future foreign currency cash flows (e.g., a US importer paying €1 million to a German supplier in 60 days)
• translation exposure: Risk from converting foreign subsidiary financial statements to the parent's reporting currency
• economic exposure: Long-term competitive risk from exchange rate changes affecting future revenues and costs

Currency forwards directly hedge transaction exposure and can partially address economic exposure.

A currency forward obligates two parties to exchange currencies at a predetermined rate on a future date. Building on our discussion of forwards in Chapter 5 of this part, the key terms include:

• Notional amount: The quantity of currency to be exchanged
• Forward rate: The agreed exchange rate
• Settlement date: When the exchange occurs
• Settlement method: Physical delivery or cash settlement

Consider a US pension fund that owns €50 million in European equities. You are bullish on European stocks but want to eliminate currency risk: you want returns driven by stock performance, not EUR/USD fluctuations.

The hedge locks in the forward rate, eliminating both downside and upside currency exposure. The unhedged portfolio benefits if EUR strengthens but suffers if EUR weakens.

At the forward's maturity, the hedge generates a profit or loss that offsets currency movements in the underlying portfolio. The profit and loss calculation is straightforward: compare what you locked in to what you would have received at the prevailing spot:

$$\text{P\&L}_{\text{hedge}} = N \times (F - S_T)$$

where:

• $N$: notional amount of foreign currency
• $F$: locked-in forward rate
• $S_T$: spot exchange rate at maturity
• $(F - S_T)$: gain or loss per unit of currency (for a short forward position)

For a short forward position (selling foreign currency forward), the interpretation is intuitive: you agreed to sell at rate $F$, but the market rate at maturity is $S_T$. If $F > S_T$, you sold at a higher rate than you could have gotten in the spot market, generating a profit. If $F < S_T$, you sold at a lower rate than the spot market, creating a loss. This gain or loss exactly offsets the currency impact on your underlying foreign asset.

For ongoing exposures, hedging typically involves rolling forward contracts. At each maturity, the old forward settles and a new one is initiated. Rolling creates "roll yield" that depends on the forward curve:

• Positive carry: If you're receiving the higher-yielding currency forward, each roll adds value
• Negative carry: If you're paying the higher-yielding currency forward, each roll costs

This cost represents the price of eliminating currency risk. Whether it's worth paying depends on your risk tolerance and views on EUR/USD.

A 100% hedge eliminates currency risk but also forgoes potential gains from favorable moves. Some investors use partial hedges based on:

• Volatility targeting: Hedge enough to achieve a target portfolio volatility
• Mean-variance optimization: Balance expected return against risk reduction
• Regime-dependent: Adjust hedge ratio based on market conditions

The volatility of a partially hedged portfolio derives from the variance of the sum of the equity position and the remaining currency exposure. A partially hedged portfolio has two sources of risk: the underlying asset and the unhedged portion of currency exposure. To calculate the portfolio volatility, we first determine the variance of the sum of these components:

$$\begin{aligned} \sigma_p^2 &= \sigma_e^2 + (1-h)^2 \sigma_f^2 + 2\rho (1-h) \sigma_e \sigma_f \\ \sigma_p &= \sqrt{\sigma_e^2 + (1-h)^2 \sigma_f^2 + 2\rho (1-h) \sigma_e \sigma_f} \end{aligned}$$

where:

• $\sigma_p$: portfolio volatility
• $\sigma_e$: volatility of the underlying asset
• $\sigma_f$: volatility of the exchange rate
• $h$: hedge ratio ($0 \le h \le 1$)
• $\rho$: correlation between asset returns and exchange rate returns
• $(1-h)^2 \sigma_f^2$: variance contribution from the unhedged portion of currency exposure
• $2\rho (1-h) \sigma_e \sigma_f$: covariance term capturing the diversification effect between asset and currency returns

The covariance term is particularly important because it captures the diversification effect. When equity and currency returns are negatively correlated, the covariance term is negative, reducing total portfolio variance. This means the currency exposure provides a natural hedge against equity risk.