11.4: Managing Exchange Rate Risk

11.4.1 Hedging Instruments at a Glance

Option rule of thumb: A put on the foreign currency protects a foreign-currency receivable (you need to sell the foreign currency later). A call on the foreign currency protects a foreign-currency payable (you need to buy the foreign currency later).

11.4.2 Which Hedge Should a Manager Use?

• Known amount, known date, no desire for upside: use a forward (or futures).
• Known amount, want upside if the rate moves favorably: buy an option (or use a collar to reduce premium).
• Long horizon or recurring exposure; align financing with revenues: consider a currency swap.
• Forward unavailable/expensive, or you prefer balance-sheet mechanics: use a money-market hedge.

11.4.3 Forwards and Futures

Forwards and futures lock in an exchange rate today for a future transaction date. They are the most direct hedges for transaction exposure (Section 11.2).

11.4.4 Options (FX Floors and Caps)

Options provide protection while preserving upside. In managerial finance terms, options are a form of insurance: you pay a premium to limit a downside outcome.

• Put on foreign currency (protect a receivable): establishes a minimum USD outcome (a floor).
• Call on foreign currency (protect a payable): establishes a maximum USD cost (a cap).

Approximate payoffs at expiration (ignoring time value):

• Receivable with a put: Minimum USD proceeds \(\approx K \times Q_{FC} - \text{Premium}\)
• Payable with a call: Maximum USD cost \(\approx K \times Q_{FC} + \text{Premium}\)

11.4.5 Money-Market Hedge (MMH)

A money-market hedge replicates a forward using borrowing and lending (a direct application of Chapter 5 TVM logic). For a foreign-currency receivable at time \(T\):

1. Borrow the present value of the receivable in foreign currency at the foreign interest rate \(i_f\):
   \[ \text{PV}_{FC}=\frac{Q_{FC}}{(1+i_f)^T} \tag{11.16} \]
2. Convert the borrowed foreign currency to home currency today at spot \(S_0\).
3. Invest the home currency today for \(T\) at the domestic rate \(i_d\).
4. At \(T\), the receivable repays the foreign-currency loan; the firm keeps the matured home-currency deposit.

Worked Example: MMH for a Receivable

Receive €2,000,000 in 180 days. Spot rate \(S_0=1.1000\ \$/€\). Annual rates (use \(T=0.5\)): \(i_{EU}=2.0\%\), \(i_{US}=4.0\%\).

\[ \text{PV}_{€}=\frac{2{,}000{,}000}{(1.02)^{0.5}}\approx 1{,}980{,}198\ € \tag{11.17} \] \[ \text{USD}_0 = 1{,}980{,}295 \times 1.10 \approx \$2{,}178{,}325 \tag{11.18} \] \[ \text{USD}_{0.5} = 2{,}178{,}325 \times (1.04)^{0.5} \approx \$2{,}221{,}464 \tag{11.19} \]

Compare this result to the forward hedge using the same spot rate and relevant forward rate. Any small difference typically comes from compounding conventions, day counts, or rounding.

BA II Plus Steps (Money-Market Hedge)

1. Find PV in foreign currency: 2nd → CLR TVM. Set \(N=0.5\), \(I/Y=2\), \(FV=2000000\), \(PMT=0\). Then CPT → PV.
2. Convert to USD today: multiply PV(€) by \(S_0\).
3. Grow USD to maturity: 2nd → CLR TVM. Set \(N=0.5\), \(I/Y=4\), \(PV=\text{USD}_0\), \(PMT=0\). Then CPT → FV.

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11.4.6 Currency Swaps (Brief)

In a currency swap, two parties exchange principal and interest payments in different currencies. Swaps are often used to:

• match debt service to the currency of revenues,
• access lower-cost funding in one market and swap into the needed currency, and
• hedge long-dated exposures beyond the depth of forward markets.

Swaps are most common when exposures are long-term or recurring, and when the firm is using global financing strategy as part of risk management (Chapter 10 logic).

11.4.7 Practice Set (Answers Shown)

1. Forward vs. No Hedge (Receivable): €1,500,000 due in 90 days; forward \(F_{0,90}=1.1120\ \$/€\). If spot in 90 days is (a) 1.0950, (b) 1.1300, compare proceeds.
   Answer Forward locks \(1{,}500{,}000\times1.1120=\$1{,}668{,}000\). No hedge yields (a) \(1{,}500{,}000\times1.0950=\$1{,}642{,}500\); (b) \(1{,}500{,}000\times1.1300=\$1{,}695{,}000\).
2. Option (Payable): ¥80,000,000 due in 60 days. Buy a call on JPY at \(K=0.00680\ \$/¥\); premium 0.8% of notional. Find the maximum USD outlay (ignore time value).
   Answer Strike cost \(=80{,}000{,}000\times0.00680=\$544{,}000\). Premium \(=0.008\times80{,}000{,}000\times0.00680=\$4{,}352\). Max \(\approx \$548{,}352\).
3. Money-Market Hedge (Receivable): FC 5,000,000 in 6 months; \(S_0=0.75\ \$/\mathrm{FC}\); \(i_f=3\%\) p.a.; \(i_d=5\%\) p.a. Compute USD in 6 months via MMH (use \(T=0.5\)).
   Answer \(\text{PV}_{FC}=5{,}000{,}000/(1.03)^{0.5}\approx4{,}926{,}108\). \(\text{USD}_0=4{,}926{,}108\times0.75\approx\$3{,}694{,}581\). \(\text{USD}_{0.5}=3{,}694{,}581(1.05)^{0.5}\approx\$3{,}786{,}000\) (rounded).
4. Collar Logic: Explain how selling a call can reduce the net cost of a protective put.
   Answer The premium received from the short call partially (or fully) offsets the premium paid for the long put, creating a lower-cost band of outcomes with a floor and a cap.

Checkpoint: You should now be able to choose an appropriate hedge, compute forward proceeds or costs, evaluate option protection including premiums, and replicate a forward hedge with a money-market hedge using TVM logic (Chapter 5). These skills prepare you to convert foreign cash flows and evaluate international projects using NPV (Chapter 9) and to consider how financing currency choices affect risk (Chapter 10).