Objectives: Consider how foreign exchange (FX) risk can be hedged with forward exchange contracts.

1. Hedging Foreign Exchange Risk • Objectives: • Consider how foreign exchange (FX) risk can be hedged with forward exchange contracts. • Analyze how the absence of arbitrage determines the forward exchange rate (Covered Interest Parity). • Consider how currency swaps can be used to hedge periodic foreign currency payments. • Understand how FX options can insurance against FX risk.

2. Many FI’s have multi-national operations. A FI’s customers who reside or do business in a foreign country may desire a financial service that results in the creation of a foreign currency denominated asset or liability for the FI. Examples: • A U.S. finance company makes a yen-denominated loan to a Japanese company. • The London branch of a French bank accepts a pound- denominated deposit from a U.K. resident. • A Dutch insurance company underwrites a life insurance policy for a U.S. resident that is denominated in dollars. • A U.S. investment bank provides euro-denominated bridge-loan financing for a merger of two Italian firms. • A British pension fund invests in Canadian dollar denominated bonds.

3. If a FI’s foreign currency denominated assets are not matched with offsetting foreign currency denominated liabilities, the FI’s net worth will be exposed to foreign exchange (FX) risk: an appreciation or depreciation of the foreign currency. • Example: A U.S. bank has offices in London and negotiates a £1,000,000 one-year loan to a credit-worthy U.K. firm at an interest rate of 7.5%. • At the current spot exchange rate of S0 = $1.6715/£, this requires funding of $1,671,500 that the bank raises by issuing a one-year dollar denominated C.D. at an interest rate of 5.5%.

4. Since the pound-denominated loan interest rate is 7.5 %, the bank will receive £1,075,000 at the end of the year. But if the £ depreciates vis-à-vis the $ during this time, the U.S. bank could suffer a lost when converting £’s for $’s at year-end. • This is because the end-of-year $ value of the loan will be • Maturity value of loan = £1,075,000 x S1 • where S1 is the random end-of-year spot $/£ exchange rate. Indeed, the $ value of the loan repayment could be less than the bank’s payment on its CD of $1,671,500 x (1.055) =$1,763,432.50 resulting in a loss on the transaction. This would occur if

5. Hedging with FX Forward Contracts • To hedge its £ exposure, the bank could take a short position in a one-year forward contract on £1,075,000. Suppose that the current one-year forward exchange rate (forward price) for trading pounds and dollars is f0 = $1.6441/£. • Thus, the maturity value of the bank’s loan plus the maturity value of its short forward position is Maturity Value of Short Position = Forward Price of £’s - Spot Market Price of £’s = £1,075,000 x $1.6441/£ - £1,075,000 x S1 =$1,767,407.50 - £1,075,000 x S1 Bank’s end-of-year investment value= £1,075,000 x S1 + $1,767,407.50 - £1,075,000 x S1 = $1,767,407.50

6. Essentially, these transactions enable the bank to satisfy its short forward position by delivering £1,075,000 (its loan payment) in exchange for receiving $1,767,407.50. Bank Balance Sheet Assets Liabilities One-Year £ Loan One-Year $ CD (£1,075,000) ($1,763,432.50) Off-Balance Sheet Forward Contract Assets Liabilities Receive $ Forward Price Deliver £ to Long Party ($1,767,407.50) (£1,075,000)

7. Note that the loan and forward transactions result in the bank earning a risk-free one-year U.S. $ interest rate of • which exceeds the 5.5% interest rate it must pay on its CD. Hence, this forward exchange hedging guarantees that the bank will make a profit on its lending to the U.K. firm. • Forward exchange contracts such as this comprise the single largest derivative market. It is an over-the-counter market consisting of dealers employed by large, international banks. • Derivatives with very similar hedging properties are FX futures contracts that are traded on exchanges such as the CME and FINEX. Dealers of forward exchange contracts often use these FX futures to hedge their positions.

8. Covered Interest Parity • In the previous example, we took the one-year forward exchange price (rate) of f0 = $1.6441/£ as given. Let us next investigate the determinants of such forward exchange rates. • As before, let S0 be the current spot foreign exchange rate in American terms, that is, in $ per foreign currency. For example, if the foreign currency is the euro (€) then on 4/7/2004, S0 = $1.2175/€. Now consider the payoff to a long position in a forward exchange contract that matures at date . At date  the long party pays $f0 in return for receiving one € worth S. Hence, the payoff can be written as • Payoff at date  to long party = S - f0 • This payoff can be replicated by borrowing in dollars and investing in euro bonds. The two actions taken at date 0 are:

9. 1) Borrow $f0/(1+i) at the date 0 U.S. $ risk-free interest rate of i. 2) Purchase a euro bond having a date  face value of € 1. If the date 0 euro interest rate is i€, the $ cost of this investment is $ S0/(1+ i€). • Actions 1) and 2) produce a net cash flow at date  of • Euro Bond Return - U.S Borrowing Repayment = • S(1+ i€) /(1+ i€)- f0 (1+i) /(1+i) = S - f0 which is exactly the payoff of the long forward position. Hence, the Law of One Price states that the value of the forward contract to the long party, PVforward, must be the present values of trades 1) and 2):

10. When the forward exchange contract is initiated, its value equals zero since the long and short parties agree to it voluntarily and no initial payments are made. The forward exchange rate, f0, adjusts to make the contract fair. Therefore, setting PVforward = 0 and solving for f0, we obtain • which is the Covered Interest Parity condition. It shows that rates in four markets are linked: the forward exchange rate, the spot exchange rate, the U.S. money market rate, the Euro money market rate. Trading in any three of these markets can replicate the fourth.

11. Example: The current Japanese yen per euro spot exchange rate is ¥115.69/€. The annualized, semi-annually compounded interest rates for borrowing or lending for six-months in euros and Japanese yen are 3.80 % and 0.16 %, respectively. According to Covered Interest Parity, what is the six-month forward exchange rate in yen per euro (¥/€ )?

12. Currency Swaps • A currency swap is an agreement between two parties to exchange payments in one currency for payments in another. • In a fixed-fixed currency swap, parties agree to exchange a pre-agreed amount of foreign currency for domestic currency at specific future dates. • Example: A Japanese investment bank issues a € 10 m., 7-year euro-denominated bond in Frankfurt. The bond makes annual coupon payments of 4 %, or € 400,000 per year. After two years, the Japanese bank wishes to reduce its euro-liabilities because its euro-denominated assets have declined or because it fears that the euro will appreciate vis-à-vis the yen.

13. To convert its euro-denominated bond into a yen-denominated one, it agrees to a 5-year currency swap in which it contracts to pay yen and receive euros. • If the current swap rate for a five-year yen for euro swap is ¥100/€, then over the next five years the bank would make annual (coupon) payments of ¥ 40 m. in exchange for receiving annual payments of € 400,000. In addition, in the final fifth year the swap would require that the bank make a principal payment of ¥ 1,000 m. in exchange for € 10 m. Bank Balance Sheet Assets Liabilities Five-year € - denominated Bond Off-Balance Sheet Currency Swap Assets Liabilities € Swap Payments ¥ Swap Payments

14. This currency swap is equivalent to five different forward exchange contracts to deliver euros for yen made at the same forward exchange rate of f0 = ¥100/€. • Thus, if S0 is the current ¥/€ spot exchange rate, i€( ) is the interest rate for borrowing or lending in euros from date 0 to date  and i¥( ) is the interest rate for borrowing or lending in yen from date 0 to date  , then the swap’s value to the party delivering (short) euros is

15. When the swap is first initiated by the two parties, PVswap= 0. Given S0, i€( ), and i¥( ) for  = 1,…,5, the five-year swap rate f0 is determined such that PVswap= 0, e.g., f0 = ¥100/€. • Similar to interest rate swaps, currency swaps are sold by FX dealers in the over-the-counter market. • Swaps can be arranged that combine the features of both currency and interest rate swaps. A fixed-floating currency swap involves exchanging fixed-interest payments in one currency for floating-rate interest payments in another. • For example, if in the previous example, the Japanese bank had issued a euro-denominated floating-rate bond tied to one-year euroLIBOR, it could become a fixed yen payer, euroLIBOR receiver in a 5-year fixed-floating swap.

16. FX Options • Options on foreign currencies can be used to insure against a foreign currency depreciation. • Example: A U.S. pension fund purchases a six-month pound- denominated C.D. from a British bank that pays £1,000,000 in six-months. • After three months, the pension fund fears that the Fed will soon raise U.S. interest rates which would likely lead to an significant appreciation of the dollar vis-à-vis the pound from the current spot exchange rate of S0 = $1.8405/£. • To insure against this pound depreciation, the pension fund purchases three-month maturity put options on £1 m. with an exercise price of X = $1.8300/£.

17. The maturity value of these put options are • Put option payoff = max[ X – Sm., 0 ] • = max[$1.83 m. – Sm., 0 ] • Combining these put options with its pound- denominated C.D. implies: • Put option + CD payoff = max[$1.83 m. – Sm., 0 ] +Sm. • = max[$1.83 m.,Sm. ] • so that its “insured” CD payment will be no less than $1.83 m. • Of course the pension fund mustpay an initial premium to the writer of the option for this insurance (e.g., $0.04/£) or $40,000. • Note that this put option on the pound is equivalent to a call option on the dollar. It pays off when the dollar appreciates (pound depreciates).