CHAPTER 5

2. While you were visiting London, you purchased a Jaguar for £35,000, payable in three months. You have enough cash at your bank in New York City, which pays 0.35% interest per month, compounding monthly, to pay for the car. Currently, the spot exchange rate is $1.45/£ and the three-month forward exchange rate is $1.40/£. In London, the money market interest rate is 2.0% for a three-month investment. There are two alternative ways of paying for your Jaguar.
(a) Keep the funds at your bank in the U.S. and buy £35,000 forward.
(b) Buy a certain pound amount spot today and invest the amount in the U.K. for three months so that the maturity value becomes equal to £35,000.
Evaluate each payment method. Which method would you prefer? Why?

Solution: The problem situation is summarized as follows:
A/P = £35,000 payable in three months
i_NY = 0.35%/month, compounding monthly
i_LD = 2.0% for three months
S = $1.45/£; F = $1.40/£.
Option a:
When you buy £35,000 forward, you will need $49,000 in three months to fulfill the forward contract. The present value of $49,000 is computed as follows:
$49,000/(1.0035)³ = $48,489.
Thus, the cost of Jaguar as of today is $48,489.
Option b:
The present value of £35,000 is £34,314 = £35,000/(1.02). To buy £34,314 today, it will cost $49,755 = 34,314x1.45. Thus the cost of Jaguar as of today is $49,755.
You should definitely choose to use “option a”, and save $1,266, which is the difference between $49,755 and $48489.

3. Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange rate is $1.52/£. The three-month interest rate is 8.0% per annum in the U.S. and 5.8% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000.
a. Determine whether the interest rate parity is currently holding.
b. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit.
c. Explain how the IRP will be restored as a result of covered arbitrage activities.

Solution: Let’s summarize the given data first:
S = $1.5/£; F = $1.52/£; I_$ = 2.0%; I_£ = 1.45%
Credit = $1,500,000 or £1,000,000.
a. (1+I_$) = 1.02
(1+I_£)(F/S) = (1.0145)(1.52/1.50) = 1.0280
Thus, IRP is not holding exactly.
b. (1) Borrow $1,500,000; repayment will be $1,530,000.
(2) Buy £1,000,000 spot using $1,500,000.
(3) Invest £1,000,000 at the pound interest rate of 1.45%;
maturity value will be £1,014,500.
(4) Sell £1,014,500 forward for $1,542,040
Arbitrage profit will be $12,040
c. Following the arbitrage transactions described above,
The dollar interest rate will rise;
The pound interest rate will fall;
The spot exchange rate will rise;
The forward exchange rate will fall.
These adjustments will continue until IRP holds.

4. Suppose that the current spot exchange rate is FF6.25/$ and the three-month forward exchange rate is FF6.28/$. The three-month interest rate is 5.6% per annum in the U.S. and 8.8% per annum in France. Assume that you can borrow up to $1,000,000 or FF6,250,000.
a. Show how to realize a certain profit via covered interest arbitrage, assuming that you want to realize profit in terms of U.S. dollars. Also determine the magnitude of arbitrage profit.
b. Assume that you want to realize profit in terms of French francs. Show the covered arbitrage process and determine the arbitrage profit in French francs.

Solution: The market data is summarized as follows:
S = FF6.25/$ = $0.16/FF;
F = FF6.28/$ = $0.1592/FF;
I_$ = 1.40%; i_FF = 2.20%
(1+I_$) = 1.014 < (1+i_FF)(F/S) = (1.022)(.1592/.16) = 1.0169

a. (1) Borrow $1,000,000; repayment will be $1,014,000.
(2) Buy FF6,250,000 spot for $1,000,000.
(3) Invest in France; maturity value will be FF6,387,500.
(4) Sell FF6,387,500 forward for $1,017,118.
Arbitrage profit will be $3,118 = $1,017,118 - $1,014,000.
b. (1) Borrow $1,000,000; repayment will be $1,014,000.
(2) Buy FF6,250,000 spot for $1,000,000.
(3) Invest in France; maturity value will be FF6,387,500.
(4) Buy $1,014,000 forward for FF6,367,920.
Arbitrage profit will be FF19,580 = FF6,387,500-FF6,367,920.
Note that only step (4) is different.

6. As of November 1, 1999, the exchange rate between the Brazilian real and U.S. dollar is R$1.95/$. The consensus forecast for the U.S. and Brazil inflation rates for the next 1-year period is 2.6% and 20.0%, respectively. How would you forecast the exchange rate to be at around November 1, 2000?

Solution: Since the inflation rate is quite high in Brazil, we may use the purchasing power parity to forecast the exchange rate.
E(e) = E( p _$) - E( p _R$)
= 2.6% - 20.0%
= -17.4%
E(S_T) = S_o(1 + E(e))
= (R$1.95/$) (1 + 0.174)
= R$2.29/$

1. Grecian Tile Manufacturing of Athens, Georgia, borrows $1,500,000 at LIBOR plus a lending margin of 1.25 percent per annum on a six-month rollover basis from a London bank. If six-month LIBOR is 4 ½ percent over the first six-month interval and 5 3/8 percent over the second six-month interval, how much will Grecian Tile pay in interest over the first year of its Eurodollar loan?

Solution: $1,500,000 x (.045 + .0125)/2 + $1,500,000 x (.05375 + .0125)/2
= $43,125 + $49,687.50 = $92,812.50.

2. A bank sells a “three against six” $3,000,000 FRA for a three-month period beginning three months from today and ending six months from today. The purpose of the FRA is to cover the interest rate risk caused by the maturity mismatch from having made a three-month Eurodollar loan and having accepted a six-month Eurodollar deposit. The agreement rate with the buyer is 5.5 percent. There are actually 92 days in the three-month FRA period. Assume that three months from today the settlement rate is 4 7/8 percent. Determine how much the FRA is worth and who pays who--the buyer pays the seller or the seller pays the buyer.
Solution: Since the settlement rate is less than the agreement rate, the buyer pays the seller the absolute value of the FRA. The absolute value of the FRA is:

$3,000,000 x [(.04875-.055) x 92/360]/[1 + (.04875 x 92/360)]
= $3,000,000 x [-.001597/(1.012458)]
= $4,732.05.

3. Assume the settlement rate in problem 2 is 6 1/8 percent. What is the solution now?

Solution: Since the settlement rate is greater than the agreement rate, the seller pays the buyer the absolute value of the FRA. The absolute value of the FRA is:

$3,000,000 x [(.06125-.055) x 92/360]/[1 + (.06125 x 92/360)]
= $3,000,000 x [.001597/(1.015653)]
= $4,717.16.

6. A bank has a $500 million portfolio of investments and bank credits. The daily standard deviation of return on this portfolio is .666 percent. Capital adequacy standards require the bank to maintain capital equal to its VAR calculated over a 10-day holding period at a maximum 1 percent loss level. What is the capital charge for the bank?

Solution: VAR = $500 million x .00666 x 2.326 x � 10 = $24.49 million.

1. Your firm has just issued five-year floating-rate notes indexed to six-month U.S. dollar LIBOR plus 1/4%. What is the amount of the first coupon payment your firm will pay per U.S. $1,000 of face value, if six-month LIBOR is currently 7.2%?

Solution: 0.5 x (.072 + .0025) x $1,000 = $37.25.

2. The discussion of zero-coupon bonds in the text gave an example of two zero-coupon bonds issued by Commerzbank. The DM300,000,000 issue due in 1995 sold at 50 percent of face value, and the DM300,000,000 due in 2000 sold at 33 1/3 percent of face value; both were issued in 1985. Calculate the implied yield to maturity of each of these two zero-coupon bond issues.

Solution: The bonds due in 1995 sold at 50% percent of face value. Since they were issued in 1985, they had a ten year maturity. Assuming a DM1,000 par value, their yield-to-maturity is: (DM1,000/DM500)^1/10 - 1 = .07177 or 7.177% per annum.
The bonds due in year 2000 sold at 33 1/3%. They have a 15 year maturity. Their yield-to-maturity is: (DM1,000/DM333.33)^1/15 - 1 =.07599 or 7.599% per annum.

3. Consider 8.5 percent Swiss franc/U.S. dollar dual-currency bonds that pay $666.67 at maturity per SF1,000 of par value. What is the implicit SF/$ exchange rate at maturity? Will the investor be better or worse off at maturity if the actual SF/$ exchange rate is SF1.35/$1.00?

Solution: Implicitly, the dual currency bonds call for the exchange of SF1,000 of face value for $666.67. Therefore, the implicit exchange rate built into the dual currency bond issue is SF1,000/$666.67, or SF1.50/$1.00. If the exchange rate at maturity is SF1.35/$1.00, SF1,000 would buy $740.74 = SF1,000/SF1.35. Thus, the dual currency bond investor is worse off with $666.67 because the dollar is at a depreciated level in comparison to the implicit exchange rate of SF1.50/$1.00.

1. On the Milan bourse, Fiat stock closed at EUR11.17 per share on Tuesday, August 19,2002. Fiat trades as and ADR on the NYSE. One underlying Fiat share equals one ADR. On August 19, the $/EUR spot exchange rate was $0.9764/EUR1.00. At this exchange rate, what is the no-arbitrage U.S. dollar price of one ADR?

Solution: The no-arbitrage ADR U.S. dollar price is: EUR11.17 x $0.9764 = $10.91.
Note to instructor: ADRs closed at $11.06 on August 19, 2002 on the NYSE.

2. If Fiat ADRs were trading at $15 when the underlying shares were trading in Milan at EUR11.17, what could you do to earn a trading profit? Use the information in problem 1, above, to help you and assume that transaction costs are negligible.

Solution: As the solution to problem 1 shows, the no-arbitrage ADR U.S. dollar price is $10.91. If Fiat ADRs were trading at $15, a wise investor would sell short the relatively overvalued ADRs. Since the ADRs are a derivative security, one would expect the ADRs to fall in price from $15 to $10.91. Assuming this happens, the short position could be liquidated for a profit of $15 - $10.91 = $4.09 per ADR.