Problem Set 1 Chapter 7 1. The $:€ exchange rate is €1 = $0.95, and the €:SFr exchange rate is SFr 1 = € 0.71. What is the $:SFr exchange rate?
Answer. SFr 1 = € 0.71 x $0.95 / € = $0.6745.
2. Suppose the direct quote for sterling in New York is 1.1110 5. How much would £500,000 cost in New York? What is the direct quote for dollars in London?
Answer. £500,000 cost £500,000 x $1.1115/£= $ 555,570. The direct quote for the dollar in London is just the reciprocal of the direct quote for the British pound in New York or 1/1.1115 1/1.1110 = 0.8997 0.9001.
3. Suppose the quote on British pounds is $1.624-31.
a. If you converted $10,000 to British pounds and then back to dollars, how many dollars would you end up with?
Answer. For $10,000, you would buy pounds at the price of $1.631, giving you £6,131.21 ($10,000/1.631) and resell them at the bid price of $1.624. The latter transaction would yield $9,957.08, resulting in a round-trip cost of $42.92.
b. Suppose you could buy pounds at the bid rate and sell them at the ask rate. How many dollars would you have to transact in order to earn $1,000 on a round-trip transaction (buying pounds for dollars and then selling the pounds for dollars)?
Answer. For every pound you could buy at the bid and sell at the ask, you would earn the spread of $0.007. To earn $1,000, you would have to transact £142,857.14 ($1,000/$0.0007). At the current bid rate of $1.624, this is equivalent to $232,000 (142,857.14 x $1.624).
4. Calculate the 30 day, 90 day, and 180 day forward discounts for the British pound.
Answer. Here are the relevant rates for the pound:
Spot: £1 = $1.8220
30 day forward: £1 = $1.8180
90 day forward: £1 = $1.8086
180 day forward: £1 = $1.7949
The 30 day forward discount is: [($1.8180 $1.8220)/$1.8220] x 12 x 100 = 2.63%
The 90 day forward discount is: [($1.8086 $1.8220)/$1.8220] x 4 x 100 = 2.94%
The 180 day forward discount is: [($1.7949 $1.8220)/$1.8220] x 2 x 100 = 2.97%
In this case, the forward discounts at these maturities are not very small, indicating that British and U.S. interest rates are quite distinct from each other.
5. The spot and 90 day forward rates for the pound are $1.1376 and $1.1350, respectively. What is the forward premium or discount on the pound?
Answer. The forward premium (discount) on the British pound is
[(f1 e0)/e0] x (360/n) = [(1.1350 1.1376)/1.1376] x 4 = .91%
which is a forward discount of .91%.
6. Suppose Credit Suisse quotes spot and 90-day forward rates of $0.7957-60, 8-13.
a. What are the outright 90-day forward rates that Credit Suisse is quoting?
Answer. The outright forwards are: bid rate = $0.7965 (0.7957 + 0.0008) and ask rate = $0.7973 (0.7960 + 0.0013).
b. What is the forward discount or premium associated with buying 90-day Swiss francs?
Answer. The annualized forward premium = [(0.7973 - 0.7960)/0.7960]x 4 = 0.65%.
c. Compute the percentage bid-ask spreads on spot and forward Swiss francs.
Answer. The bid-ask spread is calculated as follows:
Substituting in the numbers yields a spot bid-ask spread of (0.7960 - 0.7957)/0.7960 = 0.04%. The corresponding forward bid-ask spread is (0.7973 - 0.7965)/0.7973 = 0.10%.
7. Suppose you observe the following direct spot quotations in New York and Toronto, respectively: 0.8000 50 and 1.2500 60. What are the arbitrage profits per $1 million?
Answer. Converting the direct quotes in Toronto into indirect quotes yields bid ask rates for the Canadian dollar in terms of the U.S. dollar of U.S.$.7962 .8000. Hence, there is no arbitrage opportunity.
8. Suppose the euro is quoted at 0.6064 80 in London, and the pound sterling is quoted at 1.6244 59 in Frankfurt.
a. Is there a profitable arbitrage situation? Describe it.
Answer. Buy euros for £0.6080. Use the euros to buy pounds for € 1.6259. This is equivalent to selling euros for £0.6150. There is a net profit of £0.0070 per euro bought and sold a percentage yield of 1.16% (0.0070/.6080).
b. Compute the percentage bid ask spreads on the pound and euro.
Answer. The percentage bid-ask spreads on the pound and euro are calculated as follows:
£ bid-ask spread = (1.6259 - 1.6244)/1.6259 = 0.09%
Euro bid-ask spread = (0.6080 -0.6064)/0.6080 = 0.26%
9. Assuming no transaction costs, suppose £1 = $2.4110 in New York, $1 = SFr 3.997 in Zurich, and
SFr 1 = £ 0.1088 in London. How could you take profitable advantage of these rates?
Answer. Sell pounds in New York for $2.4110 apiece. Sell the dollars in Zurich for SFr 3.997, and sell the Swiss francs in London for £ 0.1088. This sequence of transactions yields 2.4110 x 3.997 x 0.1088 pounds or £1.0485 per pound initially traded.
10. Suppose Dow Chemical receives quotes of $ 0.009369-71 for the yen and $0.03675-6 for the Taiwan dollar (NT$).
a. How many U.S. dollars will Dow Chemical receive from the sale of ¥ 50 million?
Answer. Dow must sell yen at the bid rate, meaning it will receive from this sale $ 468,450 [50,000,000 x 0.009369].
b. What is the U.S. dollar cost to Dow Chemical of buying ¥ 1 billion?
Answer. Dow must buy at the ask rate, meaning it will cost Dow $ 9,371,000 [1,000,000,000 x 0.009371] to buy ¥ 1 billion.
c. How many NT$ will Dow Chemical receive for US $ 500,000?
Answer. Dow must sell at the bid rate for U.S. dollars (which is the reciprocal of the ask rate for NT$, or 1/0.03676), meaning it will receive from this sale of U.S. dollars NT$ 13,601,741 [500,000 / 0.03676].
d. How many yen will Dow Chemical receive for NT$ 200 million?
Answer. To buy yen, Dow must first sell the NT$ 200 million for U.S. dollars at the bid rate and then use these dollars to buy yen at the ask rate. The net result from these transactions is ¥ 784,334,649.45 [200,000,000 x 0.03675 / 0.009371].
e. What is the yen cost to Dow Chemical of buying NT$ 80 million?
Answer. Dow must sell the yen for dollars at the bid rate and then buy NT$ at the ask rate with the U.S. dollars. The net yen cost to Dow from carrying out these transactions is ¥ 313,886,220.51 [80,000,000 x 0.03676 / 0.009369].
11. If the Swiss franc is $0.68 on the spot market and the 180 day forward rate is $0.70, what is the annualized interest rate in the United States over the next six months? The annualized interest rate in Switzerland is 2%.
where f1 and e0 are the SFr forward and spot rates. Substituting in the numbers and recalling that everything must be converted to a semi annual basis, we have (1 + .5rus)/1.01 = .70/.68, or 1 + .5rus = 1.0397. The solution is rus = 7.94%.
12. The interest rate in the United States is 8%; in Japan the comparable rate is 2%. The spot rate for the yen is $0.007692. If interest rate parity holds, what is the 90 day forward rate on the Japanese yen?
Answer. According to the IRPT, the 90 day forward rate on the yen should equal
$.007692[(1 + .08/4)/(1 + .02/4)] = $.0078
CHAPTER 8 1. On Monday morning, an investor takes a long position in a pound futures contract that matures on Wednesday afternoon. The agreed upon price is $1.78 for £62,500. At the close of trading on Monday, the futures price has risen to $1.79. At Tuesday close, the price rises further to $1.80. At Wednesday close, the price falls to $1.785, and the contract matures. The investor takes delivery of the pounds at the prevailing price of $1.785. Detail the daily settlement process (see Exhibit 8.3). What will be the investor's profit (loss)?
Answer Time Action Cash Flow
close (1) Contract is marked-to-market. 62,500 x (1.80 -1.785) = $937.50
(2) Investor takes delivery of 62,500. (2) Investor pays 62,500 x 1.785 = $111,562.50.
Net profit is $1,250 - 937.50 = $312.50.
2. Suppose that the forward ask price for March 20 on euros is $0.9127 at the same time that the price of CME euro futures for delivery on March 20 is $0.9145. How could an arbitrageur profit from this situation? What will be the arbitrageur's profit per futures contract (contract size is € 125,000)?
Answer. Since the futures price exceeds the forward rate, the arbitrageur should sell futures contracts at $0.9145 and buy euro forward in the same amount at $0.9127. The arbitrageur will earn 125,000(0.9145 - 0.9127) = $225 per euro futures contract arbitraged.
3. On August 6, you go long one CME yen futures contract at an opening price of $0.00812 with an initial margin / performance bond of $4,590 and a maintenance margin / performance bond of $3,400. The settlement prices for August 6, 7, and 8 are $0.00791, $0.00845, and $0.00894, respectively. On August 9, you close out the contract at a price of $0.00857. Your round-trip commission is $31.48.
a. Calculate the daily cash flows on your account. Be sure to take into account your required margin / performance bond and any margin / performance bond calls.
close Contract is marked-to-market. 12,500,000 x (0.00812 - 0.00791) = -$2,625.00
August 7 Futures price rises to $0.00845. You receive
close Contract is marked-to-market. 12,500,000 x (0.00845 - 0.00791) = +$6,750.00
August 8 Futures price rises to $0.00894. You receive
close Contract is marked-to-market. 12,500,000 x (0.00894 - 0.00845) = +$6,125.00
August 9 Futures price falls to $0.00857. You pay out
close (1) Contract is marked-to-market. (1) 12,500,000 x (0.00894 - 0.00857) = -$4,625.00
(2) You close out the contract (2) None
You pay out a round-trip commission = -$31.48
Net gain on the futures contract = $5,593.52
Your margin calls and cash balances as of the close of each day were as follows:
August 6 With a loss of $2,625, your account balance falls to $1,965 ($4,590 -$2,625). You must add $2,625 ($4,590 - $1,965) to your account to restore it to the initial margin of $4,590.
With subsequent gains on the futures contract, you have no further margin / performance bond calls.
4. Suppose that DEC buys a Swiss franc futures contract (contract size is SFr 125,000) at a price of $0.83. If the spot rate for the Swiss franc at the date of settlement is SFr 1 = $0.8250, what is DEC's gain or loss on this contract?
Answer. DEC has bought Swiss francs worth $0.8250 at a price of $0.83. Thus, it has lost $0.005 per franc for a total loss of 125,000 x .005 = $625.
5. Citicorp sells a call option on Euros (contract size is € 125,000) at a premium of $0.04 per euro. If the exercise price is $0.71 and the spot price of the euro at date of expiration is $0.73, what is Citicorp's profit (loss) on the call option?
Answer. Since the spot price of $0.73 exceeds the exercise price of $0.71, Citicorp's counterparty will exercise its call option, causing Citicorp to lose 2 cents per euro. Adding in the 4 cents call premium it received gives Citicorp a net profit of 2 cents per euro on the call option for a total gain of .02 x 125,000 = $2,500.
6. Suppose you buy three June PHLX euro call options with a 90 strike price at a price of 2.3 cents / €.
a. What would be your total dollar cost for these calls, ignoring broker fees?
Answer: With each call option being for € 125,000, the three contracts combined are for € 375,000. At a price of 2.3 cents / €, the total cost is €375,000 x $ 0.0230 / € = $ 8,625.
b. After holding these calls for 60 days, you sell them for 3.8 cents / €. What is your net profit on the contracts, assuming that brokerage fees on both entry and exit were $5 per contract and that your opportunity cost was 8 percent per annum on the money tied up in the premium?
Answer: The net profit would be 1.5 cents / € for a total profit before expenses of $ 5,625 [0.015 x 375000]. Brokerage fees totaled $ 10 per contract or $ 30 overall. The opportunity cost would be $ 8,625 x 0.08 x 60 / 365 = $ 113.42. After deducting these expenses (which total $ 143.42), the net profit is 5,625 – 143.42 = $ 5,481.58.