PROBLEMS
1. Using the American term quotes from Exhibit 5.4, calculate a cross-rate matrix for the euro, Swiss franc, Japane yen, and the British pound so that the resulting triangular matrix is similar to the portion above the diagonal in Exhibit 5.6.
Solution: The cross-rate formula we want to u is:
S(j/k) = S($/k)/S($/j).
The triangular matrix will contain 4 x (4 + 1)/2 = 10 elements.
¥ SF £ $
Euro 112.75 1.4128 .8351 1.2238 Japan (100) 1.2531 .7406 1.0854 Switzerland .5911 .8662
U.K 1.4655
2. Using the American term quotes from Exhibit 5.4, calculate the one-, three-, and six-month forward cross-exchange rates between the Canadian dollar and the Swiss franc. State the forward cross-rates in “Canadian” terms.
Solution: The formulas we want to u are:
F N(CD/SF) = F N($/SF)/F N($/CD)
or
F N(CD/SF) = F N(CD/$)/F N(SF/$).
We will u the top formula that us American term forward exchange rates.
F1(CD/SF) = .8671/.9628 = .9006
F3(CD/SF) = .8686/.9624 = .9025
F6(CD/SF) = .8715/.9614 = .9065
3. A foreign exchange trader with a U.S. bank took a short position of £5,000,000 when the $/£ exchange rate was 1.55. Subquently, the exchange rate has changed to 1.61. Is this movement in the exchange rate good from the point of view of the position taken by the trader? By how much has the bank’s liability changed becau of the change in the exchange rate?
52届格莱美
CFA Guideline Answer:
The increa in the $/£ exchange rate implies that the pound has appreciated with respect to the dollar. This is unfavorable to the trader since the trader has a short position in pounds.
Bank’s liability in dollars initially was 5,000,000 x 1.55 = $7,750,000
Bank’s liability in dollars now is 5,000,000 x 1.61 = $8,050,000
4. Restate the following one-, three-, and six-month outright forward European term bid-ask quotes in forward points.
Spot 1.3431-1.3436
One-Month 1.3432-1.3442
Three-Month 1.3448-1.3463
在线口译Six-Month 1.3488-1.3508
Solution:
One-Month 01-06
Three-Month 17-27
Six-Month 57-72
5. Using the spot and outright forward quotes in problem 4, determine the corresponding bid-ask spreads in points.
Solution:
Spot 5
One-Month 10
Three-Month 15
Six-Month 20
老规矩6. Using Exhibit 5.4, calculate the one-, three-, and six-month forward premium or discount for the Canadian dollar versus the U.S. dollar using American term quotations. For simplicity, assume each roughen>you may be
month has 30 days. What is the interpretation of your results?
Solution: The formula we want to u is:
f N,CD = [(F N($/CD) - S($/CD/$)/S($/CD)] x 360/N
fuzef1,CD = [(.9628 - .9629)/.9629] x 360/30 = -.0012
f3,CD = [(.9624 - .9629)/.9629] x 360/90 = -.0021
f6,CD = [(.9614 - .9629)/.9629] x 360/180 = -.0031
The pattern of forward premiums indicates that the Canadian dollar is trading at a discount versus the U.S. dollar. That is, it becomes less expensive to buy a Canadian dollar forward for U.S. dollars (in absolute and percentage terms) the further into the future one contracts.
7. Using Exhibit 5.4, calculate the one-, three-, and six-month forward premium or discount for the U.S. dollar versus the British pound using European term quotations. For simplicity, assume each month has 30 days. What is the interpretation of your results?
Solution: The formula we want to u is:
f N,$ = [(F N (£/$) - S(£/$))/S(£/$)] x 360/N
f1,$ = [(.6824 - .6824)/.6824] x 360/30 = .0000
f3,$ = [(.6822 - .6824)/.6824] x 360/90 = -.0012
f6,$ = [(.6821 - .6824)/.6824] x 360/180 = -.0009
The pattern of forward premiums indicates that the dollar is trading at a discount versus the British pound for maturities longer than one month. The three-month discount is larger than the six-month discount in percentage but not absolute terms.
8. A bank is quoting the following exchange rates against the dollar for the Swiss franc and the Australian dollar:
SFr/$ = 1.5960--70
A$/$ = 1.7225--35
An Australian firm asks the bank for an A$/SFr quote. What cross-rate would the bank quote?
CFA Guideline Answer:
The SFr/A$ quotation is obtained as follows. In obtaining this quotation, we keep in mind that SFr/A$ = SFr/$/A$/$, and that the price (bid or ask) for each transaction is the one that is more
advantageous to the bank.
The SFr/A$ bid price is the number of SFr the bank is willing to pay to buy one A$. This transaction (buy A$—ll SFr) is equivalent to lling SFr to buy dollars (at the bid rate of 1.5960 and the lling tho dollars to buy A$ (at an ask rate of 1.7235). Mathematically, the transaction is as follows:
bid SFr/A$ = (bid SFr/$)/(ask A$/$) = 1.5960/1.7235 = 0.9260
The SFr/A$ ask price is the number of SFr the bank is asking for one A$. This transaction (ll A$—buy SFr) is equivalent to buying SFr with dollars (at the ask rate of 1.5970 and then simultaneously purchasing the dollars against A$ (at a bid rate of 1.7225). This may be expresd as follows:
ask SFr/A$ = (ask SFr/$)/(bid A$/$) = 1.5970/1.7225 = 0.9271
The resulting quotation by the bank is
SFr/A$ = 0.9260—0.9271
9. Given the following information, what are the NZD/SGD currency against currency bid-ask quotations?
American Terms European Terms
Bank Quotations Bid Ask Bid Ask
New Zealand dollar .7265 .7272 1.3751 1.3765
Singapore dollar .6135 .6140 1.6287 1.6300
Solution: Equation 5.12 from the text implies S b(NZD/SGD) = S b($/SGD) x S b(NZD/$) = .6135 x 1.3751 = .8436. The reciprocal, 1/S b(NZD/SGD)= S a(SGD/NZD)= 1.1854. Analogously, it is implied that S a(NZD/SGD) = S a($/SGD) x S a(NZD/$) = .6140 x 1.3765 = .8452. The reciprocal, 1/S a(NZD/SGD) = S b(SGD/NZD) = 1.1832. Thus, the NZD/SGD bid-ask spread is NZD0.8436-NZD0.8452 and the SGD/NZD spread is SGD1.1832-SGD1.1854.
10. Doug Bernard specializes in cross-rate arbitrage. He notices the following quotes:
Swiss franc/dollar = SFr1.5971?$
Australian dollar/U.S. dollar = A$1.8215/$
Australian dollar/Swiss franc = A$1.1440/SFr
Ignoring transaction costs, does Doug Bernard have an arbitrage opportunity bad on the quotes? If there is an arbitrage opportunity, what steps would he take to make an arbitrage profit, and how would he profit if he has $1,000,000 available for this purpo.
sarahconnor
cf名字英文CFA Guideline Answer:
A. The implicit cross-rate between Australian dollars and Swiss franc is A$/SFr = A$/$ x $/SFr = (A$/$)/(SFr/$) = 1.8215/1.5971 = 1.1405. However, the quoted cross-rate is higher at A$1.1.1440/SFr. So, triangular arbitrage is possible.
B. In the quoted cross-rate of A$1.1440/SFr, one Swiss franc is worth A$1.1440, whereas the cross-rate bad on the direct rates implies that one Swiss franc is worth A$1.1405. Thus, the Swiss franc is overvalued relative to the A$ in the quoted cross-rate, and Doug Bernard’s strategy for triangular arbitrage should be bad on lling Swiss francs to buy A$ as per the quoted cross-rate. According
ly, the steps Doug Bernard would take for an arbitrage profit is as follows:
i. Sell dollars to get Swiss francs: Sell $1,000,000 to get $1,000,000 x SFr1.5971/$ =
SFr1,597,100.
ii. Sell Swiss francs to buy Australian dollars: Sell SFr1,597,100 to buy SFr1,597,100 x A$1.1440/SFr = A$1,827,082.40.
iii. Sell Australian dollars for dollars: Sell A$1,827,082.40 for A$1,827,082.40/A$1.8215/$ = $1,003,064.73.
Thus, your arbitrage profit is $1,003,064.73 - $1,000,000 = $3,064.73.
新福尔摩斯第三季11. Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting €0.7627/$1.00 and Credit Suis is offering SF1.1806/$1.00. You learn that UBS is making a direct market between the Swiss franc and the euro, with a current €/SF quote of .6395. Show how you can make a triangular arbitrage profit by trading at the prices. (Ignore bid-ask spreads for this problem.) Assume you have $5,000,000 with which to conduct the arbitrage. What happens if you initially ll dollars for Swiss francs? What
大写字母怎么写€/SF price will eliminate triangular arbitrage?
