Problem 6.1 Visiting Guatemala Isaac Díez Peris lives in Rio de Janeiro. While attending school in Spain he meets Juan Carlos Cordero from Guatemala. Over the summer holiday Isaac decides to visit Juan Carlos in Guatemala City for a couple of weeks. Isaac's parents give him some spending money, R$4,500. Isaac wants to exchange it to Guatemalan quetzals (GTQ). He collects the following rates: Spot rate on the GTQ/€ cross rate Spot rate on the €/reais cross rate
GTQ 10.5799/€ €0.4462/R$
a. What is the Brazilian reais/Guatemalan quetzal cross rate? b. How many quetzals will Isaac get for his reais? Assumptions Amount of reais from parents Spot rate (R$/€) Spot rate (€/GTQ) a. What is the R$/GTQ cross rate? Cross rate (R$/GTQ)
Values 4,500.00 10.5799 0.4462
4.72
Reais/GTQ = R$/€ x €/GTQ b. How many quetzals will he get for his reais? Converting your reais into quetzals
21,243
Problem 6.2 Forward Premiums on the Japanese Yen Use the following spot and forward bid-ask rates for the Japanese yen/U.S. dollar (¥/$) exchange rate from September 16, 2010, to answer the following questions: Period spot 1 month 2 months 3 months 6 months 12 months 24 months
¥/$ Bid Rate 85.41 85.02 84.86 84.37 83.17 82.87 81.79
¥/$ Ask Rate 85.46 85.05 84.90 84.42 83.20 82.91 81.82
a. What is the mid-rate for each maturity? b. What is the annual forward premium for all maturities? c. Which maturities have the smallest and largest forward premiums? Since the exchange rate quotes are indirect quotes on the dollar (¥/$), the proper forward premium calculation is: Forward premium = ( Spot - Forward ) / (Forward) x (360 / days)
Period spot 1 month 2 months 3 months 6 months 12 months 24 months
Days Forward 30 60 90 180 360 720
¥/$ Bid Rate 85.41 85.02 84.86 84.37 83.17 82.87 81.79
¥/$ Ask Rate 85.46 85.05 84.90 84.42 83.20 82.91 81.82
a. Calculated Mid-Rate 85.43500 85.03500 84.88000 84.39500 83.18500 82.89000 81.80500
b. Forward Premium 5.6447% 3.9232% 4.9292% 5.4096% 3.0703% 2.2187%
The forward rates progressively require fewer and fewer Japanese yen per dollar than the current spot rate. Therefore the yen is selling forward at a premium and the dollar is selling forward at a discount. c. Which maturities have the smallest and largest forward premiums? The 24 month forward rate has the smallest premium, while the 1 month forward possesses the largest premium.
Problem 6.3 Munich to Moscow On your post-graduation celebratory trip you decide to travel from Munich, Germany to Moscow, Russia. You leave Munich with 15,000 euros in your wallet. Wanting to exchange all of these for Russian rubles, you obtain the following quotes: Spot rate on the dollar/euro cross rate Spot rate on the ruble/dollar cross rate
$1.3214/€ Rbl 30.96/$
a. What is the Russian ruble/euro cross rate? b. How many rubles will you obtain for your euros? Assumptions Beginning your trip with euros Spot rate ($/€) Spot rate (Rubles/$) a) What is the Russian ruble/euro cross rate? Cross rate (Rubles/€)
Values 15,000.00 1.3214 30.96
40.91
Rubles/ € = Rubles/$ x $/ € b) How many rubles will you obtain for your euros? Converting your euros into Rubles
613,658
Problem 6.4 Jumping to Japan After spending a week in Moscow you get an email from your friend in Japan. He can get you a really good deal on a plane ticket and wants you to meet him in Osaka next week to continue your post-graduation celebratory trip. You have 450,000 rubles left in your money pouch. In preparation for the trip you want to exchange your Russian rubles for Japanese yen so you get the following quotes: Spot rate on the rubles/dollar cross rate Spot rate on the yen/dollar cross rate
Rbl 30.96/$ ¥84.02/$
a. What is the Russian ruble/euro cross rate? b. How many rubles will you obtain for your euros? Assumptions Beginning your trip with rubles Spot rate (Rubles/$) Spot rate (¥/$) a) What is the Russian ruble/euro cross rate? Cross rate (Rubles/¥)
Values 450,000.00 30.96 84.02
0.3685
Rubles/¥ = Rubles/$ ÷ ¥/$ b) How many rubles will you obtain for your euros? Converting your Rubles into yen
1,221,177
Problem 6.5 Vancouver Exports A Canadian exporter, Canuck Exports, will be receiving six payments of €12,000, ranging from now to 12 months in the future. Since the company keeps cash balances in both Canadian dollars and U.S. dollars, it can choose which currency to change the euros to at the end of the various periods. Which currency appears to offer the better rates in the forward market?
Period spot 1 month 2 months 3 months 6 months 12 months
Period spot 1 month 2 months 3 months 6 months 12 months
Period spot 1 month 2 months 3 months 6 months 12 months
Days Forward 30 60 90 180 360 Days Forward 30 60 90 180 360
Days Forward 30 60 90 180 360
C$/euro 1.3360 1.3368 1.3376 1.3382 1.3406 1.3462
C$/euro 1.3360 1.3368 1.3376 1.3382 1.3406 1.3462
US$/euro 1.3221 1.3230 1.3228 1.3224 1.3215 1.3194
US$/euro 1.3221 1.3230 1.3228 1.3224 1.3215 1.3194 Forward Premium on the C$/euro 0.722% 0.705% 0.659% 0.693% 0.765%
Forward Premium on the US$/euro 0.817% 0.318% 0.091% -0.091% -0.204%
C$ Proceeds of € 12,000.00 16,032.00 16,041.65 16,050.84 16,058.41 16,087.54 16,154.69
Difference Over Spot $9.65 $18.84 $26.41 $55.54 $122.69
US$ Proceeds of € 12,000.00 $15,865.20 $15,876.00 $15,873.60 $15,868.80 $15,858.00 $15,832.80
Difference Over Spot $10.80 $8.40 $3.60 ($7.20) ($32.40)
The Canadian exporter will be receiving six payments of 12,000 euros, ranging from now to 12 months in the future. Since the company keeps cash balances in both Canadian dollars and US dollars, it can choose which currency to change the euros to at the end of the various periods. And since the company wishes to lock in the forward rate for each and every payment, it would appear that the company should lock in forward rates in C$ for all payments. Since the euro is selling forward at a greater premium against the Canadian dollar than the U.S. dollar, the resulting dollar proceeds are higher.
Problem 6.6 Crisis in the Pacific The Asian financial crisis which began in July 1997 wreaked havoc throughout the currency markets of East Asia.
a. Which of the following currencies had the largest depreciations or devaluations during the July to November period? b. Which seemingly survived the first five months of the crisis with the least impact on their currencies?
Country China Hong Kong Indonesia Korea Malaysia Philippines Singapore Taiwan Thailand
Currency yuan dollar rupiah won ringgit peso dollar dollar baht
July 1997 (per US$) 8.40 7.75 2,400 900 2.50 27 1.43 27.80 25.0
November 1997 (per US$ 8.40 7.73 3,600 1,100 3.50 34 1.60 32.70 40.0
Part a. Percentage Change vs dollar 0.0% 0.3% -33.3% -18.2% -28.6% -20.6% -10.6% -15.0% -37.5%
Part b. The Chinese yuan's value against the US dollar, as a result of the Chinese government maintaining its peg to the dollar, did not change at all during the crisis. The Thai baht, however, fell 37.5% in only five months, with the Indonesian rupiah a close second with a loss of 33.3%.
Problem 6.7 Bloomberg Currency Cross Rates Use the following cross rate table from Bloomberg to answer the following questions. Currency HKD AUD CAD CHF GBP JPY EUR USD
USD 7.7736 1.015 1.0097 0.9819 0.6328 83.735 0.7549
a. Japanese yen per US dollar? b. US dollars per Japanese yen? c. US dollars per euro? d. Euros per US dollar? e. Japanese yen per euro? f. Euros per Japanese yen? g. Canadian dollars per US dollar? h. US dollars per Canadian dollar? i. Australian dollars per US dollar? j. US dollars per Australian dollar? k. British pounds per US dollar? l. US dollars per British pound? m. US dollars per Swiss franc? n. Swiss francs per US dollar?
EUR 10.2976 1.3446 1.3376 1.3008 0.8382 110.9238 1.3247
JPY 0.0928 0.0121 0.0121 0.0117 0.0076 0.009 0.0119 Quote 83.735 0.0119 1.3247 0.7549 110.9238 0.009 1.0097 0.9904 1.015 0.9852 0.6328 1.5804 1.0184 0.9819
GBP 12.2853 1.6042 1.5958 1.5519 132.3348 1.193 1.5804 Calculated 0.0119 0.7549 0.0090 0.9904 0.9852 1.5803 0.9819
CHF 7.9165 1.0337 1.0283 0.6444 85.2751 0.7688 1.0184
CAD 7.6987 1.0053 0.9725 0.6267 82.9281 0.7476 0.9904
AUD 7.6584 0.9948 0.9674 0.6234 82.4949 0.7437 0.9852
HKD 0.1306 0.1299 0.1263 0.0814 10.7718 0.0971 0.1286
Problem 6.8 Forward Premiums on the Dollar/Euro ($/€) Use the following spot and forward bid-ask rates for the U.S. dollar/euro (US$/€) exchange rate from December 10, 2010, to answer the following questions:
Period spot 1 month 2 months 3 months 6 months 12 months 24 months
US$/€ Bid Rate 1.3231 1.3230 1.3228 1.3224 1.3215 1.3194 1.3147
US$/€ Ask Rate 1.3232 1.3231 1.3229 1.3227 1.3218 1.3198 1.3176
a. What is the mid-rate for each maturity? b. What is the annual forward premium for all maturities? c. Which maturities have the smallest and largest forward premiums? Since the exchange rate quotes are direct quotes on the dollar (US$/€), the proper forward premium calculation is: Forward premium = ( Forward - Spot ) / (Spot) x (360 / days)
Period spot 1 month 2 months 3 months 6 months 12 months 24 months
Days Forward 30 60 90 180 360 720
US$/€ Bid Rate 1.3231 1.3230 1.3228 1.3224 1.3215 1.3194 1.3147
US$/€ Ask Rate 1.3232 1.3231 1.3229 1.3227 1.3218 1.3198 1.3176
a) Calculated Mid-Rate 1.32315 1.32305 1.32285 1.32255 1.32165 1.31960 1.31615
b) Forward Premium -0.0907% -0.1360% -0.1814% -0.2267% -0.2683% -0.2645%
The forward rates progressively require less and less U.S. dollars per euro than the current spot rate. Therefore the dollar is selling forward at a premium and the euro is selling forward at a discount. c) Which maturities have the smallest and largest forward premiums? The 24 month forward rate has the smallest premium, while the 1 month forward possesses the largest premium.
Problem 6.9 Trading in Zurich Andreas Broszio just started as an analyst for Credit Suisse in Zurich, Switzerland. He receives the following quotes for Swiss francs against the dollar for spot, one-month forward, 3-months forward, and 6-months forward. Spot exchange rate: Bid rate Ask rate One-month forward 3-months forward 6-months forward
SF 1.2575/$ SF 1.2585/S 10 to 15 14 to 22 20 to 30
a. Calculate outright quotes for bid and ask, and the number of points spread between each. b. What do you notice about the spread as quotes evolve from spot toward six months? c. What is the 6-month Swiss bill rate? Assumptions Spot exchange rate: Bid rate (SF/$) Ask rate (SF/$) One-month forward 3-months forward 6-months forward
Values 1.2575 1.2585 10 to 15 14 to 22 20 to 30
a. Calculate outright quotes One-month forward 3-months forward 6-months forward
Bid 1.2585 1.2589 1.2595
b. What do you notice about the spread? It widens, most likely a result of thinner and thinner trading volume. c. Added/optional question: What is the 6-month Swiss bill rate? Spot rate, midrate (SF/$) 1.2580 Six-month forward rate, midrate (SF/$) 1.2605 Maturity (days) 180 6-month US dollar treasury rate (yield) 4.200% Solving for implied SF interest rate 6.450% Check calculation: the six-month forward 1.2719
Ask 1.2600 1.2607 1.2615
Spread 0.0015 0.0018 0.0020
Problem 6.10 Triangular Arbitrage Using the Swiss Franc The following exchange rates are available to you. (You can buy or sell at the stated rates.) Mt. Fuji Bank Mt. Rushmore Bank Mt Blanc Bank
¥92.00/$ SF1.02/$ ¥90.00/SF
Assume you have an initial SF12,000,000. Can you make a profit via triangular arbitrage? If so, show the steps and calculate the amount of profit in Swiss francs.
Assumptions Beginning funds in Swiss francs (SF) Mt. Fuji Bank (yen/$) Mt. Rushmore Bank (SF/$) Mt Blanc Bank (yen/SF) Try Number 1: Start with SF to $ Step 1: SF to $ Step 2: $ to yen Step 3: yen to SF Profit?
Try Number 2: Start with SF to yen Step 1: SF to yen Step 2: yen to $ Step 3: $ to SF Profit?
Values 12,000,000.00 92.00 1.0200 90.00
11,764,705.88 1,082,352,941.18 12,026,143.79 26,143.79 A profit.
1,080,000,000.00 11,739,130.43 11,973,913.04 (26,086.96) A loss.
Problem 6.11 Forward Premiums on the Australian Dollar Use the following spot and forward bid-ask rates for the U.S. dollar/Australian dollar (US$/A$) exchange rate from December 10, 2010, to answer the following questions
Period spot 1 month 2 months 3 months 6 months 12 months 24 months
US$/A$ Bid Rate 0.98510 0.98131 0.97745 0.97397 0.96241 0.93960 0.89770
US$/A$ Ask Rate 0.98540 0.98165 0.97786 0.97441 0.96295 0.94045 0.89900
a. What is the mid-rate for each maturity? b. What is the annual forward premium for all maturities? c. Which maturities have the smallest and largest forward premiums? Since the exchange rate quotes are direct quotes on the dollar (US$/A$), the proper forward premium calculation is: Forward premium = ( Forward - Spot ) / (Spot) x (360 / days)
Period spot 1 month 2 months 3 months 6 months 12 months 24 months
Days Forward 30 60 90 180 360 720
US$/A$ Bid Rate 0.98510 0.98131 0.97745 0.97397 0.96241 0.93960 0.89770
US$/A$ Ask Rate 0.98540 0.98165 0.97786 0.97441 0.96295 0.94045 0.89900
a. Calculated Mid-Rate 0.98525 0.98148 0.97766 0.97419 0.96268 0.94003 0.89835
b. Forward Premium -4.5917% -4.6252% -4.4902% -4.5816% -4.5902% -4.4100%
The forward rates progressively require fewer and fewer US dollars per Australian dollar than the current spot rate. Therefore the US dollar is selling forward at a premium and the Australian dollar is selling forward at a discount. c. Which maturities have the smallest and largest forward premiums? The 24 month forward rate has the largest premium, while the 2 month forward possesses the smallest premium.
Problem 6.12 Transatlantic Arbitrage A corporate treasury working out of Vienna with operations in New York simultaneously calls Citibank in New York City and Barclays in London. The two banks give the following quotes at the same time on the euro: Citibank NYC $0.7551-61/€
Barclays London $0.7545-75/€
Using $1 million or its euro equivalent, show how the corporate treasury could make geographic arbitrage profit with the two different exchange rate quotes.
Assumptions Beginning funds
$
Citibank NYC quotes: Bid ($/€) Ask ($/€) Barclays London quotes: Bid ($/€) Ask ($/€) Arbitrage Strategy #1 Initial investment Buy euros from Barclays (at the ask rate) Sell euros to Citibank (at the bid rate) Arbitrage profit (loss) Arbitrage Strategy #2 Initial investment Buy euros from Citibank (at the ask rate) Sell euros to Barclays (at the bid rate) Arbitrage profit (loss) The arbitrager cannot make a profit using these quotes.
Values 1,000,000.00
0.7551 0.7561 0.7545 0.7575
$ $ $
$ $ $
1,000,000.00 € 1,320,132.01 996,831.68 (3,168.32)
1,000,000.00 € 1,322,576.38 997,883.88 (2,116.12)
Problem 6.13 Venezuelan Bolivar (A) The Venezuelan government officially floated the Venezuelan bolivar (Bs) in February of 2002. Within weeks, its value had moved from the pre-float fix of BS778/$ to Bs1025/$. a. Is this a devaluation or depreciation? b. By what percentage did its value change? Assumptions Fixed rate of exchange, Bs/$ New freely floating rate (2 weeks later), Bs/$
Values 778 1,025
a. Is this a devaluation or depreciation? This is a case in which a government has changed its currency from a governmentally determined fixed rate, to a regime in which the currency is allowed to change in value based on supply and demand forces in the market. As a result of the move, the currency's value in this case was a "depreciation" against the U.S. dollar. b. By what percentage did its value change? Percentage devaluation is: % Chg = (S1 - S2) / (S2)
Devaluation then Depreciation
-24.10%
Problem 6.14 Venezuelan Bolivar (B) The Venezuelan political and economic crisis deepened in late 2002 and early 2003. On January 1st, 2003, the bolivar was trading at Bs1400/$. By February 1st, its value had fallen to Bs1950/$. Many currency analysts and forecasters were predicting that the bolivar would fall an additional 40% from its February 1st value by early summer 2003. a. What was the percentage change in January? b. Forecast value for June 2003? Assumptions Exchange rate, January 1, 2003 (Bs/$) Exchange rate, February 1, 2003 (Bs/$) Forecast fall in value from Feb 1 to early summer, 2003
Values 1,400 1,950 -40.0%
a) What was the percentage change in January? % chg = (S1 - S2)/(S2)
-28.21%
b) Forecast value for June 2003? We are actually solving the equation for S2 (Bs/$) S2 = (S1)/(1+%chg) = (1950)/(1-.40)
3,250
Problem 6.15 Indirect Quotation on the Dollar Calculate the forward premium on the dollar (the dollar is the home currency) if the spot rate is €1.3300/$ and the 3-month forward rate is €1.3400/$.
Assumptions Days forward European euro (€ per $)
Quoted Spot rate € 1.3300
90-day Forward rate 90 € 1.3400
Percent premium or discount on euro
Calculation formula for the indirect quote on the dollar: Percent premium = (S-F)/(F) x (360/90)
-2.9851%
The euro would be selling forward at a premium against the dollar, or equivalently, the dollar selling forward against the euro at a discount. In a way, the terminology is a bit tricky. One might say that the "forward premium is a premium." Check calculation One way to check percentage change calculations is to invert each of the currency quotes (1/(€/$)), and recalculate the quote using the direct quotation formula. European euro ($ per €) Percent discount = (F-S)/(S) x (360/90)
$0.7519
$0.7463 -2.9851%
Problem 6.16 Direct Quotation on the Dollar Calculate the forward discount on the dollar (the dollar is the home currency) if the spot rate is $1.5800/£ and the 6-month forward rate is $1.5550/£
Assumptions Days forward Exchange rate, US$/£
Quoted Spot rate $
1.5800
$
180-day Forward rate 180 1.5550
Percent premium or discount
Calculation formula for the direct quote on the dollar: Percent premium = ( Forward - Spot ) / ( Spot ) x ( 360 / 180 )
-3.1646%
The forward rate requires fewer US dollars in exchange for pounds than the current spot rate. The dollar is therefore selling forward at a premium against the pound (and the pound is simultaneously selling forward at a discount versus the US dollar). Check calculation Inverting the quotes (£/US$)
£0.6329
Percent forward premium = ( Spot - Forward ) / ( Forward ) x ( 360 / 180 )
£0.6431 -3.1646%
Problem 6.17 Mexican Peso - European Euro Cross Rate Calculate the cross rate between the Mexican peso (Ps) and the euro (€ ) from the following two spot rates: Ps12.45/$ and € 0.7550/$. Assumptions Mexican peso, pesos/dollar (Ps/$) European euro, euros/dollar (€/$) Calculated cross rate, pesos/euro pesos/euro = (Ps/$) / (€/$) or equivalently, euros/peso (€/Ps)
Exchange rate 12.45 0.7550 16.4901
0.0606
Problem 6.18 Pura Vida Calculate the cross rate between the Costa Rican colón (₡) and the Canadian dollar (C$ ) from the following two spot rates: ₡500.29/$ and C$1.02/$. Assumptions Costa Rican colón, colónes/dollar (₡/$) Canadian dollar, Canadian dollars/dollar (C$/$) Calculated cross rate, pesos/euro Colónes/Canadian dollar = (₡/$) / (C$/$) or equivalently, Canadian dollars/colón (C$/₡)
Exchange rate 500.29 1.0200 490.4804
0.0020
Problem 6.19 Around the Horn Around the horn. Assuming the following quotes, calculate how a market trader at Citibank with $1,000,000 can make an intermarket arbitrage profit.: Citibank quotes U.S. dollar per pound: National Westminster quotes euros per pound: Deutschebank quotes U.S. dollar per euro: Assumptions Citibank quote: US$/pound ($/£) National Westminster quote: euros/pound (€/£) Deutschebank quote: US$/euro ($/€) Initial investment Path #1: US$ to euros to pounds to US$ Start with US$ Convert to euros at Deutschebank quote Convert euros to pounds at NatWest quote Convert pounds to US$ at Citibank quote Arbitrage gain (loss) Path #2: US$ to pounds to euros to US$ Start with US$ Convert to pounds at Citibank quote Convert pounds to euros at NatWest quote Convert euros to US$ at Deutschebank quote Arbitrage gain (loss) Triangular arbitrage path #1 yields a positive profit.
$1.5900/£ €1.2000/£ $0.7550/€
$
$
$ $
$
$ $
Exchange rate 1.5900 1.2000 0.7550 1,000,000.00
1,000,000.00 € 1,324,503.31 £1,103,752.76 1,754,966.89 754,966.89
1,000,000.00 £628,930.82 € 754,716.98 569,811.32 (430,188.68)
Problem 6.20 Great Pyramids Inspired by his recent trip to the Great Pyramids, Citibank trader Ruminder Dhillon wonders if he can make an intermarket arbitrage profit using Libyan dinars and Saudi riyals. He has $1,000,000 to work with, so he gathers the following quotes: Citibank quotes U.S. dollar per Libyan dinar: National Bank of Kuwait quotes Saudi riyal per Libyan dinar: Barclay quotes U.S. dollar per Saudi riyal: Assumptions Citibank quote: US$/dinar ($/LYD) National Bank of Kuwait quote: riyal per dinar (SAR/LYD) Barclay quote: US$/riyal ($/SAR) Initial investment Path #1: US$ to riyals to dinars to US$ Start with US$ Convert to riyals at Barclay quote Convert riyals to dinars at NatBank of Kuwait quote Convert dinars to US$ at Citibank quote Arbitrage gain (loss) Path #2: US$ to dinars to riyals to US$ Start with US$ Convert to dinars at Citibank quote Convert dinars to riyals at NatBank of Kuwait quote Convert riyals to US$ at Barclay quote Arbitrage gain (loss) Triangular arbitrage path #1 yields a positive profit.
$1.9324/LYD SAR 1.9405/LYD $0.2667/SAR
$
$
$ $
$
$ $
Exchange rate 1.9324 1.9405 0.2667 1,000,000.00
1,000,000.00 SAR 3,749,953.13 LYD 1,932,467.47 3,734,300.14 2,734,300.14
1,000,000.00 LYD 517,491.20 SAR 1,004,191.68 267,787.79 (732,212.21)
