Spot rate on the GTQ/€ cross rate GTQ 10.5799/€
Spot rate on the €/reais cross rate €0.4462/R$
Assumptions Values
Amount of reais from parents 4,500.00
Spot rate (R$/€) 10.5799
Spot rate (€/GTQ) 0.4462
a. What is the R$/GTQ cross rate?
Cross rate (R$/GTQ) 4.72
Reais/GTQ = R$/€ x €/GTQ
b. How many quetzals will he get for his reais?
Converting your reais into quetzals 21,243
Problem 5.1 Isaac Díez
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$4,500. Isaac wants to exchange it to Guatemlan
quetzals (GTQ). He collects the following rates:
a. What is the Brazilian reais/Guatemalan quetzal cross rate?
b. How many quetzals will Isaac get for his reais?
Days
Period Forward C$/euro US$/euro
spot 1.3360 1.3221
1 month 30 1.3368 1.3230
2 months 60 1.3376 1.3228
3 months 90 1.3382 1.3224
6 months 180 1.3406 1.3215
12 months 360 1.3462 1.3194
Days Forward Premium C$ Proceeds of Difference
Period Forward C$/euro on the C$/euro € 12,000.00 Over Spot
spot 1.3360 16,032.00 –
1 month 30 1.3368 0.722% 16,041.65 $9.65
2 months 60 1.3376 0.705% 16,050.84 $18.84
3 months 90 1.3382 0.659% 16,058.41 $26.41
6 months 180 1.3406 0.693% 16,087.54 $55.54
12 months 360 1.3462 0.765% 16,154.69 $122.69
Days Forward Premium US$ Proceeds of Difference
Period Forward US$/euro on the US$/euro € 12,000.00 Over Spot
spot 1.3221 $15,865.20 –
1 month 30 1.3230 0.817% $15,876.00 $10.80
2 months 60 1.3228 0.318% $15,873.60 $8.40
3 months 90 1.3224 0.091% $15,868.80 $3.60
6 months 180 1.3215 -0.091% $15,858.00 ($7.20)
12 months 360 1.3194 -0.204% $15,832.80 ($32.40)
Period
C$/€US$/€
spot 1.3830 1.4389
1 month 1.3840 1.4440
2 months 1.3844 1.4400
3 months 1.3850 1.4403
Problem 5.2 Victoria Exports
The Canadian exporter will be receiving six payments of 12,000 euros, ranging from now to 12 months in the future. Since the
company keeps cash balances in both Canadian dollars and US dollars, it can choose which currency to change the euros to at the end
of the various periods. And since the company wishes to lock in the forward rate for each and every payment, it would appear that the
company should lock in forward rates in C$ 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.
A Canadian exporter, Victoria 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
¥/$
Bid Rate ¥/$
Ask Rate
spot 85.41 85.46
1 month 85.02 85.05
2 months 84.86 84.90
3 months 84.37 84.42
6 months 83.17 83.20
12 months 82.87 82.91
24 months 81.79 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 (¥/$), the proper forward premium calculation is:
Forward premium = ( Spot – Forward ) / (Forward) x (360 / days)
a. b.
¥/$ ¥/$ Calculated Forward
Period Days Forward Bid Rate Ask Rate Mid-Rate Premium
spot 85.41 85.46 85.43500
1 month 30 85.02 85.05 85.03500 5.6447%
2 months 60 84.86 84.90 84.88000 3.9232%
3 months 90 84.37 84.42 84.39500 4.9292%
6 months 180 83.17 83.20 83.18500 5.4096%
12 months 360 82.87 82.91 82.89000 3.0703%
24 months 720 81.79 81.82 81.80500 2.2187%
¥/$ ¥/$
Period Bid Rate Ask Rate
spot 114.23 114.27
1 month 113.82 113.87
2 months 113.49 113.52
The 24 month forward rate has the smallest premium, while the 1 month forward possesses the largest premium.
Problem 5.3 Yen Forward
Use the following spot and forward bid-ask rates for the Japanese yen/U.S. dollar (¥/$) exchange rate from September 16, 2010, to
answer the following questions:
The forward rates progressively require fewer and fewer Japanese yen per dollar than the current spot rate. Therefore the yen is
selling forward at a premium and the dollar is selling forward at a discount.
c. Which maturities have the smallest and largest forward premiums?
Spot exchange rate:
Bid rate SF 1.2575/$
Ask rate SF 1.2585/S
One-month forward 10 to 15
3-months forward 14 to 22
6-months forward 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 Values
Spot exchange rate:
Bid rate (SF/$) 1.2575
Ask rate (SF/$) 1.2585
One-month forward 10 to 15
3-months forward 14 to 22
6-months forward 20 to 30
a. Calculate outright quotes Bid Ask Spread
One-month forward 1.2585 1.2600 0.0015
3-months forward 1.2589 1.2607 0.0018
6-months forward 1.2595 1.2615 0.0020
b. What do you notice about the spread?
It widens, most likely a result of thinner and thinner trading volume.
Solving for implied SF interest rate 6.450%
Check calculation: the six-month forward 1.2719
Problem 5.4 Credit Suissse Geneva
Andreas Broszio just started as an analyst for Credit Suisse in Geneva, 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 rate on the dollar/euro cross rate $1.3214/€
Spot rate on the ruble/dollar cross rate Rbl 30.96/$
Assumptions Values
Beginning your trip with euros 15,000.00
Spot rate ($/€)1.3214
Spot rate (Rubles/$) 30.96
a) What is the Russian ruble/euro cross rate?
Cross rate (Rubles/€)40.91
Rubles/ € = Rubles/$ x $/ €
b) How many rubles will you obtain for your euros?
Converting your euros into Rubles 613,658
Problem 5.5 Munich to Moscow
On your post-graduation celebratory trip you decide to travel from Munich,
Germany to Moscow, Russia. You leave Munich with 15,000 euros in your wallet.
Wanting to exchange all of these for Russian rubles, you obtain the following
quotes:
a. What is the Russian ruble/euro cross rate?
b. How many rubles will you obtain for your euros?
Spot rate on the rubles/dollar cross rate Rbl 30.96/$
Spot rate on the yen/dollar cross rate ¥84.02/$
Assumptions Values
Beginning your trip with rubles 450,000.00
Spot rate (Rubles/$) 30.96
Spot rate (¥/$) 84.02
a) What is the Russian ruble/yen cross rate?
Cross rate (Rubles/¥)0.3685
Rubles/¥ = Rubles/$ ÷ ¥/$
b) How many yen will you obtain for your rubles?
Converting your Rubles into yen 1,221,177
a. What is the Russian ruble/yen cross rate?
b. How many yen will you obtain for your rubles?
Problem 5.6 Moscow to Tokyo
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
Tokyo 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:
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?
Part a.
July 1997 November 1997 Percentage
Country Currency (per US$) (per US$ Change vs dollar
China yuan 8.40 8.40 0.0%
Hong Kong dollar 7.75 7.73 0.3%
Indonesia rupiah 2,400 3,600 -33.3%
Korea won 900 1,100 -18.2%
Malaysia ringgit 2.50 3.50 -28.6%
Philippines peso 27 34 -20.6%
Singapore dollar 1.43 1.60 -10.6%
Taiwan dollar 27.80 32.70 -15.0%
Thailand baht 25.0 40.0 -37.5%
Part b.
Problem 5.7 Asian Pacific Crisis
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%.
Use the following cross rate table from Bloomberg to answer the following questions.
Currency USD EUR JPY GBP CHF CAD AUD HKD
AUD 1.0903 1.5684 0.0096 2.2375 0.9364 1.1327 0.1407
Currency USD EUR JPY GBP CHF CAD AUD HKD CAD 0.9626 1.3847 0.0084 1.9754 0.8267 0.8829 0.1242
HKD 7.7736 10.2976 0.0928 12.2853 7.9165 7.6987 7.6584 CHF 1.1644 1.675 0.0102 2.3896 1.2097 1.068 0.1502
AUD 1.015 1.3446 0.0121 1.6042 1.0337 1.0053 0.1306 GBP 0.4873 0.701 0.0043 0.4185 0.5062 0.4469 0.0629
CAD 1.0097 1.3376 0.0121 1.5958 1.0283 0.9948 0.1299 JPY 114.156 164.2134 234.2687 98.0368 118.5913 104.7005 14.7282
CHF 0.9819 1.3008 0.0117 1.5519 0.9725 0.9674 0.1263 EUR 0.6952 0.0061 1.4266 0.597 0.7222 0.6376 0.0897
GBP 0.6328 0.8382 0.0076 0.6444 0.6267 0.6234 0.0814 USD 1.4385 0.0088 2.0522 0.8588 1.0389 0.9172 0.129
JPY 83.735 110.9238 132.3348 85.2751 82.9281 82.4949 10.7718
EUR 0.7549 0.009 1.193 0.7688 0.7476 0.7437 0.0971
USD 1.3247 0.0119 1.5804 1.0184 0.9904 0.9852 0.1286
Quote Calculated
a. Japanese yen per US dollar?
83.735
b. US dollars per Japanese yen? 0.0119 0.0119
c. US dollars per euro? 1.3247
d. Euros per US dollar? 0.7549 0.7549
e. Japanese yen per euro? 110.9238
f. Euros per Japanese yen? 0.009 0.0090
g. Canadian dollars per US dollar? 1.0097
h. US dollars per Canadian dollar? 0.9904 0.9904
i. Australian dollars per US dollar? 1.015
j. US dollars per Australian dollar? 0.9852 0.9852
k. British pounds per US dollar? 0.6328
l. US dollars per British pound?
1.5804 1.5803
m. US dollars per Swiss franc? 1.0184
n. Swiss francs per US dollar? 0.9819 0.9819
Problem 5.8 Bloomberg Currency Cross Rates
US$/€US$/€
Period Bid Rate Ask Rate
spot 1.3231 1.3232
1 month 1.3230 1.3231
2 months 1.3228 1.3229
3 months 1.3224 1.3227
6 months 1.3215 1.3218
12 months 1.3194 1.3198
24 months 1.3147 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$/€), the proper forward premium calculation is:
Forward premium = ( Forward – Spot ) / (Spot) x (360 / days)
a) b)
US$/€US$/€Calculated Forward
Period Days Forward Bid Rate Ask Rate Mid-Rate Premium
spot 1.3231 1.3232 1.32315
1 month 30 1.3230 1.3231 1.32305 -0.0907%
2 months 60 1.3228 1.3229 1.32285 -0.1360%
3 months 90 1.3224 1.3227 1.32255 -0.1814%
6 months 180 1.3215 1.3218 1.32165 -0.2267%
12 months 360 1.3194 1.3198 1.31960 -0.2683%
24 months 720 1.3147 1.3176 1.31615 -0.2645%
$/€$/€
Period Bid Rate Ask Rate
spot 1.4389 1.4403
1 month 1.4440 1.4410
2 months 1.4400 1.4415
3 months 1.4403 1.4418
6 months 1.4407 1.4422
12 months 1.4408 1.4424
24 months 1.4417 1.4436
The 1 month forward rate as the smallest premium, while the 12 month forward possesses the largest premium.
Problem 5.9 Dollar/Euro Forwards
Use the following spot and forward bid-ask rates for the U.S. dollar/euro (US$/€) exchange rate from December 10, 2010, to
answer the following questions:
The forward rates progressively require less and less U.S. dollars per euro than the current spot rate. Therefore the dollar is selling
forward at a premium and the euro is selling forward at a discount.
c) Which maturities have the smallest and largest forward premiums?
Mt. Fuji Bank ¥92.00/$
Mt. Rushmore Bank SF1.02/$
Mt Blanc Bank ¥90.00/SF
Assumptions Values
Beginning funds in Swiss francs (SF) 12,000,000.00
Mt. Fuji Bank (yen/$) 92.00
Mt. Rushmore Bank (SF/$) 1.0200
Matterhorn Bank (yen/SF) 90.00
Try Number 1: Start with SF to $
Step 1: SF to $ 11,764,705.88
Step 2: $ to yen 1,082,352,941.18
Step 3: yen to SF 12,026,143.79
Profit? 26,143.79 A profit.
Try Number 2: Start with SF to yen
Step 1: SF to yen 1,080,000,000.00
Step 2: yen to $ 11,739,130.43
Step 3: $ to SF 11,973,913.04
Profit? (26,086.96) A loss.
Problem 5.10 Swissie Triangular Arbitrage
The following exchange rates are available to you. (You can buy or sell at the stated rates.)
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 (Swissies).
US$/A$ US$/A$
Period Bid Rate Ask Rate
spot 0.98510 0.98540
1 month 0.98131 0.98165
2 months 0.97745 0.97786
3 months 0.97397 0.97441
6 months 0.96241 0.96295
12 months 0.93960 0.94045
24 months 0.89770 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) a. b.
US$/A$ US$/A$ Calculated Forward
Period Days Forward Bid Rate Ask Rate Mid-Rate Premium
spot 0.98510 0.98540 0.98525
1 month 30 0.98131 0.98165 0.98148 –4.5917%
2 months 60 0.97745 0.97786 0.97766 -4.6252%
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.
The 24 month forward rate has the largest premium, while the 2 month forward possesses the smallest premium.
Problem 5.11 Aussie Dollar Forward
Use the following spot and forward bid-ask rates for the U.S. dollar/Australian dollar (US$=A$1.00) exchange rate from
December 10, 2010, to answer the following questions
c. Which maturities have the smallest and largest forward premiums?
Assumptions Values
Beginning funds 1,000,000.00$
Citibank NYC quotes:
Bid ($/€)0.7551
Ask ($/€)0.7561
Barclays London quotes:
Bid ($/€)0.7545
Ask ($/€)0.7575
Arbitrage Strategy #1
Initial investment 1,000,000.00$
Buy euros from Barclays (at the ask rate) € 1,320,132.01
Sell euros to Citibank (at the bid rate) 996,831.68$
Arbitrage profit (loss) (3,168.32)$
Arbitrage Strategy #2
Initial investment 1,000,000.00$
Buy euros from Citibank (at the ask rate) € 1,322,576.38
Problem 5.12 Transatlantic Arbitrage
Using $1 million or its euro equivalent, show how the corporate treasury could make
geographic arbitrage profit with the two different exchange rate quotes.
Citibank NYC Barclays London
$0.7551-61/€ $0.7545-75/€
A corporate treasury working out of Vienna with operations in New York
simultaneously calls Citibank in New York City and Barclays in London. The two
banks give the following quotes at the same time on the euro:
a. Is this a devaluation or depreciation?
b. By what percentage did its value change?
Assumptions Values
Fixed rate of exchange, Bs/$ 778
New freely floating rate (2 weeks later), Bs/$ 1,025
a. Is this a devaluation or depreciation? Devaluation
then
Depreciation
b. By what percentage did its value change?
Percentage devaluation is: -24.10%
% Chg = (S1 – S2) / (S2)
Problem 5.13 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/$.
This is a case in which a government has changed its currency from a
governmentally determined fixed rate, to a regime in which the currency
is allowed to change in value based on supply and demand forces in the
market. As a result of the move, the currency‘s value in this case was a
“depreciation” against the U.S. dollar.
a. What was the percentage change in January?
b. Forecast value for June 2003?
Assumptions Values
Exchange rate, January 1, 2003 (Bs/$) 1,400
Exchange rate, February 1, 2003 (Bs/$) 1,950
Forecast fall in value from Feb 1 to early summer, 2003 -40.0%
a) What was the percentage change in January?
% chg = (S1 – S2)/(S2) -28.21%
b) Forecast value for June 2003?
We are actually solving the equation for S2 (Bs/$)
S2 = (S1)/(1+%chg) = (1950)/(1-.40) 3,250
Problem 5.14 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.
Quoted 90-day Percent premium
Assumptions Spot rate Forward rate or discount on euro
Days forward 90
European euro (€ per $) € 1.3300 € 1.3400
Calculation formula for the forward premium on the dollar using indirect quotes:
Forward premium (indirect quotes) = (F-S) / (S) x (360/90) 3.0075%
In this case, “at a premium” is shown by a positive percentage difference.
Check calculation
European euro ($ per €) $0.7519 $0.7463
Forward premium (direct quotes) = (S-F) / (F) x (360/90) 3.0075%
Problem 5.15 Indirect Forward Premium on the Dollar
Calculate the forward premium on the dollar (the dollar is the home currency) if the spot rate is €1.3300/$ and the 3-
month forward rate is €1.3400/$.
The U.S. dollar would be said to be selling forward at a premium against the euro, or equivalently, the euro selling
forward at a discount against the dollar.
One way to check percentage change calculations is to invert each of the currency quotes (1/(€/$)), and recalculate
the forward premium using the direct quotation premium formula.
Quoted 180-day Percent premium
Assumptions Spot rate Forward rate or discount
Days forward 180
Exchange rate, US$/£1.5800$ 1.5550$
Calculation formula for the direct quote on the dollar:
Percent premium = ( Forward – Spot ) / ( Spot ) x ( 360 / 180 )
-3.1646%
Check calculation
Inverting the quotes (£/US$) £0.6329 £0.6431
Percent forward premium = ( Spot – Forward ) / ( Forward ) x ( 360 / 180 )
-3.1646%
Problem 5.16 Direct on the Dollar
Calculate the forward discount on the dollar (the dollar is the home currency) if the spot rate is spot rate is $1.5800/£ and
the 6-month forward rate is $1.5550/£
The forward rate requires fewer US dollars in exchange for pounds than the current spot rate. The dollar is therefore
selling forward at a premium against the pound (and the pound is simultaneously selling forward at a discount versus the
US dollar).
Assumptions Exchange rate
Mexican peso, pesos/dollar (Ps/$) 12.45
European euro, euros/dollar (€/$) 0.7550
Calculated cross rate, pesos/euro 16.4901
pesos/euro = (Ps/$) / (€/$)
or equivalently, euros/peso (€/Ps) 0.0606
Problem 5.17 Mexican Peso – European Euro Cross Rate
Calculate the cross rate between the Mexican peso (Ps) and the euro (€ ) from the
following two spot rates: Ps12.45/$ and € 0.7550/$.
Assumptions Exchange rate
Costa Rican colón, colónes/dollar (₡/$) 500.29
Canadian dollar, Canadian dollars/dollar (C$/$) 1.0200
Calculated cross rate, pesos/euro 490.4804
Colónes/Canadian dollar = (₡/$) / (C$/$)
or equivalently, Canadian dollars/colón (C$/₡) 0.0020
Problem 5.18 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$1.02/$.
Citibank quotes U.S. dollar per pound: $1.5900/£
National Westminster quotes euros per pound: €1.2000/£
Deutschebank quotes U.S. dollar per euro: $0.7550/€
Assumptions Exchange rate
Citibank quote: US$/pound ($/£) 1.5900
National Westminster quote: euros/pound (€/£)1.2000
Deutschebank quote: US$/euro ($/€)0.7550
Initial investment 1,000,000.00$
Path #1: US$ to euros to pounds to US$
Start with US$ 1,000,000.00$
Convert to euros at Deutschebank quote € 1,324,503.31
Convert euros to pounds at NatWest quote £1,103,752.76
Convert pounds to US$ at Citibank quote 1,754,966.89$
Arbitrage gain (loss) 754,966.89$
Path #2: US$ to pounds to euros to US$
Start with US$ 1,000,000.00$
Convert to pounds at Citibank quote £628,930.82
Convert pounds to euros at NatWest quote € 754,716.98
Convert euros to US$ at Deutschebank quote 569,811.32$
Arbitrage gain (loss) (430,188.68)$
Triangular arbitrage path #1 yields a positive profit.
Problem 5.19 Around the Horn
Around the horn. Assuming the following quotes, calculate how a market trader at Citibank
with $1,000,000 can make an intermarket arbitrage profit.:
Citibank quotes U.S. dollar per Libyan dinar: USD1.9324 = LYD1.00
National Bank of Kuwait quotes Saudi riyal per Libyan dinar: SAR 1.9405 = LYD1.00
Barclay quotes U.S. dollar per Saudi riyal: USD0.2667 = SAR1.00
Assumptions Exchange rate
Citibank quote: US$/dinar ($/LYD) 1.9324
National Bank of Kuwait quote: riyal per dinar (SAR/LYD) 1.9405
Barclay quote: US$/riyal ($/SAR) 0.2667
Initial investment 1,000,000.00$
Path #1: US$ to riyals to dinars to US$
Start with US$ 1,000,000.00$
Convert to riyals at Barclay quote SAR 3,749,953.13
Convert riyals to dinars at NatBank of Kuwait quote LYD 1,932,467.47
Convert dinars to US$ at Citibank quote 3,734,300.14$
Arbitrage gain (loss) 2,734,300.14$
Path #2: US$ to dinars to riyals to US$
Start with US$ 1,000,000.00$
Convert to dinars at Citibank quote LYD 517,491.20
Convert dinars to riyals at NatBank of Kuwait quote SAR 1,004,191.68
Convert riyals to US$ at Barclay quote 267,787.79$
Arbitrage gain (loss) (732,212.21)$
Triangular arbitrage path #1 yields a positive profit.
Problem 5.20 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: