Spot rate on the GTQ/€ cross rate GTQ 10.5799/€
Spot rate on the €/reais cross rate €0.4462/R$
Assumptions Values
a. What is the R$/GTQ cross rate?
b. How many quetzals will he get for his reais?
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$/euro
spot 1.3360 1.3221
company should lock in forward rates in C$ 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.
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 –
Days Forward Premium US$ Proceeds of Difference
Period Forward US$/euro on the US$/euro € 12,000.00 Over Spot
spot 1.3221 $15,865.20 –
Problem 5.2 Victoria Exports
A Canadian exporter, Victoria Exports, will be receiving six payments of €12,000, ranging from now to 12 months in the future. Since
the company keeps cash balances in both Canadian dollars and U.S. dollars, it can choose which currency to change the euros to at the
end of the various periods. Which currency appears to offer the better rates in the forward market?
Period
¥/$
Bid Rate ¥/$
Ask Rate
spot 85.41 85.46
1 month 85.02 85.05
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 (¥/$), the proper forward premium calculation is:
a. b.
¥/$ ¥/$ Calculated Forward
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.
Period Days Forward Bid Rate Ask Rate Mid-Rate Premium
spot 85.41 85.46 85.43500
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 (¥/$) exchange rate from September 16,
2010, to answer the following questions:
c. Which maturities have the smallest and largest forward premiums?
Spot exchange rate:
a. Calculate outright quotes for bid and ask, and the number of points spread between each.
b. What do you notice about the spread as quotes evolve from spot toward six months?
c. What is the 6-month Swiss bill rate?
Assumptions Values
Spot exchange rate:
a. Calculate outright quotes Bid Ask Spread
One-month forward 1.2585 1.2600 0.0015
b. What do you notice about the spread?
It widens, most likely a result of thinner and thinner trading volume.
c. Added/optional question: What is the 6-month Swiss bill rate?
Spot rate, midrate (SF/$) 1.2580
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
a) What is the Russian ruble/euro cross rate?
b) How many rubles will you obtain for your euros?
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
a) What is the Russian ruble/yen cross rate?
b) How many yen will you obtain for your rubles?
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%
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
HKD 7.7736 10.2976 0.0928 12.2853 7.9165 7.6987 7.6584
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
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
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$/€), the proper forward premium calculation is:
a) b)
US$/€US$/€Calculated Forward
selling forward at a premium and the euro is selling forward at a discount.
Period Days Forward Bid Rate Ask Rate Mid-Rate Premium
spot 1.3231 1.3232 1.32315
1 month 30 1.3230 1.3231 1.32305 -0.0907%
Problem 5.9 Dollar/Euro Forwards
Use the following spot and forward bid-ask rates for the U.S. dollar/euro (US$/€) exchange rate from December 10, 2010, to
answer the following questions:
c) Which maturities have the smallest and largest forward premiums?
Mt. Fuji Bank ¥92.00/$
Assumptions Values
Beginning funds in Swiss francs (SF) 12,000,000.00
Try Number 1: Start with SF to $
Step 1: SF to $ 11,764,705.88
Step 2: $ to yen 1,082,352,941.18
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?
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$1.00) exchange rate from
December 10, 2010, to answer the following questions
c. Which maturities have the smallest and largest forward premiums?
The forward rates progressively require fewer and fewer US dollars per Australian dollar than the current spot rate. Therefore
the US dollar is selling forward at a premium and the Australian dollar is selling forward at a discount.
Assumptions Values
Beginning funds 1,000,000.00$
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)$
Problem 5.12 Transatlantic Arbitrage
Citibank NYC Barclays London
$0.7551-61/€ $0.7545-75/€
A corporate treasury working out of Vienna with operations in New York
simultaneously calls Citibank in New York City and Barclays in London. The two
banks give the following quotes at the same time on the euro:
market. As a result of the move, the currency‘s value in this case was a
“depreciation” against the U.S. dollar.
a. Is this a devaluation or depreciation?
b. By what percentage did its value change?
Assumptions Values
a. Is this a devaluation or depreciation? Devaluation
then
b. By what percentage did its value change?
Problem 5.13 Venezuelan Bolivar (A)
The Venezuelan government officially floated the Venezuelan bolivar (Bs) in February of 2002.
Within weeks, its value had moved from the pre-float fix of BS778/$ to Bs1025/$.
This is a case in which a government has changed its currency from a
a. What was the percentage change in January?
b. Forecast value for June 2003?
Assumptions Values
Exchange rate, January 1, 2003 (Bs/$) 1,400
a) What was the percentage change in January?
b) Forecast value for June 2003?
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
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/$.
Check calculation
European euro ($ per €) $0.7519 $0.7463
Quoted 180-day Percent premium
Assumptions Spot rate Forward rate or discount
Days forward 180
Exchange rate, US$/£1.5800$ 1.5550$
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 $1.5550/£
Inverting the quotes (£/US$) £0.6329 £0.6431
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/$) 12.45
Problem 5.17 Mexican Peso – European Euro Cross Rate
Calculate the cross rate between the Mexican peso (Ps) and the euro (€ ) from the
following two spot rates: Ps12.45/$ and € 0.7550/$.
Assumptions Exchange rate
Costa Rican colón, colónes/dollar (₡/$) 500.29
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: $1.5900/£
Assumptions Exchange rate
Citibank quote: US$/pound ($/£) 1.5900
Path #1: US$ to euros to pounds to US$
Start with US$ 1,000,000.00$
Convert to euros at Deutschebank quote € 1,324,503.31
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
Problem 5.19 Around the Horn
Around the horn. Assuming the following quotes, calculate how a market trader at Citibank
with $1,000,000 can make an intermarket arbitrage profit.:
Citibank quotes U.S. dollar per Libyan dinar: USD1.9324 = LYD1.00
Assumptions Exchange rate
Citibank quote: US$/dinar ($/LYD) 1.9324
Path #1: US$ to riyals to dinars to US$
Start with US$ 1,000,000.00$
Convert to riyals at Barclay quote SAR 3,749,953.13
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
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: