Chapter 6 The Foreign Exchange Market 1
Chapter 6
Ringgit appreciation or depreciation?
Assumptions / Values
Malaysian ringgit, before the crisis (RM/$) / 2.7000
Malaysian ringgit, after the crisis (RM/$) / 3.8000
Calculation percentage appreciation or depreciation
Percentage change in the ringgitt / –28.95%
Because the ringgit fell in value: / Depreciation
Chapter 6 The Foreign Exchange Market 1
Problem 6.2 Forward premiums and discountsOn June 28, 2004, the following bid-ask outright rates were quoted on the US dollar/euro (US$/€) rate:
a) / b)
Calculated / Forward
Period / Days Forward / Bid Rate / Ask Rate / Mid-Rate / Premium
spot / 1.21810 / 1.21920 / 1.21865
1 month / 30 / 1.21732 / 1.21841 / 1.21787 / –0.7730%
2 months / 60 / 1.21679 / 1.21789 / 1.21734 / –0.6450%
3 months / 90 / 1.21648 / 1.21758 / 1.21703 / –0.5317%
6 months / 180 / 1.21617 / 1.21774 / 1.21696 / –0.2782%
12 months / 360 / 1.21804 / 1.21876 / 1.21840 / –0.0205%
24 months / 720 / 1.21021 / 1.20982 / 1.21002 / –0.3543%
a) Calculate the mid-rates from the bid-ask rate quotes.
b) Calculate the forward premium on the different maturities using the mid-rates from part a).
Note that because the dollar/euro exchange rate is in American terms ($/€), the proper forward premium calculation is: (F – S)/(S) (360/t)
Chapter 6 The Foreign Exchange Market 1
Problem 6.3 Trading in SwitzerlandCalculate the outright quotes
Assumptions / Values
Spot exchange rate:
Bid rate (SF/$) / 1.6075
Ask rate (SF/$ / 1.6085
One-month forward / 10 to 15
3-months forward / 14 to 22
6-months forward / 20 to 30
a) Calculate outright quotes / Bid / Ask
One-month forward / 1.6085 / 1.6100
3-months forward / 1.6089 / 1.6107
6-months forward / 1.6275 / 1.6115
b) What do you notice about the spread?
It widens, most likely a result of thinner and thinner trading volume.
c) What is the 6-month Swiss bill rate?
Spot rate, midrate (SF/$) / 1.6080
Six-month forward rate, midrate (SF/$) / 1.6195
Maturity (days) / 180
6-month US dollar treasury rate (yield) / 5.000%
Solving for implied SF interest rate / 6.450%
Check calculation: the six-month forward / 1.6194
Chapter 6 The Foreign Exchange Market 1
Problem 6.4 Yen forward premiumsOn June 28, 2004, the following bid-ask outright rates were quoted on the Japanese yen/US dollar (¥/$) rate:
a) / b)
Calculated / Forward
Period / Days Forward / Bid Rate / Ask Rate / Mid-Rate / Premium
spot / 107.970 / 108.020 / 107.995
1 month / 30 / 107.816 / 107.911 / 107.864 / 1.463%
2 months / 60 / 107.670 / 107.765 / 107.718 / 1.546%
3 months / 90 / 107.494 / 107.609 / 107.552 / 1.649%
6 months / 180 / 106.863 / 106.987 / 106.925 / 2.001%
12 months / 360 / 105.391 / 105.444 / 105.418 / 2.445%
24 months / 720 / 101.435 / 101.976 / 101.706 / 3.092%
a) Calculate the mid-rates from the bid-ask rate quotes.
b) Calculate the forward premium on the different maturities using the mid-rates from part a).
Chapter 6 The Foreign Exchange Market 1
Problem 6.5 Swissies forward premiumsOn June 28, 2004, the following bid-ask outright rates were quoted on the Swiss franc/euro (Sfr/€) rate:
a) / b)
Calculated / Forward
Period / Days Forward / Bid Rate / Ask Rate / Mid-Rate / Premium
spot / 1.52200 / 1.52330 / 1.52265
3 months / 90 / 1.51570 / 1.51701 / 1.51636 / 1.661%
6 months / 180 / 1.51020 / 1.51222 / 1.51121 / 1.514%
12 months / 360 / 1.50145 / 1.50258 / 1.50202 / 1.374%
a) Calculate the mid-rates from the bid-ask rate quotes.
b) Calculate the forward premium on the different maturities using the mid-rates from part a).
Problem 6.6 Traveling: Copenhagen to St. Petersburg
What is the cross rate? What is left?
Assumptions / Values
Beginning your trip with Danish kroner / 10,000.00
Spot rate (Dkr/$) / 6.0729
Spot rate (Roubles/$) / 29.070
a) Calculate the cross rate
Cross rate (Dkr/rouble) / 0.2089
b) What would be the proceeds in Rubles?
Converting your Finnish markkas into Rubles / 47,868.40
Problem 6.7 Riskless profit on the franc
Can you make a profit via triangular arbitrage?
Assumptions / Values
Beginning funds in Swiss francs (SF) / 10,000,000.00
Mt. Fuji Bank (yen/$) / 120.00
Mt. Rushmore Bank (SF/$) / 1.6000
Matterhorn Bank (yen/SF) / 80.00
Try Number 1: Start with SF to $
Step 1: SF to $ / 6,250,000.00
Step 2: $ to yen / 750,000,000.00
Step 3: yen to SF / 9,375,000.00
Profit? / (625,000.00)
A loss.
Try Number 2: Start with SF to yen
Step 1: SF to yen / 800,000,000.00
Step 2: yen to $ / 6,666,666.67
Step 3: $ to SF / 10,666,666.67
Profit? / 666,666.67
A profit.
Problem 6.8 Transatlantic arbitrage
Can the arbitrager make a profit with these quotes?
Assumptions / Values
Beginning funds / $1,000,000.00
CitibankNY quotes:
Bid ($/€) / 1.1650
Ask ($/€) / 1.1670
Barclays London quotes:
Bid ($/€) / 1.1640
Ask ($/€) / 1.1660
Arbitrage Strategy #1
Initial investment / $1,000,000.00
Buy euros from Barclays (at the ask rate) / €857,632.93
Sell euros to Citibank (at the bid rate) / $999,142.37
Arbitrage profit (loss) / ($857.63)
Arbitrage Strategy #2
Initial investment / $1,000,000.00
Buy euros from Citibank (at the ask rate) / €856,898.03
Sell euros to Barclays (at the bid rate) / $997,429.31
Arbitrage profit (loss) / ($2,570.69)
The arbitrager cannot make a profit using these quotes.
Problem 6.9 Wall Street Journal quotes and premiums
Calculate the percentage premium or discount.
US$ equivalent / US$ equivalent / Currency/US$ / Currency/US$
Assumptions / Thu / Wed / Thu / Wed
U.K. (Pound) / 1.8410 / 1.8343 / 0.5432 / 0.5452
1-month forward / 1.8360 / 1.8289 / 0.5447 / 0.5468
3-months forward / 1.8259 / 1.8187 / 0.5477 / 0.5498
6-months forward / 1.8120 / 1.8048 / 0.5519 / 0.5541
a) Forward premium (discount)
1-month forward / –3.2591% / –3.5327% / –3.3046% / –3.5113%
3-months forward / –3.2808% / –3.4018% / –3.2865% / –3.3467%
6-months forward / –3.1505% / –3.2165% / –3.1527% / –3.2124%
b) Why are the forward discounts not identical?
They would be if the “Currency/US$” quote is calculated as the reciprocal of “US$ equivalent” carrying the digits.
U.K. (Pound) / 1.8410 / 1.8343 / 0.5432 / 0.5452
1-month forward / 1.8360 / 1.8289 / 0.5447 / 0.5468
3-months forward / 1.8259 / 1.8187 / 0.5477 / 0.5498
6-months forward / 1.8120 / 1.8048 / 0.5519 / 0.5541
Forward premium (discount)
1-month forward / –3.2591% / –3.5327% / –3.2591% / –3.5327%
3-months forward / –3.2808% / –3.4018% / –3.2808% / –3.4018%
6-months forward / –3.1505% / –3.2165% / –3.1505% / –3.2165%
Problem 6.10 Financial Times quotes
Using the quotes in Exhibit 6.6, calculate the forward premiums.
From Exhibit 6.6 / Values
Spot rate, closing mid-point ($/£) / 1.8418
One month rate / 1.8368
Three months rate / 1.8268
One year rate / 1.7885
Calculating the forward premium INCORRECTLY:
One month rate: (S – F)/(F) 12 / 3.2666%
Three months rate: (S – F)/(F) 4 / 3.2844%
One year rate: (S – F)/(F) / 2.9802%
Calculating the forward premium CORRECTLY:
One month rate: (F – S)/(S) 12 / 3.2577%
Three months rate: (F – S)/(S) 4 / 3.2577%
One year rate: (F – S)/(S) / 2.8939%
Problem 6.11 Venezuelan bolivar (A)
What is the percentage revaluation or devaluation?
Assumptions / Values
Fixed rate of exchange, Bs/$ / 778
New freely floating rate (2 weeks later), Bs/$ / 1,025
a) Is this a devaluation or depreciation?
The alteration in the value of an exchange rate who value / Devaluation
is set by government is either a devaluation or revaluation. / then
In this case, the Venezuelan government moved from a fixed / Depreciation
rate to a flexible exchange rate, the bolivar falling in value.
b) By what percentage did its value change?
Percentage devaluation is: / –24.10%
% Chg (S1 – S2)/(S2)
Problem 6.12 Venezuelan bolivar (B)
Venezuelan political crisis impact on the Bolivar in 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/$) / 3,250
S2 (S1)/(1%chg) (1950)/(1 – 0.40)
Problem 6.13 Indirect quotation
Calculate the percentage premium or discount.
Quoted / 90-day / Percent Premium
Assumptions / Spot Rate / Forward Rate / or Discount on Euro
Days forward / 90
European euro (euros per $) / €1.2000 / €1.2100
Calculation formula for the indirect quote on the dollar:
Percent premium (S – F)/(F) (360/90) / 3.3058%
The euro would be selling forward at a discount against the dollar, or equivalently, the dollar selling
forward against the euro at a premium.
Check calculation
One way to check percentage change calculations is to invert each of the currency
quotes (1/(euros/$)), and recalculate the quote using the direct quotation formula.
European euro ($ per euro) / $0.8333 / $0.8264
Percent discount (F-S)/(S) (360/90) / –3.3058%
Problem 6.14 Direct quotation on the dollar
Calculate the percentage premium or discount.
Quoted / 180-day / Percent Premium
Assumptions / Spot Rate / Forward Rate / or Discount
Days forward / 180
Exchange rate, US$/pound / $1.8200 / $1.8000
Calculation formula for the direct quote on the dollar:
Percent premium (F – S)/(S) (360/180) / –2.1978%
The dollar is selling forward at a discount versus the pound, or equivalently,
the pound is selling forward at a premium against the dollar.
Check calculation
Inverting the quotes (pounds/US$) / £0.5495 / £0.5556
Percent forward premium (S – F)/(F) (360/180) / –2.1978%
Problem 6.15 Mexican peso—European euro cross rates
Calculate the cross rate between the Mexican peso and European euro.
Assumptions / Exchange Rate
Mexican peso, pesos/dollar (Ps/$) / 11.43
European euro, euros/dollar (€/$) / 0.8404
Calculated cross rate, pesos/euro / 13.6007
pesos/euro (Ps/$)/(€/$)
or equivalently, euros/peso (€/Ps) / 0.0735
Problem 6.16 Around the horn
Is there triangular arbitrage profit potential?
Assumptions / Exchange rate
Citibank quote: US$/pound / 1.8500
National Westminster quote: euros/pound / 1.5000
Deutsche Bank quote: US$/euro / 1.2400
Initial investment / $1,000,000.00
Path #1: US$ to euros to pounds to US$
Start with US$ / $1,000,000.00
Convert to euros at Deutschebank quote / €806,451.61
Convert euros to pounds at NatWest quote / £537,634.41
Convert pounds to US$ at Citibank quote / $994,623.66
Arbitrage gain (loss) / ($5,376.34)
Path #2: US$ to pounds to euros to US$
Start with US$ / $1,000,000.00
Convert to pounds at Citibank quote / £540,540.54
Convert pounds to euros at NatWest quote / €810,810.81
Convert euros to US$ at Deutschebank quote / $1,005,405.41
Arbitrage gain (loss) / $5,405.41