Question

The following table contains information on spot and forward exchange rates among U.S. dollar (USD), Malaysian ringgit (MYR), Japanese yen (JPY) and Canadian dollar (CAD).

Currencies |
3-month forward rate |
Spot rate |

USD/MYR |
4.3936 |
4.3610 |

USD/JPY |
107.3333 |
107.6400 |

USD/CAD |
1.3856 |
1.3839 |

The following table contains information on the 3-month nominal risk-free rate per annum for the four different currencies

3-month nominal risk-free rate |
|||

MYR |
USD |
CAD |
JPY |

4.00% |
1.00% |
1.50% |
0.00% |

Note that the Japanese yen 3-month nominal risk-free rate is zero percent per annum.

(a) Compute the equilibrium or arbitrage-free 3-month forward exchange rates for the three currency pairs contained in the first table.

(b) Based on your results in part (b), state if an arbitrage opportunity exists for each of the three currency pairs. Briefly explain your answer.

(c) Compute arbitrage-free 1-year forward USD/CAD exchange rate.

Answer #1

(a)

equilibrium forward exchange rates = Spot rate x [(1 + Interest rate of Home currency) / (1 + Interest rate of Foreign currency)

Forward USD/MYR = 4.3610 x [(1 + 1%) / (1 + 4%) = 4.235202

Forward USD/JPY = 107.6400 x [(1 + 1%) / (1 + 0%) = 108.7164

Forward USD/CAD = 1.3839 x [(1 + 1%) / (1 + 1.5%) = 1.377083

(b)

Since there is difference in 3-month forward rate and equilbrium forward rate there is arbitrage oppurtunity. The person can buy the 3-month forward when it is lower than Equilbrium rate and sell in viceversa condition.

(c)

The following are the spot and forward bid and ask rates for the
Japanese yen/U.S. dollar (¥/$) exchange rate from January 20, 2011.
By referring to these rates, answer the following questions (the US
dollar is the home currency):
Period Yen/$ Bidrate Yen/$ 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
a) Calculate the mid-rate for these maturities
b) Calculate the annual forward premium for these maturities

3) Suppose that the spot exchange rate S(¥/€) between the yen
and the euro is currently
¥110/€, the 1-year euro interest rate is 6% p.a., and the 1-year
yen interest rate is 3% p.a.
Which of the following statements is MOST likely to be true?
A. The high interest rate currency must sell at a forward premium
when priced in the low
interest rate currency to prevent covered interest arbitrage
Page 3 of 13
B. Real interest parity does not...

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United States Dollar to Euro 1.16 USD/EUR
Swiss Franc to Canadian Dollar 0.69 CHF/CAD
Swiss Franc to Euro 1.08 CHF/EUR.
Determine the implied USD/JPY cross rate. (2 POINTS)
Suppose that the JPY to USD exchange rate is 111 JPY/1 USD. Is
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£1,000,000.
a/ What is the implied three-month U.S.per annuminterest
rate? (round to 2 decimals in %)
b/ Does Interest Rate Parity hold?
c/ Determine the arbitrage profit (if any, otherwise
type "0") and report it...

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Suppose you believe the risk-free rate of JPN will be 3 % over the
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The spot exchange rate is 110.0JPN/USD and the semiannually
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forward with 9-month maturity is 112.9JPN/USD.
What risk-free rate of JPN is implied by this forward
price?
Suppose you believe the risk-free rate of JPN over the next 9
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Suppose you believe the risk-free rate of JPN will be 3 % over
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Currency
Spot quote
Euro (EUR/USD)
1.1278 - 1.1281
British pound (GBP/USD)
1.2845 - 1.2848
Swiss franc (USD/CHF)
1.0020 – 1.0022
Japanese yen (USD/JPY)
110.41 – 110.44
Dominican peso (USD/DOP)
50.540 – 50.600
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The current USD/JPY spot exchange rate is 110 (USD is base
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