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)