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)Computation of Arbitrage 3 month forward Exchange rate

3 MonthForward rate between MYR and USD:

Spot rate : 1 USD = 4.3610 MYR

1 USD + Interest amount for 3 months in USD = 4.3610 MYR+ Interest for 3 months in MYR

3 Month interest rate in MYR = 4% p.a

3 Month interest rate in USD= 1% p.a

1 USD + 1 USD *1% *3/12 = 4.3610 MYR+ 4..3610 MYR*4%*3/12

1 USD + 0.0025 USD = 4.3610 MYR + 0.04361 MYR

1.0025 USD = 4.40461 MYR

1 USD = 4.40461 MYR/1.0025

1 USD = 4.3936 MYR

Hence the theoretical forward price is 4.3936 MYR.

3 MonthForward rate between JPY and USD:

Spot rate : 1 USD = 107 .6400 Yen

1 USD + Interest amount for 3 months in USD = 107.6400 Yen+ Interest for 3 months in yen

3 Month interest rate in Yen = 0% p.a

3 Month interest rate in USD= 1% p.a

1 USD + 1 USD *1% *3/12 = 107.6400 Yen+ 107.6400 yen*0%*3/12

1 USD + 0.0025 USD = 107.6400 Yen +0

1.0025 USD = 107.6400 Yen

1 USD = 107.6400 Yen /1.0025

1 USD = 107.3716 Yen

Hence the theoretical forward price is 107.3716 Yen

3 Month Forward rate between CAD and USD:

Spot rate : 1 USD = 1.3839 CAD

1 USD + Interest amount for 3 months in USD = 1.3839 CAD+ Interest for 3 months in CAD

3 Month interest rate in CAD = 1.5% p.a

3 Month interest rate in USD= 1% p.a

1 USD + 1 USD *1% *3/12 = 1.3839 CAD+ 1.3839 CAD*1.5%*3/12

1 USD + 0.0025 USD = 1.3839 CAD+0.005189625 CAD

1.0025 USD = 1.389089625 CAD

1 USD = 1.389089625 CAD/1.0025

1 USD = 1.3856 CAD

Hence the theoretical forward price is 1.3856 CAD

b)

Particulars	3 Months Forward Price	3 Month Theoretical Forward price	Arbitrage Oppurtunity	Strategy
USD/MYR	4.3936	4.3936	Since Theoretical Forward price = Quoted Forward price, so there is no arbitrage oppurtunity
USD/JPY	107.3333	107.3716	Theoretical Forward price is not equal to quoted forward price, so there is arbitrage oppurtunity.	Since USD in undervalued in Quoted market, to derive arbitrage benefit, we should borrow in yen and invest in USD.
USD/CAD	1.3856	1.3856	Since Theoretical Forward price = Quoted Forward price, so there is no arbitrage oppurtunity

c) Computation of arbitrage-free 1-year forward USD/CAD exchange rate.

1 year Forward rate between CAD and USD :

Spot rate : 1 USD = 1.3839 CAD

1 USD + Interest amount for 1 year in USD = 1.3839 CAD+ Interest for 1 year in CAD

3 Month interest rate in CAD = 1.5% p.a

3 Month interest rate in USD= 1% p.a

1 USD + 1 USD *1% = 1.3839 CAD+ 1.3839 CAD*1.5%

1 USD + 0.001 USD = 1.3839 CAD+0.0207585 CAD

1.001 USD = 1.4046585 CAD

1 USD = 1.4046585 CAD/1.001

1 USD = 1.40325 CAD

Hence 1 year forward rate is 1.40325 CAD.

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