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) We calculate arbitrage-free 3-Months forward rate by using Interest rate parity.

First We calculate the interest rate for 3 Month

MYR = 4% p.a. so 3-Months = 1%

USD = 1% p.a. so 3-Months = 0.25%

CAD = 1.50% p.a. so 3-Months = 0.375%

JPY = 0% p.a. so 3-Months = 0%

USD/MYR = Spot Rate x (1+Interest Rate of MYR) / (1+Interest Rate of USD)

= 4.3610 x (1+0.01) / (1+0.0025)

= 4.3610 x 1.01/1.0025

= 4.3936

USD/JPY = Spot Rate x (1+Interest Rate of JPY) / (1+Interest Rate of USD)

= 107.6400 x (1+0.00) / (1+0.0025)

= 107.6400 x 1/1.0025

= 107.3716

USD/CAD = Spot Rate x (1+Interest Rate of CAD) / (1+Interest Rate of USD)

= 1.3839 x (1+0.00375) / (1+0.00250)

= 1.3839 x 1.00375/1.00250

= 1.3856

(b) As we calculate the Arbitrage-free 3-Months forward rate and compare with the actual trading rate than we got same rate in USD/MYR and USD/CAD so no arbitrage opportunity exist in that but while we compared the USD/JPY rate 3-Months arbitrage-free 3-Months forward rate 107.3716 and actual trading rate is 107.3333 means arbitrage opportunity exist so arbitrager can make profit by buying forward contract and borrow money from USD @1% p.a. and Convert it into JPY at spot rate and invest into JPY @0% p.a. for 3-Months and after 3-Months execute the forward contract and pay USD borrowing and earn Profit.

Borrow 1 USD at spot

Convert it into JPY at spot rate = 107.6400

Invest @0% p.a. and enter into Forward Contract

USD payable after 3-Months = 1 USD x (1+0.0025) = 1.0025 USD

JPY invested money after 3-Months = 107.64 x (1+0.00) = 107.6400 (Here Invest or not doesn't make any difference as the Interest earn @0%)

Execute the Forward Contract = 1.0025 USD x 107.3333 = 107.6016

Net Profit per USD borrow = 107.6400 - 107.6016 = 0.0384 JPY

(c) We calculate the arbitrage -free-1-Year forward rate of USD/CAD using the Interest rate Parity

USD/CAD = Spot Rate x (1+Interest Rate of CAD) / (1+Interest Rate of USD)

= 1.3839 x (1+0.0150) / (1+0.0100)

= 1.3839 x 1.0150 / 1.0100

= 1.39075

So USD/CAD 1-Year Forward rate (Arbitrage-Free) = 1.39075