Question

You work as a trader for the arbitrage desk at Goldman Sachs, monitoring spot and futures foreign exchange rates. At 9am Eastern time you observe the following market prices and rates. The spot exchange rate between US$ and Canadian dollar is $1.1100/C$, while futures price of Canadian dollar for the contract maturing in 6 months is $1.0400/C$. The US 6-month interest rate is 6.5% per annum, while Canadian 6-month interest rate is 3.5% per annum. Both interest rates are based on continuous compounding.

1. What is the no-arbitrage futures exchange rate? (8 pts)

2. Given your answer in part (a) and data provided, describe in detail the arbitrage strategy that will earn profit and calculate your profit, assuming that you can lend or borrow 1000 units of a currency. (14 pts)

Now assume that many other traders can follow the arbitrage strategy you described in part b.

3. Will US$/C$ futures exchange rate go up or down? (3 pts)

4. Will US$/C$ spot exchange rate go up or down? (3 pts)

Answer 1

As per Interest Rate Parity,

Theoretical Forward/Future Rate $/C$ = Spot $/C$*(1+Interest Rate in US)/(1+Interest Rate in Canada)

= 1.1100*[e^(0.065/2)]/[ e^(0.035/2)]

= 1.1100*1.03305/1.01765

No Arbitrage Futures Rate = 1.1268

Actual Forward Rate < Theoretical Forward Rate

As the Rates are different, there is a Covered Interest Arbitrage Opportunity.

Therefore, Actual Forward Rate of $ is Undervalued

To make an Arbitrage Gain, Sell $ in Spot and Buy in Forward

Steps to make an Arbitrage Gain:

Now,

(1)   Borrow $1000 for 6 months

(2)   Buy C$ at Spot Rate using $1000 and receive 1000*1.1100 = C$1110

(3)   Invest C$1110 for 6 months

(4)   Enter into Forward Contract to Sell 1110*(1.01765) = C$1129.5915

After 6 months,

(5)   Realize Investments and receive 1110*(1.01765) = C$1129.5915

(6)   Sell C$1129.5915 under Forward Contract and receive 1129.5915/1.0400 = $1086.1457

(7)   Repay the borrowings along with interest and pay 1000*(1.03305) = $1033.05

(8)   Arbitrage Gain = Difference = $1086.1457 - $1033.05 = $53.0957

To make an Arbitrage Gain, Traders will Sell Spot and Buy Futures

Therefore, Spot Rate will Go Down and Futures Rate will Go Up and After one time, No Arbitrage Futures Price will equal the Actual Futures Price and then Arbitrage Opportuniy will Cease to Exist.