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.

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

- 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.

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

- 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.**

Use the following information to answer question 1 and
2
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