Question

3. Arbitrage in Montr´eal. As an arbitrageur with Banque de Montr´eal in Montreal, Province Qu´ebec, Canada you see the following CAD/USD information on your customized trading system as inputs for algorithmic execution:

Spot rate                                           CAD 1.1520/USD

6M forward rate                              CAD 1.1635/USD

6M CAD money market rate         10.00% p.a.

6M USD money market rate         7.50% p.a.

Having only recently started in your position fresh out of school your position limit is CAD

10m or its USD equivalent. Transaction costs for trading in these markets total around USD

1,700 and would be paid at the end of the 6 months. Being based in Canada any arbitrage profit should accrue in CAD. Assuming that you can trade, borrow and invest at the above quoted rates.

(a) What principle links the four prices? What is the relevant mathematical formulation?

(b) Identify any arbitrage opportunities and explain how they might have come about.

(c) How would you build up an arbitrage position? Describe your strategy and its mechanics.

(d) Calculate your profit resulting from the preceding arbitrage strategy.

Answer 1

(a) we can apply here INTEREST RATE PARITY (IRP) THEORM.

ALL FOUR PRICES CAN BE LINKED

MATHEMATICAL FOMULATION IS KNOWN AS IRP THEORM :

F = S *((1+IF)/(1+ID))

F=FORWARD RATE, S =SPOT RATE

IF = INTEREST RATE FOREIGN CURRENCY

ID =INTEREST RATE DOMESTIC CURRENCY

(b) ARBITRAGE POSSIBILITY : IF IRP THEORM DOES NOT HOLD TRUE, THEN ARBITRAGE IS POSSIBLE.

SPOT RATE = CAD 1.1520 = 1 $ (S)

6M FORWARD RATE CAD 1.1635 = 1$ (F)

CAD INTEREST RATE = 10% P.A. (ID), SO HALF YEARLY RATE IS 5%

USD =7.5% P.A. (IF), SO HALF YEARLY RATE IS 3.75%

LET US CHECK THEORM

F = S *((1+IF)/(1+ID))

1.1635 = 1.1520 * ((1 + 0.0375)/(1+0.05))

1.1635 = 1.1381 (NOT CORRECT)

THEORM DOES NOT HOLD TRUE, ARBITRAGE IS POSSIBLE

(c) ARBITRAGE STRATEGY

AS RATE IS LOWER IN US, BORROW IN US DOLLAR

SPOT RATE :

SPOT RATE = CAD 1.1520 = 1 $

STEP 1

CONVERT 100,00,000 CAD IN DOLLAR, DOLLAR WILL BE 100,00,000/1.1520 = $8680555.55

SO BORROW $8680555.55

STEP 2

AFTER A YEAR, REPAYMENT WITH INTEREST IS : $8680555.55 X (1.0375) =$9006076.39

STEP 3 :

CONVERT $8680555.55 IN CAD AT SPOT RATE, WHICH IS EQUAL TO 100,00,000 CAD

INVEST IT : 100,00,000 CAD (1+0.05) =105,00,000

STEP 4:

SELL 105,00,000CAD AT FORWARD RATE IN MARKET TODAY

SO WILL RECEIVE = 105,00,000/ 1.1635 = $9024495.06 AT THE END OF 6 MONTHS

STEP 5 :

PROFIT = $9024495.06 - $9006076.39 = $18418.67 - $1700 (BROKERAGE) =$16718.67

(d) profit

AS CAD IS MAIN CURRENCY, WE CONVERT PROFIT INTO CAD

$16718.67 X 1.1635= 19452.17 CAD

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