Question

Given the following information: Canada is your home country and the US is a foreign country. The spot exchange rate St is, CA$ 1.30 = US$ 1 Forward exchange rate Ft is, CA$ 1.32 = US$ 1 Expected future exchange rate Set+1 is, CA$ 1.33 = US$ 1 Interest rate in Canada is, rt = 5 % Interest rate in the US is, rt = 3% (i) If you want to borrow from the US and invest in Canada what return will you earn on $100 from covered interest arbitrage? Is it worthwhile undertaking? (ii) If you want to borrow from Canada and invest in the US what return will you earn on $100 from covered interest arbitrage? Is it worthwhile undertaking? (iii) Suppose that your guess about the expected future exchange rate Set+1 is correct. If you want to borrow from the US and invest in Canada what return will you earn on $100 from uncovered interest arbitrage? Is it worthwhile undertaking? (iv) Suppose that your guess about the expected future exchange rate Sºt+1 is correct. If you want to borrow from Canada and invest in the US what return will you earn on $100 from uncovered interest arbitrage? Is it worthwhile undertaking?

Answer 1

(I) Borrow 100$ from USA

Convert it into CA$= 100$*1.30= 130CA$

Enter into long forward contract to buy US $

INVEST 130CA$ into Canada at 5% = 130*1.05

amount accumulated after one year = 136.5 CA$

exercise the long forward contract and buy $ at 1.32CA$/US$

= 136.5/1.32

= 103.41$

Amount repayment that has been borrowed from us = =100*1.03

=103$

Arbitrage profit = 103.41$-103$ = 0.41$

It is worthwhile undertaking.

(II)

Borrow from Canada = 100 CA$

Convert it into $ = 100/1.30 = 76.92$

Enter into short forward contract to sale $

Invest into USA = 76.92*1.03 = 79.23

Excercise short forward contract and sell $ = 79.2$*1.32

= 104.58CA$

Amount payable for borrowed 100CA$ = 100*1.05 = 105

Loss = 105-104.58 = 0.42 CA$

No, It is not worthwhile undertaking

(III)

Borrow 100$ from USA

Convert it into CA$= 100$*1.30= 130CA$

INVEST 130CA$ into Canada at 5% = 130*1.05

amount accumulated after one year = 136.5 CA$

Convert your earnings in $ after 1 year @ 1.33CA$/1$

= 136.5/1.33

= 102.63

Amount repayment that has been borrowed from us = =100*1.03

=103$

Arbitrage loss = 102.63-103$ = (0.37$)

No it's not worthwhile undertaking

(IV)

Borrow from Canada = 100 CA$

Convert it into $ = 100/1.30 = 76.92$

Invest into USA = 76.92*1.03 = 79.23$

Convert your earnings into CA$ = 79.23$*1.33= 105.38CA$

Amount payable for borrowed 100CA$ = 100*1.05 = 105

Profit = 105.38-105 = 0.38$

Yes it is worthwhile undertaking