Question

1. Assume the following information:

Spot rate of Canadian dollar : $.80

90-day forward rate of Canadian dollar : $.79

90-day Canadian interest rate : 4%

90-day U.S. interest rate : 2.5%

a) What would be the return to a U.S. investor who used covered interest arbitrage from investing in Canada? (assume the investor invests $1,000,000). Does the return exceed the return from investing in the U.S. over the 90-day period? Is it worthwhile for the U.S. investor to invest in Canada?

b) Explain completely the market forces on the spot market and the forward market to eliminate the covered interest arbitrage

Answer 1

a)

Quote for Canadian dollars in USD is exressed as USD/ CAD which mean 1 CAD is equal to 0.80 USD
Spot Rate	$0.80
Forward Rate ( 90 day)	$0.79
90 Day canadian Interest rate	4%
90 day USD Interest rate	2.50%

Step 1 - $ 1000000 @ $0.80 - C$1250000.

Step 2 - Invest in Canada @ 1250000 *1.04*90/360 = $ 1262500

Step 3 - Convert to USD 1262500 * 0.79 = $ 997375.

So clearly it is not worthwhile for the investor to invest in Canada.

Let us now follow covered interest rate strategy and see the return.

As per the strategy, first step is to calculate the implied forward rate.  If the actual forward rate is higher than the implied rate sell in the forward market and buy in the spot market and if the acutal forward rate is lower then buy in forward rate and sell in the spot market.

Forward rate for USD / CAD using covered interest rate parity = S0 { 1+Ra (days /360) / 1+Rb (days/360) }

0.8 * (1.025(90/360) /1.04 (90/360) = $.079703

The forward rate of $ 0.79 is lower than the implied forward rate

Strategy suggests: buy forward and sell spot

Step 1 - Borrow in Canadian dollars C$1250000 ($ 1000000 equivalent). The total amount to be repaid with interest is C$1262500 at the end of 90 days

Step 2 - Sell CAD in spot and invest USD 1000000 @ 2.5%. This will give you a return of 1006250 USD in 90 days.

Step 3 - Buy CAD @ forward contract rate of 0.79 and get C$1273734/-

Step 4 - Repay the debt of C$1262500 from the CAD bought.

This leaves you with a profit of C$ 11234/-

So, it is the worthwhile for the investor to invest in Canada.

b) The very meaning of covered in covered interest rate arbitrage is " bound by arbitrage". As per the covered interest rate arbitrage the forward premium or forward discount in currency nullifies the interest rate differentials between the two countries. Investors are always trying to benefit from any arbitrage opportunities - riskless profit with zero investment. This approach finally nullifies the interest rate differential between two countries. If Country A's interest rates are higher than Country B then depreciation of the Country A currency will nullify the higher interest rate.