Question

KDV, Ltd., is a Canadian company. It can borrow or lend funds in
Canada at an interest rate of 3.82%. KDV, Ltd., also has operations
in Brazil where it can borrow or lend funds at an interest rate of
7.44%. The spot exchange rate between the Brazilian Real and the
Canadian Dollar is 4.1792 Brazilian Reals per Canadian Dollar. The
360-day forward exchange rate is 4.3594 Brazilian Reals per
Canadian Dollar. By borrowing 100,000.0000 of one currency, determine an
arbitrage that will make KDV a profit.

Questions:

1. Which country (1=Canada, 2= Brazil) would KDV borrow this money
to make this arbitrage profit?

2. When KDV converts this money to the other country?s currency,
how much of this other country?s currency would KDV receive?
3. Units for #2's answer: (1 = Canadian $s, 2 Brazilian Reals)

4. Should KDV buy or sell a 360-day forward contract at time 0?
(1 = buy, 2 = sell)

5. For how many Canadian $s should KDV?s forward contract be for?

6. KDV should then lend this money in this other country. In one
year, how much will KDV receive from the loan they made?
7. Units for #6's answer: (1 = Canadian $s, 2 Brazilian Reals)

8. In one year, after KDV receives their loan plus interest, when
KDV converts these proceeds to the original country?s currency,
how much of the original country?s currency will KDV receive?
9. Units for #8's answer: (1 = Canadian $s, 2 Brazilian Reals)

10. In one year, how much will KDV have to pay for principal and
interest on the funds they borrowed?
11. Units for #10's answer: (1 = Canadian $s, 2 Brazilian Reals)

12. Arbitrage Profit = ???? amount
13. Units for #12's answer: (1 = Canadian $s, 2 Brazilian Reals)

Answer 1

The covered interest rate parity that determines the forward no arbitrage foreign exchange rate from the current spot rate and the interest rates prevailing in two countries is given below:

F = S* (1 + id) / (1 + if)

Where,

F = forward foreign exchange rate

S = spot foreign exchange rate

id = interest rate in the domestic currency or the price currency

if = interest rate in the foreign currency or the base currency

The exchange rate is quoted as number of units of domestic currency per unit of foreign currency.

Since the currency in the given question is quotes as number of Brazilian real per unit of Canadian dollar, Brazilian real becomes the domestic currency and Canadian dollar becomes the foreign currency for the purpose of covered interest rate parity application.

Thus, the values given in the question are as follows:

if = 3.82%

id = 7.44%

S = 4.1792 Brazilian Real / Canadian dollar

Quoted 360 day forward rate = 4.3594 Brazilian Real / Canadian dollar

Using the covered interest rate parity formula as shown above, the no-arbitrage forward rate should be:

F = 4.1792 * (1 + 7.44%) / (1 + 3.82%)

   = 4.1792 * (1.0744)/1.0382)

   = 4.1792 * 1.0349

   = 4.3249 Brazilian real / Canadian dollar              

However, the quoted forward rate is 4.3594 Brazilian Real / Canadian dollar. Thus using the buy-low, sell-high principle, profit can be made as follows:

Step 1: Borrow 1 Brazilian real at 7.44%. Thus the payment due in one year is 1*(1+7.44%)=1.0744

Step 2: Convert the borrower Brazilian real at current spot rate to Canadian dollar at 4.1792 real /dollar. Thus, you obtain 1 / 4.1792 = 0.2393 Canadian dollars and invest this amount at Canadian rate of 3.82%. Thus, you receive 0.2393 * (1+3.82%) = 0.2484 Canadian dollars after an year

Step 3: After one year, convert the Canadian dollars at the fixed forward rate of 4.3594 real/dollar to receive 0.2484 * 4.3594 = 1.0829 Brazilian Reals.

Step 4: Make the payment of 1.0744 brazilian real in domestic market using the 1.0829 Reals received from foreign exchange market to earn a profit of 0.0086 reals per Canadian dollar

1. From the above calculation, KDV would borrow 100,000 of Brazilian Reals to make the arbitrage profit

2. KDV will convert the 100,000 Brazilian Reals at the spot rate of 4.1792 Reals/dollar and receive 1000,000 / 4.1792 = 23,928.02 Canadian dollars

3. Units for 2’s answer is Canadian dollars

4. KDV should buy the 360-day forward contract quoted at 3594 Reals/Dollar to lock in the higher conversion rate compared to the one expected using covered interest rate parity of 4.3249 Brazilian Reals/Canadian Dollar