The spot rate of the Brazilian Real (BRL) is $0.44 US. The one-year U.S. interes

Question

The spot rate of the Brazilian Real (BRL) is $0.44 US. The one-year U.S. interest rate is 5.75% and the one-year Brazilian interest rate is 9.52%.

Question 1: Assuming the existence of interest rate parity, determine the forward premium or discount of the Brazilian Real (be sure to identify whether it is a premium or a discount).

Question 2: Given the forward discount for the Real in question 1, now estimate the forward exchange rate of the Brazilian Real.

Question 3: Given interest rate parity, assume that the forward rate of the Brazilian Real is the same as the spot rate, one BRL = $0.44 US. Explain how U.S. investors could use covered interest arbitrage to lock in a higher yield than 5.75%.

Explanation / Answer

Question 1:

Given 1 BRL = 0.44 USD

S = 0.44 USD/BRL, r(USD) = 5.75%, r(BRL) = 9.52%

Over the 1-year

F = S*(1 + r(USD))/(1 + r(BRL))

F/S = (1 + r(USD))/(1 + r(BRL))

(F - S)/S = (r(USD) - r(BRL))/(1 + r(BRL)) = (0.0575 - 0.0952)/1.0952 = -0.034423

(F - S) = -0.015146 USD/BRL

Negative sign indicates forward discount.

Forward discount = 0.015146 USD/BRL

Question 2:

F = S - 0.015146 = 0.424854 = 0.42 USD/BRL

Question 3:

Start with 1 USD

Convert it into BRL at t = 0; it becomes (1/0.44) BRL

Invest into BRL for 1 year; it becomes after 1 year 1.0952*(1/0.44) BRL

As F = 0.44 USD/BRL at t = 1, convert accumulated investment in USD;

It becomes 1.0952*(1/0.44)*0.44 USD = 1.0952 USD

You started with 1 USD and it become 1.0952 USD in 1 year

Return = 0.0952 = 9.52%

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