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Question 2: One year US and Brazilian Treasury yields are 4.5% and 9.5% respectively. Current spot...

Question 2: One year US and Brazilian Treasury yields are 4.5% and 9.5% respectively. Current spot rate is USD/BRL 2.9580. If the US real interest rates are 2.00%,

a. What should be 1 year IFE forecast of USD/BRL future spot rate?

b. What should be the expected inflation in Brazil for the year ahead if IFE holds? [Use exact formula, not approximation]

Solutions

Expert Solution

a) In the given question

US treasury yield ( Nominal rate) = 4.5%

Brazilian treasury ( Nominal rate ) = 9.5%

Spot rate USD per BRL = 2.9580

US real interest rate = 2%

Formula for IFE forecast foe future spot rate  (USD/BRL)

Forward rate ( USD/BRL) / Spot rate (USD/BRL) = ( 1+ US Interest rate) / ( 1 + BRL Interest rate)

Since as per theory of international fisher effect the difference between exchange rates of two countries is equal to the difference of their nominal interest rate.

Hence the formula for forward exchange rate ( UDS/ BRL) = Spot rate ( USD/BRL) * ( 1+ US Nominal rate) / ( 1+ Brazilian Nominal rate)

= 2.9580 * ( 1+ 4.5%) / ( 1+ 9.5%)

= 2.823 Forward spot rate ( USD/BRL)

b) If International fisher effects hold that means real interest rate between two countries would be same .Nominal interest rate is the sum of real interest and inflation rate. In the given theory it is mentioned that inflation portion of nominal interest rate is set off with the difference of exchange rates which bring purchase parity between two currencies.

Hence real interest rate of brazil is equal to the real interest rate of US = 2%

Formula for Expected inflation = [ ( 1+ Nominal rate ) / ( 1+ real rate ) ] - 1

= [ ( 1+ 9.5%) / ( 1+ 2%) ] -1

= 7.353 %

Rahul Sunny answered 1 year ago
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