Question

Problem 1

(a) The spot rate is $1 = 2.238 BRL (Braxilian Real). If the one year risk-free rate in the U.S. is 2% and the one year risk-free rate in Brazil is 5%, calculate a fair price for a six month forward contract.

(b) There is a six-month futures contract available where each contract is for the purchase of 100,000 BRL using dollars. If the quote for the six month BRL/USD futures contract is .30315 calculate and show the details of how you would make arbitrage profits.

Answer 1

(a)Interest rate Parity Equation:

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

F=Forward Rate

S=spot Rate

If=Interest rate in foreign country

Id=domestic interest rate

S=Spot Rate=1$=2.238 BRL

If=Risk free rate for six monthsin Brazil=(5/2)%=2.5%=0.025

Id=domestic interest rate for six months=(2/2)%=1%=0.01

F=S*((1+if)/(1+id))=2.238*(1+0.025)/(1+0.01)=2.238*(1.025/1.01)= 2.271238

Fair price for a six months forward contract $1=2.271238 BRL

.(b)BRL/USD=0.30315

USD/BRL=1/0.30315=3.298697

Forward rate of BRL is cheaper

Arbitrage should be to buy in forward market and sell short in spot market.

Borrow 100000 BRL and sell to get (100000/2.238 )USD= $ 44,028.86 in the spot market

Purchase 102500 BRL in futures market

USD44028.86 invested in US for six months will be =44028.86*1.01= $ 44,469.15

After six months wr need to pay 100000*1.025=102500 BRL

The cost of purchase of 102500 BRL=(102500/3.298697 )USD= $ 31,072.88

Arbitrage profit=(44469.15-31072.88)= $ 13,396.27