An arbitrager at Deutsche Bank notices that the yield on Brazilian Real 6-month

Question

An arbitrager at Deutsche Bank notices that the yield on Brazilian Real 6-month risk-free bills is 5.5% per annum and the yield on U.S. 6-month T-bills is 7% per annum. The arbitrager also observes that the spot exchange rate is $0.6507/BRL and 6-month forward exchange rate is $0.6617/BRL. Assume that the spread in the borrowing and lending rates in either currency is zero.

Given the above quotes, compare the covered yield in BRL with the nominal yield in dollar and infer whether a covered interest arbitrage opportunity exists and what does it imply for funds flow due to arbitrage. (2+1 Points)

What transactions will the arbitrageur undertake to realize arbitrage profits in dollars net of transaction cost? Write all the steps clearly and show your calculations in each step. Assume that the bank has allowed a transaction size of $10 million or its BRL equivalent at the current spot rate. Also assume that the transaction cost is 0.2% of the transaction size to be deducted from the gross arbitrage profits at the end of 6-month period. (5 Points)

Suppose the nominal interest rates stay at the levels quoted above, what should be the no-arbitrage annualized forward premium/discount on BRL against $? (2 Points).

Explanation / Answer

A)

The covered yield in BRL is 2*[(1+.055*(180/360))*($0.6617/BRL/ $0.6507/BRL)-1] = 2*0.04487=0.08974 or 8.974% which is greater than 7% the nominal yield in dollar thus invest in a higher yield currency BRL and borrow in the lower yield currency US $ thus funds should flow from US $ to Brazil BRL.

B) Steps for arbitrage

1)Borrow 10,000,000 $ at  7-percent p.a. in the U.S for 6 months and convert it into BRL using  spot exchange rate  ($0.6507/BRL) so that total BRL= 10,000,000 $ /($0.6507/BRL), transaction cost=.002*10,000,000 $=$ 20,000

2) Invest converted BRL at annual 5.5 percent in the Brazil for 6 months so that at end of period investment becomes (10,000,000 $ /($0.6507/BRL))*(1+.055*180/360),simultaneously enter into a forward contract to sell BRL at 180-days forward rate of $0.6617/BRL

3) Now recover BRL investment after 6 months and convert it into $ using the forward contract, so value obtained is (10,000,000 $ /($0.6507/BRL))*(1+.055*180/360)* $0.6617/BRL =$10448697.556 transaction cost=.002*$10448697.556 = $ 20897.395

4) Pay the borrowed amount in $ at end of 6 months of Investment in US= 10,000,000 $ *(1.035) =$10350000

5) Profit from the net amount $10448697.556-$10350000=$98697.556 is the risk less arbitrage profit made. Considering total transaction cost=$ 20,000+ $ 20897. 395= $40897.395, the risk less arbitrage profit made net of total transaction cost=98697.556-40897.395= $57800.161

C) Using Covered Interest Rate parity relation, 180 days=6 months

Use relation, forward rate($/BRL)(T days)

= spot exchange rate* {((1+(R$*T/360))/(1+(RBRL*T/360))}($/BRL)

180-days forward rate($/BRL)= ($0.6507/BR)*{((1+(.07*180/360))/(1+(.055*180/360))}

180-days forward rate($/BRL)= ($0.6507/BR)*{((1+.035)/(1+.0275)}

180-days forward rate($/BRL)= ($0.6507/BR)*(1.035)/(1.0275)

180-days forward rate($/BRL)= $0.6555/BR

$0.6617/BRL-$0.6555/BR =$.0062/BRL should be the no-arbitrage annualized forward discount on BRL against $ so that no arbitrage opportunity is exploited.

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