Question

2. Assume the following information:

Spot rate of Mexican peso : $.100

180-day forward rate of Mexican peso : $.098

180-day Mexican interest rate : 6%

180-day U.S. interest rate : 5%

a) What would be the return to a Mexican investor who has 1,000,000 Mexican pesos from using covered interest arbitrage? (i.e. the Mexican investor will convert the peso into U.S. dollar at the spot rate and invest it in the U.S. for 180 days, and simultaneously sell a U.S. dollar currency forward contract with the same maturity). Does the return exceed the return from investing in Mexico over the 180-day period? Is it worthwhile for the Mexican investor to invest in the U.S.?

b) Is it worthwhile for a U.S. investor who uses a covered interest arbitrage for investing in Mexico?

Answer 1

(a)

The theoretical 180-day forward rate of Mexican peso = 0.100x{ 1 + (180/360)x(0.05 - 0.06) } = $0.0995 > $.098 (market rate)

Thus Mexican peso is cheaper in the forward market or US dollar is dearer in the forward market.1

Therefore there is an of opportunity of covered interest arbitrage wherein a risk-free profit can be locked in either by

• buying US dollars in the spot market and selling in the forward market or
• buying Mexican peso in the forward market and short selling in the spot market.

Spot rate of Mexican peso = $.100

$\large \Rightarrow$Spot rate of UD dollar =  ₱(1/0.1) =  ₱10

Proceeds from converting  ₱1000000 to US dollars is $(1000000x0.1) = $100000

Investing $100000 in US for 180 days @ 5%, the accumulation at the end of 180 days = $100000x( 1 + 0.5x.05) = $102500

Proceeds from selling $102500 under the forward contract @ ₱(1/0.098) /USD =  ₱(100000/0.098) =  ₱1045918.37

Therefore return r to the Mexican investor is given by 1000000(1 + 0.5r) = 1045918.37  $\large \Rightarrow$ r =9.184%

This exceeds the return from investing in Mexico by 9.184 - 6 = 3.184%

Therefore it is worthwhile for the Mexican investor to invest in the US.

(b)

A US investor will have to short sell Mexican peso in the spot market. If short selling is allowed and if the US investor can borrow Mexican peso in the spot market at the prevailing rate then only it can be worthwhile for the US investor to use a covered interest arbitrage.