During the 1960s and into the 1970s, the Mexican government pegged the value of the Mexican peso to the U.S. dollar at 12 pesos per dollar. Because interest rates in Mexico were higher than those in the United States, many investors (including banks) bought bonds in Mexico to earn higher returns than were available in the United States. The benefits of the higher interest rates, however, masked the possibility that the peso would be allowed to float and lose substantial value compared to the dollar. Suppose you are an investor and believe that the probability of the exchange rate for the next year remains at 12 pesos per dollar is 0.9, but that the rate could soar to 24 per dollar with probability 0.1.
(a) Consider two investments: Deposit $1,000 today in a U.S. savings account that pays 8% annual interest (rates were high in the 1970s), or deposit $1,000 in a Mexican account that pays 16% interest. The latter requires converting the dollars into pesos at the current rate of 12 pesos/dollar, and then after a year converting the pesos back into dollars at whatever rate then applies. Which choice has the higher expected value in one year? (In fact, the peso fell in value in 1976 by nearly 50%, catching some investors by surprise.)
(b) Now suppose you are a Mexican with 12,000 pesos to invest. You can convert these pesos to dollars, collect 8% interest, and then convert them back at the end of the year, or you can get 16% from your local Mexican investment. Compare the expected value in pesos of each of these investments. Which looks better?
(c) Explain the difference in strategies that obtain the higher expected value.