Question

Dollar Return on Foreign Investments -

(A) Over the past year, the dollar has appreciated by about 8 percent against the peso. A year ago you borrowed in the U.S. at an interest rate of 4 percent and you invested the money in a Mexican mutual fund that paid a 12 percent peso return. What net return did you earn on all of these transactions over the year? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

(B) Explain the following statement: If inflation differences are the only reason that interest rates are higher in one country than another, it is highly unlikely that arbitrage profits will exist in these countries' financial markets. (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

Inflation and Exchange Rates -

(C) Suppose oranges sell for $2 per dozen in the U.S. and they sell for 200 pesos per dozen in Mexico. Suppose further the exchange rate is $0.01 per peso. If U.S. inflation is 2 percent next year, Mexican inflation is 12 percent, and exchange rates do not change, how could you make an arbitrage profit in the orange market? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

(D) Suppose U.S. interest rates on a risk-free, one-year bond are 3 percent and Mexican interest rates on a risk-free, one-year bond are 12 percent. Suppose further that inflation is 2 percent in the U.S. and 7 percent in Mexico. Assume it takes one year for the exchange rate to adjust to inflation differences. What is the predicted change in the $/peso exchange rate for the next year? Given that, what would the dollar return on a Mexican bond be for this year? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

Answer 1

Assume 1$=1 Peso.

Dollar appreciated by 8%,

A year ago I have converted $1000 into 1000 pesos (Just an assumption to make it easy)

Now, as the dollar interest payment 4%, I have to pay $1000(1+0.04)=$1040

Now our investment in Pesos have grown 12% therefore 1000 pesos(1.12)=1120 pesos

Now dollar has appreciated against peso by 8%, therefore $1= 1.08 peso now,

Therefore now we require equivalent return ins 1120/1.08 = 1037 $, Equivalent return in Dollars.

Need to pay back $1040 (Loan)

Net return= 1037(Eqvalent return in dollar invested in mutual fund)-1040(Loan amount)= -3$

therefore investor lost 0.3%.

Q 2 If inflation differences are the only reason that interest rates are higher in one country than another, it is highly unlikely that arbitrage profits will exist in these countries' financial markets.

The formula: Nominal Rate=Real+Inflation

Now, if inflation is the only reason that interest rates are higher in one country than another, then real interest is same in both the countries, therefore what amount of return you get in this country as purchasing power you have in home country will be same as in foreign country (where we have invested), therefore a condition for arbitrage does not exist.

Q3)Exchange rate is $1= 100 pesos

Now, price of dozen oranges next year will be $2(1.02)=$2.04

In Mexico, price is 200(1.12)=224 or 224/100 =2.24

Spread is 2.24-2.04= $0.20, therefore 0.20$ is the profit for every dozen sold if the Oranges are imported form America.

Q4) Rf (USA)=3%

Mexico=12%

Spot Exchange rate is 1

Formula is Future rate= Spot Rate *( 1+ Rf of foreign)/(1+Rf of domestic) = 1*(1.12)/(1.03)-1 =8.7% , the dollar will appreciate 8.7% against Mexican Peso