Spring Semester 2011

Homework Assignments

Assignment Three: Exchange Rate Parity Conditions

1) According to the IFE (RIP), if U.S. investors expect a 3% rate of domestic inflation over one year, and a 6% rate of inflation in European countries that use the EUR, and require a 4% real return on invest¬ments over one year, what should the nominal interest rate on one year U.S. Treasury securities be? Explain why a US investor in the EUR, assuming RIP holds, will earn the same real return as a USD investment. Explain your answer in terms of RIP and PPP theory.

If the IFE holds real returns are the same everywhere:

i* – Pf = i – Pd

Plugging the known variables into the equation, we can solve for both i and i* given that we know the figure for real returns:

i* – 6% = i – 3%

We are told that US investors expect a real return of 4%, therefore

i – 3% = 4%

i = 7% = the nominal interest rate on one year U.S. Treasury securities.

Nominal returns in the US must be 7% if real returns are to be 4%.

We can now solve for the foreign (EUR) interest rate consistent with RIP holding:

i* – 6% = 7% – 3%

i* = 10%

The inflation differential tells us what the expected change in the exchange rate will be (PPP):

e = Pd - Pf

e = 3% - 6%

e = -3%

The USD is expected to appreciate by 3%, therefore a EUR investment, earning a nominal return of 10% p.a. will be worth 7% in USD terms when we add in the loss from the EUR depreciation. This is only a nominal return. The real return depends on the US inflation rate, which is 3%, making the real return 4% as indicted by the RIP equation.

i* – Pf = i – Pd

10% - 6% = 7% - 3%

2) Assume that the nominal interest rate in Mexico is 47 percent and the interest rate in the United States is 8 percent for one year securities that are free from default risk. What does the IFE suggest about the differential in expected inflation in these two countries?...

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