INTERNATIONAL FOREIGN EXCHANGE PARITY RELATIONSHIPS
Practice Problems
1. Suppose the nominal South African interest rate is 9.0% and the expected inflation
rate is 3.5%. Calculate the real interest rate.
a. Use the linear approximation method.
.09 = real + .035
real = .09 – .035 = .055 = 5.5%
b. Use the exact methodology (Fisher Effect).
1.09 = (1 + real)(1.035)
(1.09/1.035) – 1 = real
.053 = 5.3%
2. Suppose that the Eurozone expected inflation rate is 9.0%, and that the expected
South African inflation rate is 13.0%. The nominal interest rate in the Eurozone is
10.09%. Use the international Fisher relation to approximate the nominal
interest rate in South Africa.
In Europe:
10.09% – 9.0% = 1.09%
In South Africa:
r – 13.0% = 1.09%
r = 14.09%
3. The 2010 Big Mac Index, perhaps the most popular example of the Law of One
Price or absolute PPP methodology in the world, reported that the average price
of a Big Mac in the United States was $3.58 while the dollar-equivalent price in the
People’s Republic of China was $1.83.
a. Was RMB undervalued or overvalued in 2010? By how much?
1- ($1.83 / $3.58) = -48.9%
The RMB was undervalued against the dollar by 48.9%, according to the 2010 Big
Mac Index.
b. How does this comparison compare to that of the Big Mac Index in 2015
(listed in our IFC 2 Powerpoint presentation)?
According to the Big Mac Index, the past five years have seen significant strides for
the RMB vis-à-vis the dollar. Whereas in 2010, the RMB was extremely undervalued
by 48.9%, by 2015 the RMB had made up some of this gap, although it was still very
undervalued by 42%.
4. One of the most common examples of the relative PPP methodology is the
consumer price index (CPI). The average price of gasoline in India in 1980 was 20
Rs/liter. If we use the price levels of 1967 as our base year, the CPI is said to be 100
in that year. In 1980, the CPI is 210 and, in 2015, it is 440.
a. What should the price of gasoline per liter be in India, assuming that the
value of gasoline has stayed flat over the past 35 years?
20 * (440/210) = 41.90 Rs/liter
b. Obviously, gasoline has become more dear since 1980, but by how much
has the real price risen by if gas sells for Rs 55/liter in 2015?
(55 – 41.90)/41.90 = 31.25%
5. The current spot rates are:
 1.32 USD/EUR
 95 JPY/USD
The current inflation rates are:
 US: 4.00%
 Eurozone: 6.50%
 Japan: 8.00%
Using the spot exchange rates and the inflation rate information provided,
a. Calculate the USD/EUR one year from today.
1.32 * (1.04/1.065) = S1
1.32*0.9765 = 1.289 USD/EUR
b. Calculate the JPY/USD six months from today.
95 * (1.08/1.04)0.5 = S0.5
95*√1.0385 = 96.81 JPY/USD
6. Suppose the spot exchange rate quote is 1.0120 Canadian dollars (C$) per U.S.
dollar. The 1-year nominal interest rate in Canada is 3.0% and the 1-year nominal
interest rate in the United States is 1.0%. The expected exchange rate at the end of
the year using the uncovered interest rate parity is closest to
a. C$1.0320
b. C$0.9923
c. C$0.9918
For this question, you do not even need to calculate the specific number because the
CAD must by definition appreciate because its nominal interest rate is higher. Thus,
choice A is the only potential answer. Were this not a multiple choice question, the
calculation would be:
C$1.012 * (1.03/1.01) = C$1.032
7. The forward rate for the USD/EUR exchange rate one year from today is $1.1255 ,
while the spot rate is currently $1.1163 per euro. According to forward parity, I
can predict with confidence that the future spot rate will experience how much
appreciation from today’s spot rate?
(1.1255 – 1.1163) / 1.1163 = 0.008242 = .8242%