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Course: Finance
Level: Undergraduate
Question:
Note: Please show work so that I can see how to resolve for upcoming final. Thanks.
1. Exchange Rate Relationships:
a. How many Japanese yen do you get for your dollar?
b. What is the 1-year forward rate for the yen?
c. Is the yen at a forward discount or premium on the dollar?
d. Calculate the annual percentage discount or premium on the yen.
e. If the interest rate on dollars is 6.5 percent, what do you think is the interest rate on yen?
f. According to the expectations theory, what is the expected spot rate for the yen in 1 year's time?
g. According to purchasing power parity, what is the expected difference in the rate of
price inflation in the United States and Japan?
2. Now look at Table 23–1, which has been adapted from the daily table of exchange rates in the London Financial Times. The first column of figures in the table shows the exchange rate for a number of countries on June 20, 2002. By custom, the prices of most currencies are expressed as indirect quotes. Thus you can see that you could buy 9.755 Mexican pesos for one dollar. However, to make things confusing, the price of the euro and the British pound are generally expressed as direct quotes. So Table 23–1 shows that it cost $.9644 to buy one euro (€1).
Table of Exchange rates:
Note: Rates show the number of units of foreign currency per dollar (indirect quotes), except for the euro and the U.K. pound, which show the number of dollars per unit of foreign currency (direct quotes).
Table 23-1. Some simple theories linking spot and forward exchange rates, interest rates, and inflation rates.
Answer:
a. How many Japanese yen do you get for your dollar?
$123.380
b. What is the 1-year forward rate for the yen?
$123.63
c. Is the yen at a forward discount or premium on the dollar?
Since it takes more yen to buy a dollar forward than in the spot market, the yen is at a forward discount and the dollar is at a forward premium relative to the yen.
d. Calculate the annual percentage discount or premium on the yen.
($123.63 - $123.38)/$123.63 = 0.2026%
e. If the interest rate on dollars is 6.5 percent, what do you think is the interest rate on yen?
The paper does not give information on the one-year forward rate. However, we have data on the six-month rate:
The six-month rate in dollars is 6.5%/12 = 0.5417%.
Using interest rate parity, (1+ rĄ) = (1+ 0.5417%)(120.38/120.63) = 0.0232.
So the implied one year interest rate in yen is 0.0232%.
f. According to the expectations theory, what is the expected spot rate for the yen in 1 year's time?
The 1 year forward rate is 120.63 yen per dollar. According to the expectations theory, that is the expected spot rate in one year.
g. According to purchasing power parity, what is the expected difference in the rate of price inflation in the United States and Japan?
According to relative PPP,
(1 + iĄ)/(1 + i$) = forward rate/spot rate
Plugging in numbers,
(1 + iĄ)/(1 + i$) = 120.63/120.38 = 1.0021
So the six-month inflation rate is expected to be about 0.15% more in Japan than in the U.S.
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