558 CHAPTER 15 Multinational Financial Management
return will be higher than the investment’s stated return if the currency in which your
investment is denominated appreciates relative to your home currency. Likewise, your
overall return will be lower if the foreign currency you receive declines in value.
To illustrate interest rate parity, consider the case of a U.S. investor who can buy
default-free 180-day Swiss bonds that promise a 4 percent nominal annual return. The
180-day Swiss interest rate, rf, is 4%/2 2% because 180 days is one-half of a 360-day
year. Assume also that the indirect quotation for the spot exchange rate is 1.6592 Swiss
francs per dollar, as shown in Table 15-3. Finally, assume that the 180-day forward
exchange rate is 1.6583 Swiss francs per dollar, which means that in 180 days the
investor can exchange one dollar for 1.6583 Swiss francs.
The U.S. investor could receive a 4 percent annualized return denominated in
Swiss francs, but if he or she ultimately wants to consume goods in the United States,
those Swiss francs must be converted to dollars. The dollar return on the investment
depends, therefore, on what happens to exchange rates over the next six months.
However, the investor can lock in the dollar return by selling the foreign currency in
the forward market. For example, the investor could simultaneously:
- Convert $1,000 to 1,659.2 Swiss francs in the spot market: $1,000(1.6592 Swiss
francs per dollar) 1,659.2 Swiss francs.
- Invest the Swiss francs in a 180-day Swiss bond that has a 4 percent annual return,
or a 2 percent semiannual return. This investment will pay 1,659.2(1.02)
1,692.38 Swiss francs in 180 days.
- Agree today to exchange the Swiss francs in 180 days at the rate of 1.6583 Swiss
francs per dollar, for a total of (1,692.38 Swiss francs)/(1.6583 Swiss francs per
dollar) $1,020.55.
This investment, therefore, has an expected 180-day return of $20.55/$1,000
2.055%, which translates into a nominal annual return of 2(2.055%) 4.11%. In this
case, 4 percent of the expected 4.11 percent is coming from the bond itself, and 0.11
percent arises because the market believes the Swiss franc will strengthen relative to
the dollar. Note that by locking in the forward rate today, the investor has eliminated
all exchange rate risk. And since the Swiss bond is assumed to be default-free, the in-
vestor is certain to earn a 4.11 percent annual dollar return.
Interest rate parity implies that an investment in the United States with the same
risk as the Swiss bond should also have a return of 4.11 percent. We can express inter-
est rate parity by the following equation:
(15-1)
Here rhis the periodic interest rate in the home country, rfis the periodic interest rate
in the foreign country, and the forward and exchange rates are expressed as direct quo-
tations (that is, dollars per foreign currency).
Using Table 15-3, the direct spot quotation is 0.60270 dollar per Swiss franc
(1/1.6592 Swiss francs per dollar), and the direct 180-day forward quotation is
0.60303 (1/1.6583). Using Equation 15-1, we can solve for the equivalent home
rate, rh:
.
(15-1a)
The periodic home interest rate is 2.0558 percent, and the annualized home interest
rate is (2.0558%)(2) 4.11%, the same value we found above.
(1rh) a
0.60303
0.60270
b(10.02)1.020558
Forward exchange rate
Spot exchange rate
(1rh)
(1rf)
(1rh)
(10.02)
0.60303
0.60270
Forward exchange rate
Spot exchange rate
(1rh)
(1rf)
,
552 Multinational Financial Management
