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5 Applying the Rate of Return Formulas

# 5 Applying the Rate of Return Formulas

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0.02 % per year

E04 ¥ / \$

104 ¥ / \$

E05¥ / \$

120 ¥ / \$

Again, imagine that the decision is to be made in 2004, looking forward into 2005. However, we calculate
this in hindsight after we know what the 2005 exchange is. Thus we plug in the 2005 rate for the expected
exchange rate and use the 2004 rate as the current spot rate. Note also that the interest rate in
Japan really was 0.02 percent. It was virtually zero.
Before calculating the rate of return, it is necessary to convert the exchange rate to the yen equivalent
rather than the dollar equivalent. Thus

E04\$/¥= 1104 = 0.0096 and E05\$/¥= 1120 = 0.0083.
Now, the ex-post (i.e., after the fact) rate of return on Japanese deposits is given by

RoR¥ =0.0002+(1+0.0002) 0.0083−0.0096
0.0096
which simplifies to

RoR¥ − 0.0002 + (1 + 0.0002)(−0.1354) = −0.1352 or −13.52%.
A negative rate of return means that the investor would have lost money (in dollar terms) by purchasing
the Japanese asset.
Since RoR\$ = 2.37% > RoR¥ = −13.52%, the investor seeking the highest rate of return should have
deposited his money in the U.S. account.

Example 3
Consider the following data for interest rates and exchange rates in the United States and South Korea.
Note that South Korean currency is in won (W).

iS
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2.37% per year

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iw

4.04% per year

E04 W/\$

1,059 W/\$

E05W/\$

1,026 W/\$

As in the preceding examples, the decision is to be made in 2004, looking forward to 2005. However,
since the previous year interest rate is not listed, we use the current short-term interest rate. Before
calculating the rate of return, it is necessary to convert the exchange rate to the won equivalent rather
than the dollar equivalent. Thus

E04\$/W= 1
= 0.000944 and E05\$/W=1
= 0.000975.
1059
1026
Now, the ex-post (i.e., after the fact) rate of return on Italian deposits is given by

RoRW = 0.0404 + (1+0.0404) 0.000975− 0.000944
0.000944
which simplifies to

RoRW = 0.0404 + (1 + 0.0404)(0.0328) = 0.0746 or +7.46%.
In this case, the positive rate of return means an investor would have made money (in dollar terms) by
Also, since RoR\$ = 2.37 percent < RoRW = 7.46 percent, the investor seeking the highest rate of return
should have deposited his money in the South Korean account.

KEY TAKEAWAY

An investor should choose the deposit or asset that promises the highest expected rate of return
assuming equivalent risk and liquidity characteristics.

EXERCISES

1. Consider the following data collected on February 9, 2004. The interest rate given is for a
one-year money market deposit. The spot exchange rate is the rate for February 9. The
expected exchange rate is the one-year forward rate. Express each answer as a
percentage.
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a.

2.5%

EUS\$/C\$

0.7541 US\$/C\$

EeUS\$/C\$

0[0].7468 US\$/C\$

Use both RoR formulas (one from Chapter 4 "Foreign Exchange Markets and Rates of

Return", Section 4.3 "Calculating Rate of Returns on International Investments", the other
from Chapter 4 "Foreign Exchange Markets and Rates of Return", Section 4.4 "Interpretation of
the Rate of Return Formula", Step 5) to calculate the expected rate of return on the Canadian
money market deposit and show that both formulas generate the same answer.
b. What part of the rate of return arises only due to the interest earned on the deposit?
c. What part of the rate of return arises from the percentage change in the value of the
principal due to the change in the exchange rate?
d. What component of the rate of return arises from the percentage change in the value of
the interest payments due to the change in the exchange rate?
Consider the following data collected on February 9, 2004. The interest rate
given is for a one-year money market deposit. The spot exchange rate is the rate for
February 9. The expected exchange rate is the one-year forward rate. Express each

E\$/£
Ee\$/£

4.5%
1.8574 \$/£
1.7956 \$/£

Use both RoR formulas (one from Chapter 4 "Foreign Exchange Markets and Rates of
Return", Section 4.3 "Calculating Rate of Returns on International Investments", the
other from Chapter 4 "Foreign Exchange Markets and Rates of Return", Section 4.4
"Interpretation of the Rate of Return Formula", Step 5) to calculate the expected rate of
return on the British money market deposit and show that both formulas generate the
a. What part of the rate of return arises only due to the interest earned on the deposit?
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b. What part of the rate of return arises from the percentage change in the value of the
principal due to the change in the exchange rate?
c. What component of the rate of return arises from the percentage change in the value of
the interest payments due to the change in the exchange rate?
[1] These numbers were taken from the Economist, Weekly Indicators, December 17, 2005, p.
90, http://www.economist.com.

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Chapter 5: Interest Rate Parity
Interest rate parity is one of the most important theories in international finance because it is probably
the best way to explain how exchange rate values are determined and why they fluctuate as they do. Most
of the international currency exchanges occur for investment purposes, and therefore understanding the
prime motivations for international investment is critical.
The chapter applies the rate of return formula developed in Chapter 4 "Foreign Exchange Markets and
Rates of Return" and shows how changes in the determinants of the rate of return on assets affect investor
behavior on the foreign exchange market, which in turn affects the value of the exchange rate. The model
is described in two different ways: first, using simple supply and demand curves; and second, using a rate
of return diagram that will be used later with the development of a more elaborate macro model of the
economy.

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5.1 Overview of Interest Rate Parity

LEARNING OBJECTIVES

1.

Define the interest rate parity condition.

2. Learn the asset approach to exchange rate determination.
Interest rate parity (IRP) is a theory used to explain the value and movements of exchange rates. It is also
known as the asset approach to exchange rate determination. The interest rate parity theory assumes that
the actions of international investors—motivated by cross-country differences in rates of return on
comparable assets—induce changes in the spot exchange rate. In another vein, IRP suggests that
transactions on a country’s financial account affect the value of the exchange rate on the foreign exchange
(Forex) market. This contrasts with the purchasing power parity theory, which assumes that the actions of
importers and exporters, whose transactions are recorded on the current account, induce changes in the
exchange rate.

Interest Rate Parity Condition
Interest rate parity refers to a condition of equality between the rates of return on comparable assets
between two countries. The term is somewhat of a misnomer on the basis of how it is being described
here, as it should really be called rate of return parity. The term developed in an era when the world was
in a system of fixed exchange rates. Under those circumstances, and as will be demonstrated in a later
chapter, rate of return parity did mean the equalization of interest rates. However, when exchange rates
can fluctuate, interest rate parity becomes rate of return parity, but the name was never changed.
In terms of the rates of return formulas developed in Chapter 4 "Foreign Exchange Markets and Rates of
Return", interest rate parity holds when the rate of return on dollar deposits is just equal to the expected
rate of return on British deposits, that is, when

RoR\$ = RoR£.

Plugging in the above formula yields

i\$ = i£ + (1+i£) Ee\$/£−E\$/£
E\$/£
This condition is often simplified in many textbooks by dropping the final term in which the British
interest rate is multiplied by the exchange rate change. The logic is that the final term is usually very small
especially when interest rates are low. The approximate version of the IRP condition then is
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i\$−i£ = Ee\$/£−E\$/£
E\$/£
One should be careful, however. The approximate version would not be a good approximation when
interest rates in a country are high. For example, back in 1997, short-term interest rates were 60 percent
per year in Russia and 75 percent per year in Turkey. With these interest rates, the approximate formula
would not give an accurate representation of rates of return.

Interest Rate Parity Theory
Investor behavior in asset markets that results in interest parity can also explain why the exchange rate
may rise and fall in response to market changes. In other words, interest parity can be used to develop a
model of exchange rate determination. This is known as the asset approach, or the interest rate parity
model.
The first step is to reinterpret the rate of return calculations described previously in more general
(aggregate) terms. Thus instead of using the interest rate on a one-year certificate of deposit (CD), we will
interpret the interest rates in the two countries as the average interest rates that currently prevail.
Similarly, we will imagine that the expected exchange rate is the average expectation across many
different individual investors. The rates of return then are the average expected rates of return on a wide
Figure 5.1 The Forex for British Pounds

variety of assets between two countries.
Next, we imagine that investors trade currencies
in the foreign exchange (Forex) market. Each
day, some investors come to a market ready to
supply a currency in exchange for another, while
others come to demand currency in exchange for
another.
Consider the market for British pounds (£) in
New York depicted in Figure 5.1 "The Forex for
British Pounds". We measure the supply and
demand of pounds along the horizontal axis and
the price of pounds (i.e., the exchange rate E\$/£)
on the vertical axis. Let S£ represent the supply

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