Investments, tenth edition

 Figure 25.1 

Per capita GDP and market capitalization as percent of GDP.      Panel A:  

Log scale, 2000 data;    Panel B:  Log scale, 2010 data. 

U.S.

Japan

U.K.

Canada

France

Germany

Brazil

India

Russia

China

100

1,000

10,000

100,000

A

1

10

100

1000

Per Capita GDP ($)

Market Capitalization as % of GDP

Developed Countries

Emerging Markets

Regression Line

Developed Countries

Emerging Markets

Regression Line

B

U.S.

Japan

Canada

France

Germany

Brazil

India

Russia

Taiwan

China

100

1,000

10,000

100,000

1

10

100

1000

Per Capita GDP ($)

Market Capitalization as % of GDP

    25.2 

Risk Factors in International Investing 

  Opportunities in international investments do not come free of risk or of the cost of special-

ized analysis. Two risk factors that are unique to international investments are exchange 

rate risk and political risk, discussed in the next two sections.  

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P A R T   V I I

  Applied Portfolio Management

   Exchange Rate Risk 

 It is best to begin with a simple example. 

 

 Using the data in Example 25.1, calculate the 

rate of return in dollars to a U.S. investor hold-

ing the British bill if the year-end exchange rate 

is: ( a )  E  

1

   5  $2.00/£; ( b )  E  

1

   5  $2.20/£. 

 CONCEPT CHECK 

25.1 

 

We can generalize from  

Example 25.1 

. The $20,000 is exchanged for $20,000/ 

E  

0

  

pounds, where  E  

0

  denotes the original exchange rate ($2/£). The U.K. investment grows to 

(20,000/ E  

0

 )[1  1   r  

 f  

 (UK)] British pounds, where  r  

 f  

 (UK) is the risk-free rate in the United 

Kingdom. The pound proceeds ultimately are converted back to dollars at the subsequent 

exchange rate  E  

1

 , for total dollar proceeds of 20,000( E  

1

 / E  

0

 )[1   1     r  

 f  

 (UK)].  The  dollar-

denominated return on the investment in British bills, therefore, is   

 

1

1 r(US) 5 31 1 r

f

(UK)

4E

1

/E

0

 

 (25.1)   

 We see in Equation 25.1 that the dollar-denominated return for a U.S. investor equals 

the pound-denominated return times the exchange rate “return.” For a U.S. investor, the 

investment in British bills is a combination of a safe investment in the United Kingdom 

and a risky investment in the performance of the pound relative to the dollar. Here, the 

pound fared poorly, falling from a value of $2 to only $1.80. The loss on the pound more 

than offset the earnings on the British bill. 

  Figure  25.2  illustrates this point. It presents rates of 

returns on stock market indexes in several countries for 

2010. The colored bars depict returns in local currencies, 

while the dark bars depict returns in dollars, adjusted for 

exchange rate movements. It’s clear that exchange rate 

fluctuations over this period had large effects on dollar-

denominated returns in several countries.  

 

 Pure     exchange  rate  risk    is the risk borne by invest-

ments in foreign safe assets. The investor in U.K. bills of 

Example 25.1 bears the risk of the U.K./U.S. exchange rate only. We can assess the mag-

nitude of exchange rate risk by examining historical rates of change in various exchange 

rates and their correlations. 

  Table  25.3 , panel A shows historical exchange rate risk measured by the standard 

deviation of monthly percent changes in the exchange rates of major currencies against 

the U.S. dollar over the period 2001–2011. The data show that currency risk is quite 

high. The annualized standard deviation of the percent changes in the exchange rate 

ranged from 9.13% (Japanese yen) to 13.87% (Australian dollar). The standard  deviation 

 Consider an investment in risk-free British government bills paying 10% annual interest 

in British pounds. While these U.K. bills would be the risk-free asset to a British inves-

tor, this is not the case for a U.S. investor. Suppose, for example, the current exchange 

rate is $2 per pound, and the U.S. investor starts with $20,000. That amount can be 

exchanged for £10,000 and invested at a riskless 10% rate in the United Kingdom to 

provide £11,000 in 1 year. 

 What happens if the dollar–pound exchange rate varies over the year? Say that dur-

ing the year, the pound depreciates relative to the dollar, so that by year-end only $1.80 

is required to purchase £1. The £11,000 can be exchanged at the year-end exchange 

rate for only $19,800 ( 5  £11,000  3  $1.80/£), resulting in a loss of $200 relative to the 

initial $20,000 investment. Despite the positive 10% pound-denominated return, the 

dollar-denominated return is negative 1%. 

 Example  25.1 

Exchange Rate Risk 

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0

5%

10%

15%

20%

25%

30%

Japan

Australia

Norway

Germany

U.K.

Pakistan

India

Russia

Brazil

China

Return (in Local Currencies)

Return (in U.S. $)

15.59

0.71

14.73

0.66

11.82

12.51

9.32

16.91

8.80

12.22

27.06

29.05

20.95

16.22

19.40

20.30

6.81

1.72

4.83

5.10

  C H A P T E R  

2 5

 International 

Diversification 

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