Investments, tenth edition

A. Standard deviation (annualized %)

Euro (€)

U.K. (£)

Switzerland 

(SF)

Japan (¥)

Australia 

(A$)

Canada 

(C$)

11.04

9.32

11.94

9.13

13.87

10.04

B. Correlation matrix

Euro (€)

U.K. (£)

Switzerland 

(SF)

Japan (¥)

Australia 

(A$)

Canada 

(C$)

U.K. (£)

0.63

1

Switzerland (SF)

0.83

0.51

1

Japan (¥)

0.27

0.08

0.42

1

Australia (A$)

0.75

0.6

0.61

0.05

1

Canada (C$)

0.51

0.49

0.37

2

0.02

0.72

1

C. Average annual returns from rolling over one-month LIBOR rates (%)

Country

Currency

Return 

in Local 

Currency

Expected 

Gain from 

Currency

Actual 

Gain from 

Currency

Actual 

Return in 

U.S. Dollars

Surprise 

Component 

of Return

SD of 

Annual 

Return

U.S.

$

2.18

2.18

Euro

€

2.38

2

0.20

4.38

6.77

4.58

11.04

U.K.

£

3.51

2

1.32

1.09

4.60

2.41

9.32

Switzerland

SF

0.90

1.28

6.46

7.36

5.17

11.94

Japan

¥

0.24

1.94

5.75

5.99

3.81

9.13

Australia

A$

5.25

2

3.07

7.94

13.19

11.01

13.87

Canada

C$

2.50

2

0.31

5.01

7.51

5.32

10.04

Table 25.3

Rates of change in major currencies against the U.S. dollar, 2002–2011 (annualized monthly rate)

Source: Exchange rates: Datastream, online.thomsonreuters.com/datastream; LIBOR rates: www.economagic.com.

exchange rate risk is largely diversifiable, as  Table  25.3 , panel B shows, and hence we 

would expect similar dollar returns from cash investments in major currencies. 

 We can illustrate exchange rate risk using a yen-denominated investment during this 

period. The low yen-denominated LIBOR rate, .24%, compared to the U.S.-dollar LIBOR 

rate, 2.18%, suggests that investors expected the yen to appreciate against the dollar by 

around 1.94%, the interest rate differential across the two countries. But those expectations 

were not realized; in fact, the yen actually appreciated against the dollar at an annual rate 

of 5.75%, leading to an annual dollar-denominated return on a yen investment of 5.99% 

(the .24% yen interest rate together with the realized exchange rate appreciation of 5.75%). 

However, such deviations between prior expectations and actual returns of this magnitude 

are not shocking. The “surprise” return in a yen LIBOR investment (converted into dollars) 

was the difference between the actual return in dollars, 5.99%, and the dollar-denominated 

LIBOR rate of 2.18%, amounting to 3.81%. This surprise is actually considerably less than 

the yen standard deviation of 9.13%. In fact, none of the six surprises exceeded the stan-

dard deviation, which is actually the  surprising event here. 

 Investors can hedge exchange rate risk using a forward or futures contract in foreign 

exchange. Recall that such contracts entail delivery or acceptance of one currency for 

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  C H A P T E R  

2 5

  International Diversification  

891

 How many pounds would the investor in 

Example 25.2 need to sell forward to hedge 

exchange rate risk if: ( 

a )  

r  (UK)   5   20%; and 

( b )  r  (UK)  5  30%? 

 CONCEPT CHECK 

25.2 

another at a stipulated exchange rate. To illustrate, recall Example 25.1. In this case, to 

hedge her exposure to the British pound, the U.S. investor would agree to deliver pounds 

for dollars at a fixed exchange rate, thereby eliminating the future risk involved with con-

version of the pound investment back into dollars.  

 You may recall that the hedge underlying Example 25.2 is the same type of hedging 

strategy at the heart of the spot-futures parity relationship first discussed in Chapter 22. 

In  both instances, futures or forward markets are used to eliminate the risk of holding 

another asset. The U.S. investor can lock in a riskless dollar-denominated return either by 

investing in United Kingdom bills and hedging exchange rate risk or by investing in risk-

less U.S. assets. Because investments in two riskless strategies must provide equal returns, 

we conclude that [1  1   r  

 f  

 (UK)] F  

0

 / E  

0

   5  1  1   r  

 f  

 (US), which can be rearranged to   

 

F

0

E

0

5

1

1 r

f

(US)

1

1 r

f

(UK)

 

 (25.2)   

 

This relationship is called the