Investments, tenth edition

   SOLUTIONS TO CONCEPT CHECKS 

    1. 

    a.  Dollar-weighted return:   

 

240 1

26

1

1 r

1

21

(1

1 r)

2

5 0

 r

5 .1191, or 11.91%   

Time

Action

Cash Flow

0

Buy two shares

2

40

1

Collect dividends; then sell one of the shares

4 1 22

2

Collect dividend on remaining share, then sell it

2 1 19

 Table 24A 

 Williamson capital performance data, 

1999–2010 

Average annual rate of return

22.1%

Beta

1.2

Standard deviation of returns

16.8%

 Table 24B 

 Joyner asset management performance data, 

1999–2010 

Average annual rate of return

24.2%

Beta

0.8

Standard deviation of returns

20.2%

bod61671_ch24_835-881.indd   880

bod61671_ch24_835-881.indd   880

7/25/13   3:14 AM

7/25/13   3:14 AM

Final PDF to printer

---

Visit us at www

.mhhe.com/bkm

  C H A P T E R  

2 4

  Portfolio Performance Evaluation 

881

   b.  Time-weighted return: 

     The rates of return on the stock in the 2 years were:   

   r

1

5

2

1 (22 2 20)

20

5 .20

 r

2

5

2

1 (19 2 22)

22

5 2.045

 (r

1

1 r

2

)/2

5 .077,  or  7.7%

      

   2.  Sharpe:     (r

2 r

f

)/s    

 S

P

5 (35 2 6)/42 5 .69

 S

M

5 (28 2 6)/30 5 .733  

     Alpha:       r

2 3r

f

1 b(r

M

2 r

f

)

4    

 a

P

5 35 2 36 1 1.2(28 2 6)4 5 2.6

 a

M

5 0

  

 Treynor:     (r

2 r

f

)/b    

 T

P

5 (35 2 6)/1.2 5 24.2

 T

M

5 (28 2 6)/1.0 5 22   

 Information ratio:  a / s ( e )   

 I

P

5 2.6/18 5 .144

 I

M

5 0

   

   3.  The alpha exceeds zero by .2/2  5  .1 standard deviations. A table of the normal distribution (or, 

somewhat more appropriately, the distribution of the  t- statistic) indicates that the probability of 

such an event, if the analyst actually has no skill, is approximately 46%.  

 

 

 

4. The timer will guess bear or bull markets completely randomly. One-half of all bull 

markets will be preceded by a correct forecast, and similarly for bear markets. Hence 

 P  

1

   1   P  

2

   2  1  5  ½  1  ½  2  1  5  0.  

   5.  First compute the new bogey performance as (.70  3  5.81)  1  (.25  3  1.45)  1  (.05  3  .48)  5  4.45.

     a.   Contribution of asset allocation to performance:  

Market

(1) 

Actual 

Weight in 

Market

(2) 

Benchmark 

Weight in 

Market

(3) 

Active 

or Excess 

Weight

(4) 

Market 

Return 

(%)

 (5) 5 (3) 3 (4)

Contribution to 

 Performance (%)

Equity

.70

.70

.00

5.81

.00

Fixed-income

.07

.25

2

.18

1.45

2

.26

Cash

.23

.05

.18

0.48

 .09

   Contribution of asset allocation

2

.17

    b.   Contribution of selection to total performance:             

Market

(1) 

Portfolio 

 Performance 

(%)

(2) 

Index 

 Performance 

(%)

(3) 

Excess 

 Performance 

(%)

(4) 

Portfolio 

Weight

(5) 5 (3) 3 (4) 

Contribution (%)

Equity

7.28

5.00

2.28

.70

1.60

Fixed-income

1.89

1.45

0.44

.07

0.03

  Contribution of selection within markets

1.63

bod61671_ch24_835-881.indd   881

bod61671_ch24_835-881.indd   881

7/25/13   3:14 AM

7/25/13   3:14 AM

Final PDF to printer

---

25 

2

  ALTHOUGH WE IN 

the United States cus-

tomarily use a broad index of U.S. equities 

as the market-index portfolio, the practice is 

increasingly inappropriate. U.S. equities rep-

resent less than 40% of world equities and 

a far smaller fraction of total world wealth. 

In this chapter, we look beyond domestic 

markets to survey issues of international 

and extended diversification. In one sense, 

international investing may be viewed as 

no more than a straightforward generaliza-

tion of our earlier treatment of portfolio 

selection with a larger menu of assets from 

which to construct a portfolio. Similar issues 

of diversification, security analysis, security 

selection, and asset allocation face the inves-

tor. On the other hand, international invest-

ments pose some problems not encountered 

in domestic markets. Among these are the 

presence of exchange rate risk, restrictions 

on capital flows across national boundar-

ies, an added dimension of political risk and 

country-specific regulations, and differing 

accounting practices in different countries. 

Therefore, in this chapter we review the 

major topics covered in the rest of the book, 

emphasizing their international aspects. We 

start with the central concept of portfo-

lio theory—diversification. We will see that 

global diversification offers opportunities 

for improving portfolio risk–return trade-

offs. We also will see how exchange rate 

fluctuations and political risk affect the risk 

of international investments. We next turn 

to passive and active investment styles in the 

international context. We will consider some 

of the special problems involved in the inter-

pretation of passive index portfolios, and 

we will show how active asset allocation can 

be generalized to incorporate country and 

currency choices in addition to traditional 

domestic asset class choices. Finally, we dem-

onstrate performance attribution for inter-

national investments.  

 CHAPTER TWENTY-FIVE