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Chapter_07Introduction to Risk, Return, and the Opportunity Cost of Capital(Brealey & Myers)

发布时间:2014-01-25 12:00:57  

Principles of Corporate Finance
Seventh Edition

Chapter 7
Introduction to Risk, Return, and the Opportunity Cost of Capital

Richard A. Brealey Stewart C. Myers

Slides by Matthew Will
McGraw Hill/Irwin
Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 2

Topics Covered
? 75 Years of Capital Market History ? Measuring Risk ? Portfolio Risk ? Beta and Unique Risk ? Diversification

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 3

The Value of an Investment of $1 in 1926
S&P Small Cap Corp Bonds Long Bond T Bill

6402 2587

1000

64.1 48.9

Index

10

16.6

1
0.1 1925

1940

1955

1970

1985

2000

Source: Ibbotson Associates
McGraw Hill/Irwin

Year End
Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 4

The Value of an Investment of $1 in 1926
S&P Small Cap Corp Bonds Long Bond T Bill

Real returns
660 267

1000

Index

10

6.6 5.0

1
0.1 1925

1.7

1940

1955

1970

1985

2000

Source: Ibbotson Associates
McGraw Hill/Irwin

Year End
Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 5

Rates of Return 1926-2000
60

Percentage Return

40 20 0 -20 -40
26 30 35 40 45 50
Common Stocks Long T-Bonds T-Bills

55

60

65

70

75

80

85

90

95

Year
Source: Ibbotson Associates
McGraw Hill/Irwin
Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

20

00

-60

7- 6

Average Market Risk Premia (1999-2000)
Risk premium, %
11 10 9 8 7 6 5 4 3 2 1 0

4.3

5.1

7.1 7.5 6 6.1 6.1 6.5 6.7

8

9.9 10 11 9.9 8.5

Can

Den

Ger

Swi

Bel

Neth

USA

Aus

Jap

Spa

Country
McGraw Hill/Irwin
Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

Swe

Fra

UK

Ire

It

7- 7

Measuring Risk
Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation - Average value of squared deviations from mean. A measure of volatility.

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 8

Measuring Risk
Coin Toss Game-calculating variance and standard deviation
(1) + 40 + 10 + 10 - 20 (2) + 30 0 0 - 30 (3) 900 0 0 900 450 = 21.2%

Percent Rate of Return Deviation from Mean Squared Deviation

Variance = average of squared deviations = 1800 / 4 = 450 Standard deviation = square of root variance =

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 9

Measuring Risk
Histogram of Annual Stock Market Returns
# of Years
13 12 11 10 9 8 7 6 5 4 3 2 1 0

13 4
-10 to 0

13 12 13 11 3
0 to 10 10 to 20 20 to 30 30 to 40 40 to 50

1
-50 to -40

1
-40 to -30

2
-30 to -20

2
50 to 60

Return %

McGraw Hill/Irwin

-20 to -10

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 10

Measuring Risk
Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Unique Risk - Risk factors affecting only that firm. Also

called “diversifiable risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 11

Measuring Risk

Portfolio rate of return

=

+

( (

fraction of portfolio

in first asset

fraction of portfolio

in second asset

)( )(
x x

rate of return

on first asset

rate of return

on second asset

) )

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 12

Measuring Risk
Portfolio standard deviation

0 5 10 15 Number of Securities

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 13

Measuring Risk
Portfolio standard deviation

Unique risk Market risk

0 5 10 15 Number of Securities

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 14

Portfolio Risk
The variance of a two stock portfolio is the sum of these four boxes

Stock1 Stock1 Stock 2
2 2 x1 σ1

Stock 2 x 1x 2σ 12 ? x 1x 2ρ 12σ 1σ 2
2 x2 σ 2 2

x 1x 2σ 12 ? x 1x 2ρ 12σ 1σ 2

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 15

Portfolio Risk
Example

Suppose you invest 65% of your portfolio in CocaCola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% and on Reebok it is 20% x 35% = 7.0%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 16

Portfolio Risk
Example Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% and on Reebok it is 20% x 35% = 7.0%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.

Coca - Cola Coca - Cola Reebok
2 2 x1 σ1 ? (.65) 2 ? (31.5) 2

Reebok x 1 x 2 ρ12 σ1σ 2 ? .65 ? .35 ? 1 ? 31.5 ? 58.5
2 2 2 x2 σ ? (. 35 ) ? ( 58 . 5 ) 2 2

x 1 x 2 ρ12 σ1σ 2 ? .65 ? .35 ? 1 ? 31.5 ? 58.5

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 17

Portfolio Risk
Example Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% and on Reebok it is 20% x 35% = 7.0%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.

Portfolio Valriance ? [(.65) 2 x(31.5) 2 ] ? [(.35) 2 x(58.5) 2 ] ? 2(.65x.35x 1x31.5x58. 5) ? 1,006 .1 Standard Deviation ? 1,006.1 ? 31.7 %
McGraw Hill/Irwin
Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 18

Portfolio Risk

Expected Portfolio Return ? (x 1 r1 ) ? ( x 2 r2 )

2 2 2 Portfolio Variance ? x1 σ 1 ? x2 σ 2 2 ? 2( x 1x 2ρ 12σ 1σ 2 )

McGraw Hi

ll/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 19

Portfolio Risk
The shaded boxes contain variance terms; the remainder contain covariance terms.
1
2 3 STOCK 4 5 6

To calculate portfolio variance add up the boxes

N 1
McGraw Hill/Irwin

2

3

4

5

6

N

STOCK
Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 20

Beta and Unique Risk
1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes Expected stock return beta +10% -10%

- 10%
-10%

+10%

Expected market return

Copyright by The McGraw-Hill Companies, Inc Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved McGraw1996 Hill/Irwin

7- 21

Beta and Unique Risk
Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 22

Beta and Unique Risk

? im Bi ? 2 ?m

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved

7- 23

Beta and Unique Risk
? im Bi ? 2 ?m

Covariance with the market

Variance of the market

McGraw Hill/Irwin

Copyright ? 2003 by The McGraw-Hill Companies, Inc. All rights reserved


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