Principles of Corporate Finance

Seventh Edition

Richard A. Brealey

Stewart C. Myers

Slides by

Matthew Will

Chapter 7

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Introduction to Risk, Return, and the Opportunity Cost of

Capital

7- 2

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Topics Covered

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

7- 3

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The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

0.1

10

1000

1925 1940 1955 1970 1985 2000

S&PSmall CapCorp BondsLong BondT Bill

Inde

x

Year End

1

6402

2587

64.1

48.9

16.6

7- 4

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0.1

10

1000

1925 1940 1955 1970 1985 2000

S&PSmall CapCorp BondsLong BondT Bill

Source: Ibbotson Associates

Inde

x

Year End

1

660

267

6.6

5.0

1.7

Real returns

The Value of an Investment of $1 in 1926

7- 5

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Rates of Return 1926-2000

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

Common Stocks

Long T-Bonds

T-Bills

Year

Per

cent

age

Ret

urn

7- 6

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Average Market Risk Premia (1999-2000)

4.35.1 6 6.1 6.1 6.5 6.7 7.1 7.5 8

8.5 9.9 9.9 10 11

0123456789

1011

Den Bel

Can Sw

i

Spa UK Ire

Net

h

US

A

Sw

e

Aus

Ger

Fra

Jap It

Risk premium, %

Country

7- 7

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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.

7- 8

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Measuring Risk

Coin Toss Game-calculating variance and standard deviation

(1) (2) (3)

Percent Rate of Return Deviation from Mean Squared Deviation

+ 40 + 30 900

+ 10 0 0

+ 10 0 0

- 20 - 30 900

Variance = average of squared deviations = 1800 / 4 = 450

Standard deviation = square of root variance = 450 = 21.2%

7- 9

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Measuring Risk

1 1 24

1311

13 12 13

3 20123456789

10111213

-50

to -

40

-40

to -

30

-30

to -

20

-20

to -

10

-10

to 0

0 to

10

10 t

o 20

20 t

o 30

30 t

o 40

40 t

o 50

50 t

o 60

Return %

# of Years

Histogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns

7- 10

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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.”

7- 11

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Measuring Risk

Portfolio rate

of return=

fraction of portfolio

in first assetx

rate of return

on first asset

+fraction of portfolio

in second assetx

rate of return

on second asset

((

((

))

))

7- 12

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Measuring Risk

0

5 10 15

Number of Securities

Po

rtfo

lio s

tan

da

rd d

ev

iati

on

7- 13

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Measuring Risk

0

5 10 15

Number of Securities

Po

rtfo

lio s

tan

da

rd d

ev

iati

on

Market risk

Uniquerisk

7- 14

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Portfolio Risk

22

22

211221

1221

211221

122121

21

σxσσρxx

σxx2Stock

σσρxx

σxxσx1Stock

2Stock 1Stock

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

7- 15

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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.

7- 16

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Portfolio Risk

2222

22

211221

2112212221

21

)5.58()35(.σx5.585.311

35.65.σσρxxReebok

5.585.311

35.65.σσρxx)5.31()65(.σxCola-Coca

ReebokCola-Coca

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.

7- 17

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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.

% 31.7 1,006.1 Deviation Standard

1.006,15)1x31.5x58.2(.65x.35x

]x(58.5)[(.35)

]x(31.5)[(.65) Valriance Portfolio22

22

7- 18

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Portfolio Risk

)rx()r(x Return PortfolioExpected 2211

)σσρxx(2σxσxVariance Portfolio 21122122

22

21

21

7- 19

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Portfolio Risk

The shaded boxes contain variance terms; the remainder contain covariance terms.

1

2

3

4

5

6

N

1 2 3 4 5 6 N

STOCK

STOCKTo calculate portfolio variance add up the boxes

7- 20

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Beta and Unique Risk

beta

Expected

return

Expectedmarketreturn

10%10%- +

-10%+10%

stock

Copyright 1996 by The McGraw-Hill Companies, Inc

-10%

1. Total risk = diversifiable risk + market risk2. Market risk is measured by beta, the sensitivity to market changes

7- 21

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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.

7- 22

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Beta and Unique Risk

2m

imiB

7- 23

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Beta and Unique Risk

2m

imiB

Covariance with the market

Variance of the market