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

Principles of Corporate FinanceBrealey and Myers Sixth Edition

Slides by

Matthew Will Chapter 7

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7- 2

Topics Covered

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

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7- 3

The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

0.1

10

1000

1925 1933 1941 1949 1957 1965 1973 1981 1989 1997

S&P

Small Cap

Corp Bonds

Long Bond

T Bill

Inde

x

Year End

1

5520

1828

55.38

39.07

14.25

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7- 4

0.1

10

1000

1925 1933 1941 1949 1957 1965 1973 1981 1989 1997

S&P

Small Cap

Corp Bonds

Long Bond

T Bill

The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

Inde

x

Year End

1

613

203

6.15

4.34

1.58

Real returns

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7- 5

Rates of Return 1926-1997

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Common Stocks

Long T-Bonds

T-Bills

Year

Per

cent

age

Ret

urn

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7- 6

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.

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7- 7

Measuring RiskCoin 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%

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7- 8

Measuring Risk

1 1 24

12 1113

1013

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

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7- 9

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.”

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7- 10

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

((

(())

))

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7- 11

Measuring Risk

0

5 10 15

Number of Securities

Po

rtfo

lio s

tan

da

rd d

ev

iati

on

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7- 12

Measuring Risk

0

5 10 15

Number of Securities

Po

rtfo

lio s

tan

da

rd d

ev

iati

on

Market risk

Uniquerisk

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7- 13

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:

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7- 14

Portfolio Risk

Example

Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The expected dollar return on your BM is .10 x 55 = 5.50 and on McDonald’s it is .20 x 45 = 9.90. The expected dollar return on your portfolio is 5.50 + 9300 = 14.50. The portfolio rate of return is 14.50/100 = .145 or 14.5%. Assume a correlation coefficient of 1.

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7- 15

Portfolio Risk

2222

22

211221

2112212221

21

)8.20()45(.σx8.201.171

45.55.σσρxxsMcDonald'

8.201.171

45.55.σσρxx)1.17()55(.σxMyers-Bristol

sMcDonald'Myers-Bristol

Example

Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The expected dollar return on your BM is .10 x 55 = 5.50 and on McDonald’s it is .20 x 45 = 9.90. The expected dollar return on your portfolio is 5.50 + 9300 = 14.50. The portfolio rate of return is 14.50/100 = .145 or 14.5%. Assume a correlation coefficient of 1.

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7- 16

Portfolio Risk

Example

Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The expected dollar return on your BM is .10 x 55 = 5.50 and on McDonald’s it is .20 x 45 = 9.90. The expected dollar return on your portfolio is 5.50 + 9300 = 14.50. The portfolio rate of return is 14.50/100 = .145 or 14.5%. Assume a correlation coefficient of 1.

% 18.7 352.1 DeviationStandard

352.108)1x17.1x20.2(.55x.45x

]x(20.8)[(.45)

]x(17.1)[(.55) Valriance Portfolio22

22

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7- 17

Portfolio Risk

)rx()r(x Return PortfolioExpected 2211

)σσρxx(2σxσxVariance Portfolio 21122122

22

21

21

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7- 18

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

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7- 19

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.

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7- 20

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.

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Beta and Unique Risk

2m

imiB

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7- 22

Beta and Unique Risk

2m

imiB

Covariance with the market

Variance of the market