Introduction to Risk, Return, and the Opportunity Cost of Capital Principles of Corporate Finance...

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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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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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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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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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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Beta and Unique Risk

2m

imiB

Covariance with the market

Variance of the market