Chapter 7 Introduction to Risk, Return, and The Opportunity Cost of Capital Principles of Corporate...

Chapter 7

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

Principles of

Corporate FinanceEighth Edition

Slides by

Matthew Will

Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved

McGraw-Hill/Irwin


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McGraw-Hill/Irwin

Topics Covered

Over a Century of Capital Market HistoryMeasuring Portfolio RiskCalculating Portfolio RiskBeta and Unique RiskDiversification & Value Additivity


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McGraw-Hill/Irwin

The Value of an Investment of $1 in 1900

$1

$10

$100

$1,000

$10,000

$100,000

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Start of Year

Dol

lars

Common Stock

US Govt Bonds

T-Bills

15,578

14761

2004


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McGraw-Hill/Irwin

The Value of an Investment of $1 in 1900

$1

$10

$100

$1,000

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Start of Year

Dol

lars

Equities

Bonds

Bills

719

6.81

2.80

2004

Real Returns


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McGraw-Hill/Irwin

Average Market Risk Premia (by country)

4.3 4.7 5.1 5.3 5.8 5.9 5.9 6.3 6.4 6.67.6 8.1 8.2 8.6

9.310

10.7

0123456789

1011

Den

mar

k

Bel

giu

m

Sw

itze

rlan

d

Sp

ain

Can

ada

Irel

and

Ger

man

y

UK

Ave

rage

Net

her

lan

ds

US

A

Sw

eden

Sou

th A

fric

a

Au

stra

lia

Fra

nce

Jap

an

Ital

y

Risk premium, %

Country


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McGraw-Hill/Irwin

Rates of Return 1900-2003

Source: Ibbotson Associates

-60%

-40%

-20%

0%

20%

40%

60%

80%

1900 1920 1940 1960 1980 2000

Year

Per

cent

age

Ret

urn

Stock Market Index Returns


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McGraw-Hill/Irwin

Measuring Risk

1 14

1012

19

15

24

13

32

0

4

8

12

16

20

24

-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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McGraw-Hill/Irwin

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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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%


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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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McGraw-Hill/Irwin

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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Measuring Risk

0

5 10 15

Number of Securities

Po

rtfo

lio s

tan

da

rd d

ev

iati

on


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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


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McGraw-Hill/Irwin

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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Portfolio Risk

Example

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is:

%12)1540(.)1060(. ReturnExpected


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Portfolio Risk

2222

22

211221

2112212221

21

)3.27()40(.σx3.272.181

60.40.σσρxxCola-Coca

3.272.181

60.40.σσρxx)2.18()60(.σxMobil-Exxon

Cola-CocaMobil-Exxon

Example

Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.


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McGraw-Hill/Irwin

Portfolio Risk

Example


% 21.8 0.477 Deviation Standard

0.4773)1x18.2x27.2(.40x.60x

]x(27.3)[(.40)

]x(18.2)[(.60) Variance Portfolio22

22


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McGraw-Hill/Irwin

Portfolio Risk

In real life, the correlation coefficient is 0.4


% 18.3 9.333 Deviation Standard

9.333x27.3)0x0.4x18.22(0.40x0.6

]x(27.3)[(.40)

]x(18.2)[(.60) Variance Portfolio22

22


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McGraw-Hill/Irwin

Portfolio Risk

)rx()r(x Return PortfolioExpected 2211

)σσρxx(2σxσxVariance Portfolio 21122122

22

21

21


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McGraw-Hill/Irwin

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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McGraw-Hill/Irwin

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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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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2m

imiB


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McGraw-Hill/Irwin


2m

imiB

Covariance with the market

Variance of the market


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Web Resources

www.globalfindata.com

www.econ.yale.edu/~shiller

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Chapter 7 Introduction to Risk, Return, and The Opportunity Cost of Capital Principles of Corporate...

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