Risk, return and Opp.Cost of Capital

8/14/2019 Risk, return and Opp.Cost of Capital

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7- 1

Introductionto Risk, Return, and

the Opportunity Cost of Capital

Chapter 10


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7- 2

Topics Covered

w 75 Years of Capital Market History

w Measuring Risk

w Portfolio Risk

w Beta and Unique Risk

w Diversification


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7- 3

The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

0.1

10

1000

1925 1940 1955 1970 1985 2000

S&P

Small Cap

Corp Bonds

Long Bond

T Bill

Index

Year End

1

6,402

2,587

64.1

48.9

16.6

Assuming reinvestment of all dividend and interest


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7- 4

0.1

10

1000

1925 1940 1955 1970 1985 2000

S&P

Small Cap

Corp Bonds

Long Bond

T Bill


Index

Year End

1

660

267

6.6

5.0

1.7

Real returns

The Value of an Investment of $1 in 1926


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7- 5

Rates of Return 1926-2000


-60

-40

-20

0

20

40

60

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

2000

Common Stocks

Long T-BondsT-Bills

Year

PercentageR

eturn


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7- 6

Average Rates of Return (1926-2000)

Portfolio

Average AnnualRate of Return

Average RiskPremium (ExtraReturn vs. TreasuryBills)

Nominal Real

Treasury Bills 3.9 0.8 0

Government Bonds 5.7 2.7 1.8

Corporate Bonds 6.0 3.0 2.1

Common Stocks (S&P 500)

13.0 9.7 9.1Small Firm Common Stocks 17.3 13.8 13.4

Figures are in percent per year.


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7- 7

Average vs. Compounded Returns

w If the cost of capital is estimated fromhistorical returns or risk premiums, usearithmetic averages, not compounded

annual rates of return.


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7- 8

Average Market Risk Premia (1900-2000)

4.35.1

6 6.1 6 .1 6.5 6.77.1 7.5

88.5 9.9

9.9 10 11

0

12

3

45

67

8

9

10

11

DenBel

Can

Swi

Spa

UK Ir

e

Neth

USA

Swe

Aus

Ger

Fra

Jap It

Risk premium, %

Country


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7- 9

Evaluating Cost of Capital

w For estimating the cost of capital, can we usehistorical market returns?

w Likely Candidates:

Market return, rm Risk-free rate plus risk premium

w Is the expected future risk premium the same

as the historic risk premium?


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7-10

Measuring Risk

Variance Expected squared deviation from expected

return, denoted by 2.When it is estimated from a sample ofobserved returns,

mean return is taken as the expected return.

Standard Deviation The square root of variance, denotedby .

=

=N

t

tt rrN

r

1

22 )(1

1)(


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7-11

Measuring Risk

1 1 2

4

1311

13 12 13

3201

23456789

10111213

-50to-40

-40to-30

-30to-20

-20to-10

-10to0

0to10

10to20

20to30

30to40

40to50

50to60

Return %

# of YearsHistogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns


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Annual st.dev. and variances(U.S. 1926-2000)

Portfolio StandardDeviation Variance

Treasury Bills 3.2 10.1

Government Bonds 9.4 88.7

Corporate Bonds 8.7 75.5

Common Stocks (S&P 500) 20.2 406.9Small Firm Common Stocks 33.4 1118.4


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Does volatility remain constant?

Period(NYSE)

Market St.Dev.( m)1926-1930 21.7

1931-1940 37.8

1941-1950 14.0

1951-1960 12.1

1961-1970 13.0

1971-1980 15.8

1981-1990 16.5

1991-2000 13.4


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Volatility Across Markets

Market Standard DeviationFrance 21.5

Switzerland 19.0Finland 43.2

Japan 18.2

Argentina 34.3

September 1996-August 2001Percent per year


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7-15

Volatility of Individual Securities

Stock Standard Deviation

Amazon 110.6

Boeing 30.9Coca-Cola 31.5

Dell Computer 62.7

Exxon Mobil 17.4

General Electric 26.8

General Motors 33.4

McDonalds 27.4Pfizer 29.3

August 1996-July 2001

Percent per year


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7-16

Volatility of Market vs.Individual Stocks

w Individual Stocks are much more variablethan the market index.

wWhy doesnt the volatility of the marketportfolio reflect the average variability of

its components, individual stocks?

w Diversification reduces variability.


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7-17

Measuring Risk

Diversification- Strategy designed to reduce risk byspreading the portfolio across many investments.

Unique Risk- Risk factors affecting only that firm.Also called diversifiable risk.

Market Risk- Economy-wide sources of risk thataffect the overall stock market. Also calledsystematic risk.

7


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Measuring Risk

0

5 10 15

Number of Securities

Portfo

lio

standard

deviation

7


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Measuring Risk

0

5 10 15

Number of Securities

Portfo

lio

standard

deviation

Market risk

Unique

risk

7


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7-20

Measuring Risk

==n

i

ii rx1

p ..r

Where:xi=Fraction of portfolio in asset i

ri=Rate of return on asset i

Portfolio Return:

7


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7-21

Measuring Risk

)(2 2112212

2

2

2

2

1

2

1p

2

xxxx ++=

Where:xi=Fraction of portfolio in asset i

i=standard deviation of asset i

Portfolio Variance:(for a two-asset portfolio)

7


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7-22

Portfolio Variance

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

Stock 1 Stock 2

Stock 1

x12 12

x1x2 12=x1x2 12 12

Stock 2x1x2 12=x1x2 12 1 2 x22 22

7


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Covariance between stocks

w Portfolio variance depends on: Variance of the individual stocks (diagonal

boxes)

Covariance between the stocks (off-diagonalboxes)

w Covariance can be expressed as product of :

Individual standard deviations

Correlation Coefficient,

211212 =

7


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7-24

Portfolio Risk

Example

Suppose you invest 65% of your portfolio in Coca-Cola and35% in Reebok. Expected return for Coca-Cola stock is 10%and for Reebok, 20%.

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%.

Past standard deviation of returns was 31.5 % for Coca-Colaand 58.5% for Reebok. Assume a correlation coefficient of 0.2.

What is the standard deviation of your portfolio?

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7-25

Portfolio Risk

222

2

2

2

211221

211221222

1

2

1

)5.58()35(.x5.585.312.0

35.65.xxReebok

5.585.312.0

35.65.xx)5.31()65(.xCola-Coca

ReebokCola-Coca

=

=

=

=

ExampleSuppose you invest 65% of your portfolio in Coca-Cola and 35% inReebok. 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 yourportfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of

0.2.

7-


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Portfolio Risk

ExampleSuppose you invest 65% of your portfolio in Coca-Cola and 35% inReebok. The expected dollar return on your CC is 10% x 65% = 6.5% andon Reebok it is 20% x 35% = 7.0%. The expected return on your portfoliois 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 0.2.

%31.71,006.1DeviationStandard

1.006,18.5)0.2x31.5x52(.65x.35x

]x(58.5)[(.35)

]x(31.5)[(.65)VariancePortfolio

22

22

==

=+

+

=

7-


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727

Portfolio Risk

)rx()r(xReturnPortfolioExpected 2211 +=

)xx(2xxVariancePortfolio211221

2

2

2

2

2

1

2

1

++=

7-


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728

Portfolio Risk

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

1

2

3

4

5

6

N

1 2 3 4 5 6 N

STOCK

STOCK

To calculateportfoliovariance addup the boxes

7-


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729

Individual Securitiesand Portfolio Risk

w Portfolio managers are not interested in thestandard deviations of individual securities,but in the effect that each stock will have

on the risk of their portfolio.w The risk of a well-diversified portfolio

depends on the market risk of the securities

included in the portfolio.w And market risk is measured by .

7-


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730

Volatility of Individual Securities

Stock

Amazon 3.25 110.6

Boeing 0.56 30.9Coca-Cola 0.74 31.5

Dell Computer 2.21 62.7

Exxon Mobil 0.40 17.4

General Electric 1.18 26.8

General Motors 0.91 33.4

McDonalds 0.68 27.4Pfizer 0.71 29.3

August 1996-July 2001Percent per year

7-


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Beta and Unique Risk

beta

Expected

return

Expected

marketreturn

10%10%- +

-10%+10%

stock

Copyright 1996 by The McGraw-Hill Companies, Inc

-10%

1. Total risk =diversifiable risk +market risk2. Market risk ismeasured by beta,the sensitivity tomarket changes

7-


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Market Portfolio- Portfolio of all assets in theeconomy. In practice a broad stock marketindex, such as the S&P Composite, is used

to represent the market.

Beta - Sensitivity of a stocks return to the

return on the market portfolio.

7-


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2

m

imiB

=


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Risk, return and Opp.Cost of Capital

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