GSB-711-Lecture-Note-05-Risk-Return-and-CAPM

GSB711 Managerial Finance – Topic 05 Page No. 1 GSB711 Managerial Finance – Topic 05 Page No. 1

Risk, Return and Capital Asset Pricing Model

Topic 05GSB711 – Managerial Finance

Readings: Chapter: Introduction to Risk, Return and the Opportunity Cost of Capital (Pages

220 – 246) Questions: 1, 3, 6, 7 and Problems: 9, 13, 16, 20, 21 and 23.

Chapter: Risk, Return and Capital Budgeting (Pages 248 – 273)Questions: 1, 2, 4 and Problems: 6, 7, 9, 10, 13, 16, 17, 21, 25 and 29.


Topics Covered

• Rates of Return: A Review• A Century of Capital Market History• Measuring Risk• Risk & Diversification• Measuring Market Risk

– Beta• Risk and Return

– CAPM• Capital Budgeting and Project Risk


Rates of Return

26.1%or .261=

75.06

37.123.18 =Return Percentage

P e rc e n ta g e R e tu rn = C a p i ta l G a in + D iv id e n d In i t ia l S h a re P r ic e


Rates of Return

D iv id e n d Y ie ld = D iv id e n d In i t ia l S h a re P r ic e

C a p i t a l G a in Y ie ld = C a p i t a l G a inIn i t i a l S h a r e P r i c e


Rates of Return

%1.8or 018.75.06

1.37= Yield Dividend

%24.3or 243.75.06

18.23= YieldGain Capital


Rates of ReturnNominal vs. Real

1+ real ror = 1 + nominal ror1 + inflation rate

%1.21ror real

211.1=ror real+1 .041 + 1.261 + 1


Market Indexes

Dow Jones Industrial Average (The Dow)Value of a portfolio holding one share in each of 30 large industrial firms.

Standard & Poor’s Composite Index (The S&P 500)Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues.


The Value of an Investment of $1 in 1900

Source: Ibbotson Associates

1

10

100

1000

10000

100000

Common StocksLong T-BondsT-Bills

Inde

x

Year Start

$22,745

$192

$69

2008


Rates of Return

-60.00%

-40.00%

-20.00%

0.00%

20.00%

40.00%

60.00%R

etu

rn (

%)

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Year

Common Stocks (1900-2007)

2007


Expected Return

7.6+2.2=9.8% (2008)

7.6+14=21.6% (1981)

premium

risk normal+

billsTreasury

on rateinterest =

return

market Expected


What is Risk?• Risk, in traditional terms, is viewed as a ‘negative’.

Webster’s dictionary, for instance, defines risk as “exposing to danger or hazard”. The Chinese symbols for risk, reproduced below, give a much better description of risk

• The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity.

GSB711 Managerial Finance – Topic 05 Page No. 12

Country Risk Premia (%)

0

2

4

6

8

10

12Italy

Japan

France

Germany

Australia

S Africa

Sweden

USA

Average

Netherlands

UK

Norway

Canada

Ireland

Spain

Switzerland

Belgium

Denmark


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.


Expected Returns

• Expected returns are based on the probabilities of possible outcomes

• In this context, “expected” means average if the process is repeated many times

• The “expected” return does not even have to be a possible return

n

iiiRpRE

1

)(


Example: Expected Returns

• Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?– State Probability C T– Boom 0.3 15 25– Normal 0.5 10 20– Recession ??? 2 1

• RC = .3(15) + .5(10) + .2(2) = 9.99%• RT = .3(25) + .5(20) + .2(1) = 17.7%


Variance and Standard Deviation

• Variance and standard deviation still measure the volatility of returns

• Using unequal probabilities for the entire range of possibilities

• Weighted average of squared deviations

n

iii RERp

1

22 ))((σ


Example: Variance and Standard Deviation

• Consider the previous example. What are the variance and standard deviation for each stock?

• Stock C– 2 = .3(15-9.9)2 + .5(10-9.9)2 + .2(2-9.9)2 =

20.29– = 4.5

• Stock T– 2 = .3(25-17.7)2 + .5(20-17.7)2 + .2(1-

17.7)2 = 74.41– = 8.63


Portfolios

• A portfolio is a collection of assets• An asset’s risk and return are important in how

they affect the risk and return of the portfolio• The risk-return trade-off for a portfolio is

measured by the portfolio expected return and standard deviation, just as with individual assets


Example: Portfolio Weights

• Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security?– $2000 of DCLK– $3000 of KO– $4000 of INTC– $6000 of KEI

• DCLK: 2/15 = .133• KO: 3/15 = .2• INTC: 4/15 = .267• KEI: 6/15 = .4


Portfolio Expected Returns

• The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio

• You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities

m

jjjP REwRE

1

)()(


Example: Expected Portfolio Returns

• Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?– DCLK: 19.69%– KO: 5.25%– INTC: 16.65%– KEI: 18.24%

• E(RP) = .133(19.69) + .2(5.25) + .167(16.65) + .4(18.24) = 13.75%


Portfolio Variance

• Compute the portfolio return for each state:RP = w1R1 + w2R2 + … + wmRm

• Compute the expected portfolio return using the same formula as for an individual asset

• Compute the portfolio variance and standard deviation using the same formulas as for an individual asset


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%


Histogram of Returns

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 5502468

1012

Common Stocks

Return, percent

Nu

mb

er

of Y

ea

rs

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 550

10

20

30

40

50

Treasury Bonds

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 550

20

40

60

80

Treasury Bills


Risk and Diversification

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.”



Deviations from SquaredYear Rate of Return, % Average Return, % Deviations

2002 -20.9 -29.4 864.362003 31.6 23.1 533.612004 12.5 4.0 16.002005 6.4 -2.1 4.412006 15.8 7.3 53.292007 5.6 -2.9 8.41

Total 51.0 1,480.08

Average return = 51.0/6 = 8.50%246.6815.71%

Variance = average of squared deviations = 1,480.08/6 = Standard deviation = square root of variance =



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

((

((

))

))


Diversification

• Portfolio diversification is the investment in several different asset classes or sectors

• Diversification is not just holding a lot of assets• For example, if you own 50 internet stocks, you

are not diversified• However, if you own 50 stocks that span 20

different industries, then you are diversified


29

Portfolio diversification with additional stocks in a portfolio


The Principle of Diversification

• Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns

• This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another

• However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion


Portfolio diversification and numbers of stocks in a portfolio


Diversifiable Risk

• The risk that can be eliminated by combining assets into a portfolio

• Often considered the same as unsystematic, unique or asset-specific risk

• If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away


Total Risk

• Total risk = systematic risk + unsystematic risk• The standard deviation of returns is a measure of

total risk• For well-diversified portfolios, unsystematic risk is

very small• Consequently, the total risk for a diversified

portfolio is essentially equivalent to the systematic risk


Systematic Risk Principle

• There is a reward for bearing risk• There is not a reward for bearing risk

unnecessarily• The expected return on a risky asset depends

only on that asset’s systematic risk since unsystematic risk can be diversified away


Measuring Systematic Risk

• How do we measure systematic risk?• We use the beta coefficient to measure

systematic risk• What does beta tell us?

– A beta of 1 implies the asset has the same systematic risk as the overall market

– A beta < 1 implies the asset has less systematic risk than the overall market

– A beta > 1 implies the asset has more systematic risk than the overall market


Total versus Systematic Risk

• Consider the following information: Standard Deviation Beta– Security C 20% 1.25– Security K 30% 0.95

• Which security has more total risk?• Which security has more systematic risk?• Which security should have the higher expected

return?


Beta and the Risk Premium

• Remember that the risk premium = expected return – risk-free rate

• The higher the beta, the greater the risk premium should be

• Can we define the relationship between the risk premium and beta so that we can estimate the expected return?– YES!


Stock Market Volatility 1900-2007

0

10

20

30

40

50

60

1900

1905

1910

1915

1920

1925

1930

1935

1940

1945

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

Std

Dev

200

7


The Value of Investments

Aug-0

4

Nov 0

4

Feb 0

5

May

05

Aug 0

5

Nov 0

5

Feb 0

6

May

06

Aug 0

6

Nov 0

6

Feb 0

7

May

07

Aug 0

7

Nov 0

70

20

40

60

80

100

120

140

160

Network Mining

Ford

Portfolio

Val

ue (

Aug

ust

2004

= 1

00)



05 10 15

Number of Securities

Po

rtfo

lio

sta

nd

ard

dev

iati

on


05 10 15

Number of Securities

Po

rtfo

lio

sta

nd

ard

dev

iati

on

Market risk

Uniquerisk



Measuring Market Risk

Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index is used to represent the market.

Beta - Sensitivity of a stock’s return to the return on the market portfolio.



Example - Turbo Charged Seafood has the following % returns on its stock, relative to the listed changes in the % return on the market portfolio. The beta of Turbo Charged Seafood can be derived from this information.



Month Market Return % Turbo Return %

1 + 1 + 0.8

2 + 1 + 1.8

3 + 1 - 0.2

4 - 1 - 1.8

5 - 1 + 0.2

6 - 1 - 0.8

Example - continued



B = = 0.81.62

• When the market was up 1%, Turbo average % change was +0.8%

• When the market was down 1%, Turbo average % change was -0.8%

• The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8.

Example - continued


Measuring Market RiskExample - continued

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Market Return %

Turbo return %


Portfolio Betas

• Diversification decreases variability from unique risk, but not from market risk.

• The beta of your portfolio will be an average of the betas of the securities in the portfolio.

• If you owned all of the S&P Composite Index stocks, you would have an average beta of 1.0


Stock Betas

BBetas calculated with price data from January 2003 thru December 2007

Stock BetaAmazon.com 2.39Ford 2.46Newmont Mining 0.84Intel 1.59Microsoft 1.04Dell Computer 1.27Boeing 1.23McDonalds 1.44Pfizer 0.67Dupont 1.24Disney 1.00ExxonMobil 0.81IBM 1.13Wal-Mart 0.24Campbell Suop 0.46GE 0.76Heinz 0.59


Risk and Return

-10

-8

-6

-4

-2

0

2

4

6

8

10

-10 -8 -6 -4 -2 0 2 4 6 8 10

Market Return (%)

Va

ngu

ard

Exp

lore

r R

etu

rn (

%)

Vanguard Explorer Fund return


Risk and ReturnVanguard Index 500 return

-10 -8 -6 -4 -2 0 2 4 6 8 10

-10

-8

-6

-4

-2

0

2

4

6

8

10

Market Return (%)

Va

ngu

ard

Re

turn

(%

)


Measuring Market RiskMarket Risk Premium - Risk premium of

market portfolio. Difference between market return and return on risk-free Treasury bills.

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

Beta

Exp

ecte

d R

etu

rn (

%)

. Market Portfolio


Measuring Market RiskCAPM - Theory of the relationship

between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.

Market risk premium = r - r

Risk premium on any asset = r - r

Expected Return = r + B(r - r )

m f

f

f m f


Measuring Market RiskSecurity Market Line - The graphic

representation of the CAPM.

Beta

Exp

ecte

d R

etu

rn (

%)

.

Rf

Rm

Security Market Line

1.0


Capital Asset Pricing Model

R = rf + B ( rm - rf )

CAPM


Testing the CAPM

Avg Risk Premium 1931-2005

Portfolio Beta1.0

SML30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium


Testing the CAPM

0.1

1

10

10019

26

1936

1946

1956

1966

1976

1986

1996

2006

High-minus low book-to-market

Return vs. Book-to-MarketDollars(log scale)

Small minus big

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

200

7


Stock Expected Returns

)(rE

Stock Expected returnAmazon.com 19.8Ford 20.2Newmont Mining 8.9Intel 14.1Microsoft 10.3Dell Computer 11.9Boeing 11.6McDonalds 13.1Pfizer 7.7Dupont 11.7Disney 10.0ExxonMobil 8.7IBM 10.9Wal-Mart 4.7Campbell Suop 6.2GE 8.3Heinz 7.1


Capital Budgeting & Project Risk

• We discuss more on capital budgeting in a later topic

• The project cost of capital depends on the use to which the capital is being put. Therefore, it depends on the risk of the project and not the risk of the company.


Capital Budgeting & Project

Example - Based on the CAPM, ABC Company has a cost of capital of 17%. [4 + 1.3(10)]. A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used?

1/3 Nuclear Parts Mfr. B=2.01/3 Computer Hard Drive Mfr. B=1.31/3 Dog Food Production B=0.6

AVG. B of assets = 1.3

Risk


Capital Budgeting & Project Risk

Example - Based on the CAPM, ABC Company has a cost of capital of 17%. (4 + 1.3(10)). A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used?

R = 4 + 0.6 (14 - 4 ) = 10%

10% reflects the opportunity cost of capital on an investment given the unique risk of the project.


Alternative Models

• CAPM emphasizes market as the major determinant of expected return

• Major criticism from Fama and French in early 1990s

• Other models take into account other aspects– Arbitrage pricing theory and Multi factor

models• Is beta dead?• Long-live beta

Education

GSB-711-Lecture-Note-05-Risk-Return-and-CAPM