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Chapter 13. Risk & Return Chapter 13. Risk & Return in in Asset Pricing Models Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

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Page 1: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

Chapter 13. Risk & Return inChapter 13. Risk & Return inAsset Pricing ModelsAsset Pricing Models

Chapter 13. Risk & Return inChapter 13. Risk & Return inAsset Pricing ModelsAsset Pricing Models

• Portfolio Theory

• Managing Risk

• Asset Pricing Models

• Portfolio Theory

• Managing Risk

• Asset Pricing Models

Page 2: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

I. Portfolio TheoryI. Portfolio TheoryI. Portfolio TheoryI. Portfolio Theory

• how does investor decide among group of assets?

• assume: investors are risk averse• additional compensation for risk• tradeoff between risk and expected

return

• how does investor decide among group of assets?

• assume: investors are risk averse• additional compensation for risk• tradeoff between risk and expected

return

Page 3: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

goalgoalgoalgoal

• efficient or optimal portfolio• for a given risk, maximize exp.

return• OR• for a given exp. return, minimize

the risk

• efficient or optimal portfolio• for a given risk, maximize exp.

return• OR• for a given exp. return, minimize

the risk

Page 4: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

toolstoolstoolstools

• measure risk, return

• quantify risk/return tradeoff• measure risk, return

• quantify risk/return tradeoff

Page 5: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

return = R = change in asset value + income

initial value

Measuring ReturnMeasuring ReturnMeasuring ReturnMeasuring Return

• R is ex post• based on past data, and is known

• R is typically annualized

• R is ex post• based on past data, and is known

• R is typically annualized

Page 6: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

example 1example 1example 1example 1

• Tbill, 1 month holding period

• buy for $9488, sell for $9528

• 1 month R:

• Tbill, 1 month holding period

• buy for $9488, sell for $9528

• 1 month R:

9528 - 9488

9488= .0042 = .42%

Page 7: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• annualized R:• annualized R:

(1.0042)12 - 1 = .052 = 5.2%

Page 8: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

example 2example 2example 2example 2

• 100 shares IBM, 9 months

• buy for $62, sell for $101.50

• $.80 dividends

• 9 month R:

• 100 shares IBM, 9 months

• buy for $62, sell for $101.50

• $.80 dividends

• 9 month R:

101.50 - 62 + .80

62= .65 =65%

Page 9: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• annualized R:• annualized R:

(1.65)12/9 - 1 = .95 = 95%

Page 10: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

Expected ReturnExpected ReturnExpected ReturnExpected Return

• measuring likely future return

• based on probability distribution

• random variable

• measuring likely future return

• based on probability distribution

• random variable

E(R) = SUM(Ri x Prob(Ri))

Page 11: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

example 1example 1example 1example 1

R Prob(R)

10% .2 5% .4-5% .4

E(R) = (.2)10% + (.4)5% + (.4)(-5%)

= 2%

Page 12: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

example 2example 2example 2example 2

R Prob(R)

1% .32% .43% .3

E(R) = (.3)1% + (.4)2% + (.3)(3%)

= 2%

Page 13: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

examples 1 & 2examples 1 & 2examples 1 & 2examples 1 & 2

• same expected return

• but not same return structure• returns in example 1 are more

variable

• same expected return

• but not same return structure• returns in example 1 are more

variable

Page 14: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

RiskRiskRiskRisk

• measure likely fluctuation in return• how much will R vary from E(R)• how likely is actual R to vary from

E(R)

• measured by• variance (• standard deviation

• measure likely fluctuation in return• how much will R vary from E(R)• how likely is actual R to vary from

E(R)

• measured by• variance (• standard deviation

Page 15: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

= SUM[(Ri - E(R))2 x Prob(Ri)]

SQRT(

Page 16: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

example 1example 1example 1example 1

= (.2)(10%-2%)2

= .0039

+ (.4)(5%-2%)2

+ (.4)(-5%-2%)2

= 6.24%

Page 17: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

example 2example 2example 2example 2

= (.3)(1%-2%)2

= .00006

+ (.4)(2%-2%)2

+ (.3)(3%-2%)2

= .77%

Page 18: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• same expected return

• but example 2 has a lower risk• preferred by risk averse investors

• variance works best with symmetric distributions

• same expected return

• but example 2 has a lower risk• preferred by risk averse investors

• variance works best with symmetric distributions

Page 19: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

symmetric asymmetric

E(R)R

prob(R)

R

prob(R)

E(R)

Page 20: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

II. Managing riskII. Managing riskII. Managing riskII. Managing risk

• Diversification• holding a group of assets• lower risk w/out lowering E(R)

• Diversification• holding a group of assets• lower risk w/out lowering E(R)

Page 21: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• Why?• individual assets do not have same

return pattern• combining assets reduces overall

return variation

• Why?• individual assets do not have same

return pattern• combining assets reduces overall

return variation

Page 22: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

two types of risktwo types of risktwo types of risktwo types of risk

• unsystematic risk• specific to a firm• can be eliminated through

diversification• examples:

-- Safeway and a strike

-- Microsoft and antitrust cases

• unsystematic risk• specific to a firm• can be eliminated through

diversification• examples:

-- Safeway and a strike

-- Microsoft and antitrust cases

Page 23: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• systematic risk• market risk• cannot be eliminated through

diversification• due to factors affecting all assets

-- energy prices, interest rates, inflation, business cycles

• systematic risk• market risk• cannot be eliminated through

diversification• due to factors affecting all assets

-- energy prices, interest rates, inflation, business cycles

Page 24: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

exampleexampleexampleexample

• choose stocks from NYSE listings

• go from 1 stock to 20 stocks• reduce risk by 40-50%

• choose stocks from NYSE listings

• go from 1 stock to 20 stocks• reduce risk by 40-50%

Page 25: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

# assets

systematicrisk

unsystematic risk

totalrisk

Page 26: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

measuring relative riskmeasuring relative riskmeasuring relative riskmeasuring relative risk

• if some risk is diversifiable,• then is not the best measure of

risk • σ is an absolute measure of risk

• need a measure just for the systematic component

• if some risk is diversifiable,• then is not the best measure of

risk • σ is an absolute measure of risk

• need a measure just for the systematic component

Page 27: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

Beta, Beta, Beta, Beta,

• variation in asset/portfolio return

relative to return of market portfolio• mkt. portfolio = mkt. index

-- S&P 500 or NYSE index

• variation in asset/portfolio return

relative to return of market portfolio• mkt. portfolio = mkt. index

-- S&P 500 or NYSE index

= % change in asset return

% change in market return

Page 28: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

interpreting interpreting interpreting interpreting • if

• asset is risk free

• if • asset return = market return

• if • asset is riskier than market index

• asset is less risky than market index

• if • asset is risk free

• if • asset return = market return

• if • asset is riskier than market index

• asset is less risky than market index

Page 29: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

Sample betas Sample betas Sample betas Sample betas

Amazon 2.23

Anheuser Busch -.107

Microsoft 1.62

Ford 1.31

General Electric 1.10

Wal Mart .80

(monthly returns, 5 years back)

Page 30: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

measuring measuring measuring measuring

• estimated by regression• data on returns of assets• data on returns of market index• estimate

• estimated by regression• data on returns of assets• data on returns of market index• estimate

mRR

Page 31: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

problemsproblemsproblemsproblems

• what length for return interval?• weekly? monthly? annually?

• choice of market index?• NYSE, S&P 500• survivor bias

• what length for return interval?• weekly? monthly? annually?

• choice of market index?• NYSE, S&P 500• survivor bias

Page 32: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• # of observations (how far back?)• 5 years?• 50 years?

• time period?• 1970-1980?• 1990-2000?

• # of observations (how far back?)• 5 years?• 50 years?

• time period?• 1970-1980?• 1990-2000?

Page 33: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

III. Asset Pricing ModelsIII. Asset Pricing ModelsIII. Asset Pricing ModelsIII. Asset Pricing Models

• CAPM• Capital Asset Pricing Model• 1964, Sharpe, Linter• quantifies the risk/return tradeoff

• CAPM• Capital Asset Pricing Model• 1964, Sharpe, Linter• quantifies the risk/return tradeoff

Page 34: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

assumeassumeassumeassume

• investors choose risky and risk-free asset

• no transactions costs, taxes

• same expectations, time horizon

• risk averse investors

• investors choose risky and risk-free asset

• no transactions costs, taxes

• same expectations, time horizon

• risk averse investors

Page 35: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

implicationimplicationimplicationimplication

• expected return is a function of• beta• risk free return• market return

• expected return is a function of• beta• risk free return• market return

Page 36: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

]R)R(E[R)R(E fmf or

]R)R(E[R)R(E fmf

fR)R(E is the portfolio risk premium

where

fm R)R(E is the market risk premium

Page 37: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

so if so if so if so if

• portfolio exp. return is larger than exp. market return

• riskier portfolio has larger exp. return

• portfolio exp. return is larger than exp. market return

• riskier portfolio has larger exp. return

fR)R(E fm R)R(E

)R(E )R(E m

>

>

Page 38: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

so if so if so if so if

• portfolio exp. return is smaller than exp. market return

• less risky portfolio has smaller exp. return

• portfolio exp. return is smaller than exp. market return

• less risky portfolio has smaller exp. return

fR)R(E fm R)R(E

)R(E )R(E m

<

<

Page 39: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

so if so if so if so if

• portfolio exp. return is same than exp. market return

• equal risk portfolio means equal exp. return

• portfolio exp. return is same than exp. market return

• equal risk portfolio means equal exp. return

fR)R(E fm R)R(E

)R(E )R(E m

=

=

Page 40: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

so if so if so if so if

• portfolio exp. return is equal to risk free return

• portfolio exp. return is equal to risk free return

fR)R(E

)R(E fR

= 0

=

Page 41: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

exampleexampleexampleexample

• Rm = 10%, Rf = 3%, = 2.5• Rm = 10%, Rf = 3%, = 2.5

]R)R(E[R)R(E fmf %]3%10[5.2%3)R(E

%5.17%3)R(E %5.20)R(E

Page 42: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• CAPM tells us size of risk/return tradeoff

• CAPM tells use the price of risk

• CAPM tells us size of risk/return tradeoff

• CAPM tells use the price of risk

Page 43: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

Testing the CAPMTesting the CAPMTesting the CAPMTesting the CAPM

• CAPM overpredicts returns• return under CAPM > actual return

• relationship between β and return?• some studies it is positive• some recent studies argue no

relationship (1992 Fama & French)

• CAPM overpredicts returns• return under CAPM > actual return

• relationship between β and return?• some studies it is positive• some recent studies argue no

relationship (1992 Fama & French)

Page 44: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models
Page 45: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• other factors important in determining returns• January effect• firm size effect• day-of-the-week effect• ratio of book value to market value

• other factors important in determining returns• January effect• firm size effect• day-of-the-week effect• ratio of book value to market value

Page 46: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

problems w/ testing CAPMproblems w/ testing CAPMproblems w/ testing CAPMproblems w/ testing CAPM

• Roll critique (1977)• CAPM not testable

• do not observe E(R), only R

• do not observe true Rm

• do not observe true Rf

• results are sensitive to the sample period

• Roll critique (1977)• CAPM not testable

• do not observe E(R), only R

• do not observe true Rm

• do not observe true Rf

• results are sensitive to the sample period

Page 47: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

APTAPTAPTAPT

• Arbitrage Pricing Theory

• 1976, Ross

• assume:• several factors affect E(R)• does not specify factors

• Arbitrage Pricing Theory

• 1976, Ross

• assume:• several factors affect E(R)• does not specify factors

Page 48: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

• implications• E(R) is a function of several

factors, F

each with its own

• implications• E(R) is a function of several

factors, F

each with its own

NN332211f F....FFFR)R(E

Page 49: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

APT vs. CAPMAPT vs. CAPMAPT vs. CAPMAPT vs. CAPM

• APT is more general• many factors• unspecified factors

• CAPM is a special case of the APT• 1 factor• factor is market risk premium

• APT is more general• many factors• unspecified factors

• CAPM is a special case of the APT• 1 factor• factor is market risk premium

Page 50: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

testing the APTtesting the APTtesting the APTtesting the APT

• how many factors?

• what are the factors?

• 1980 Chen, Roll, and Ross• industrial production• inflation• yield curve slope• other yield spreads

• how many factors?

• what are the factors?

• 1980 Chen, Roll, and Ross• industrial production• inflation• yield curve slope• other yield spreads

Page 51: Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

summarysummarysummarysummary

• known risk/return tradeoff• how to measure risk?• how to price risk?

• neither CAPM or APT are perfect or free of testing problems

• both have shown value in asset pricing

• known risk/return tradeoff• how to measure risk?• how to price risk?

• neither CAPM or APT are perfect or free of testing problems

• both have shown value in asset pricing