Fourth Edition1

Chapter 7

Capital Asset Pricing

Fourth Edition2

Outline

1. Beta: the market risk

2. Relationship between risk and return: CAPM

3. Security Market Line: graphic representation of CAPM

5-3

1. Beta

Fourth Edition4

Breaking down sources of risk

Stand-alone risk = Market risk + Firm-specific risk

• Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta.

• Firm-specific risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification.

Fourth Edition5

Beta

• Measures a stock’s market risk, and shows a stock’s volatility relative to the market.

• Indicates how risky a stock is if the stock is held in a well-diversified portfolio.

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Calculating betas

= [COV(ri,rm)] / m2

• Run a regression of past returns of a security against past returns on the market.

• The slope of the regression line is defined as the beta coefficient for the security.

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Comments on beta

• If beta = 1.0, the security is just as risky as the average stock.

• If beta > 1.0, the security is riskier than average.

• If beta < 1.0, the security is less risky than average.

• Most stocks have betas in the range of 0.5 to 1.5.

• Check beta in real world

Fourth Edition8

Creating a portfolio:Beginning with one stock and adding randomly selected stocks to portfolio

• σp decreases as stocks added, because they would not be perfectly correlated with the existing portfolio.

• Expected return of the portfolio would remain relatively constant.

• Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, σp tends to converge to 20%.

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Illustrating diversification effects of a stock portfolio

# Stocks in Portfolio10 20 30 40 2,000+

Company-Specific Risk

Market Risk

20

0

Stand-Alone Risk, p

p (%)35

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Portfolio beta

• Since beta cannot be diversified away, Portfolio beta is the weighted average of individual stock beta. The weight is the proportion of individual stock to whole portfolio.

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2. CAPM

Fourth Edition12

What risk do we care?

• Stand alone?

• Risk that can not be diversified?

Fourth Edition13

Capital Asset Pricing Model (CAPM)

• Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification.

Fourth Edition14

Capital Asset Pricing Model (CAPM)

• Model linking risk and required returns. CAPM suggests that a stock’s required return equals the risk-free return plus a risk premium that reflects the stock’s risk after diversification.

ri = rRF + (rM – rRF) bi • Ri: required return of stock i

• rM : Expected return of the market

• Risk premium RP: additional return to take additional risk

• The market (or equity) risk premium is (rM – rRF)

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Calculating required rates of return

• Risk free rate:5.5%, market return:10.5%Investment BetaHigh Tech 1.32Market 1US Rubber 0.88T bill 0Collection -0.87

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Calculating required rates of return

• rHT = 5.5% + (5.0%)(1.32)

= 5.5% + 6.6% = 12.10%

• rM = 5.5% + (5.0%)(1.00) = 10.50%

• rUSR = 5.5% + (5.0%)(0.88) = 9.90%

• rT-bill = 5.5% + (5.0%)(0.00) = 5.50%

• rColl = 5.5% + (5.0%)(-0.87) = 1.15%

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Applying CAPM

• Computing other variables: risk free rate, market return, market risk premium

• Computing the difference of return between two stocks.

• Computing price in the future when current price is given

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3. SML

Fourth Edition19

E(r)E(r)

E(rE(rMM))

rrff

SMLSML

MMßßßß = 1.0= 1.0

Security Market Line

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SML Relationships

= [COV(ri,rm)] / m

2

Slope SML = E(rm) - rf

= market risk premium

SML = rf + [E(rm) - rf]

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Sample Calculations for SML

E(rm) - rf = .08 rf = .03

x = 1.25

E(rx) = .03 + 1.25(.08) = .13 or 13%

y = .6

e(ry) = .03 + .6(.08) = .078 or 7.8%

Fourth Edition22

E(r)E(r)

RRxx=13%=13%

SMLSML

mm

ßß

ßß1.01.0

RRmm=11%=11%RRyy=7.8%=7.8%

3%3%

xxßß1.251.25

yyßß.6.6

.08.08

Graph of Sample Calculations