The Capital Asset Pricing Model

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• The Capital Asset Pricing Model

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Review

• Review of portfolio diversification
• Capital Asset Pricing Model
• Capital Market Line (CML)
• Security Market Line (SML)

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Capital Asset Pricing Model (CAPM)

• It is the equilibrium model that underlies all
  modern financial theory.
• Derived using principles of diversification with
  simplified assumptions.
• Markowitz, Sharpe, Lintner and Mossin are
  researchers credited with its development.

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Assumptions

• Single-period investment horizon.
• Investors forecasts agree with respect to
  expectations, standard deviations, and
  correlations of the returns of risky securities
• Therefore all investors hold risky assets in the
  same relative proportions
• Investors behave optimally
• In equilibrium, prices adjust so that aggregate
  demand for each security is equal to its supply

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Market Portfolio

• Since every investors relative holdings of the
  risky security is the same, the only way the
  asset market can clear is if those optimal
  relative proportions are the proportions in which
  they are valued in the market place
• All investors will hold the same portfolio for
  risky assets market portfolio.

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Capital Market Line (CML) and the CAPM

• CAPM says that in equilibrium, any investors
  relative holding of risky assets will be the same
  as in the market portfolio
• Depending on their risk aversions, different
  investors hold portfolios with different mixes of
  riskless asset and the market portfolio
• Example (online two stocks)

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Capital Market Line
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Capital Market Line
E(r)
CML
M
E(rM)
rf
?
?m
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What determines the market risk premium?

• Risk premium on the the market depends on the
  average risk aversion (A) of all market
  participants.
• Example

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Beta and Security Market Line

• If risk is defined as the measure such that as it
  increases, a risk-averse investor would have to
  be compensated by a larger expected return in
  order for her to hold it in her optimal
  portfolio, then the measure of a securitys risk
  is its beta, b, not its standard deviation!
• b tells you how much the securitys rate of
  return changes when the return on the market
  portfolio changes

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CAPM Risk Premium on any Asset

• According to the CAPM, in equilibrium, the risk
  premium on any asset is equal to the product of
• b (or Beta), and
• the risk premium on the market portfolio

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The Security Market Line

• The plot of a securitys risk premium Eri-rf (or
  sometimes security returns) against security beta
  b is the security market line
• Note that the slope of the security market line
  is the market premium
• By CAPM theory, all securities must fall
  precisely on the SML (hence its name)

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Security Market Line (SML)
E(r)
SML
E(rM)
rf
b
bM 1.0
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Security Market Line (SML) Relationships

• SML ri rf ?iE(rm) - rf
• ??????????????????
• ?i? COV(ri,rm) / ?m2
• Slope SML E(rm) - rf
• market risk premium

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The Beta of a Portfolio in CAPM

• When determining the risk of a portfolio
• using standard deviation results in a formula
  thats quite complex
• using beta, the formula is linear

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Examples 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

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Graph of Sample Calculations
E(r)
SML
Rx13
.08
Rm11
Ry7.8
3
b
1.0
1.25 bx
.6 by

• By

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Disequilibrium Example
E(r)
SML
15
Rm11
rf3
b
1.25
1.0
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Disequilibrium Example

• Suppose a security with a ? of 1.25 is offering
  expected return of 15.
• According to SML, it should be 13.
• Under-priced offering too high of a rate of
  return for its level of risk.

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Alpha

• Underpriced stocks plot above the SML
• Overpriced stocks plot below the SML
• The difference between the fair and actually
  expected rates of return on a stock is called the
  stocks alpha.
• Example an alpha fund with alpha1, beta0.5,
  standard deviation0.15, market return0.14, risk
  free rate is 0.06, market standard deviation0.2