Asset Pricing Theory

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• Asset Pricing Theory
• (chapter 5)

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Capital Asset Pricing Model (CAPM)

• Elegant theory of the relationship between risk
  and return
• Used for the calculation of cost of equity and
  required return
• Incorporates the risk-return trade off
• Very used in practice
• Developed by William Sharpe in 1963, who won the
  Nobel Prize in Economics in 1990

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CAPM Basic Assumptions

• Investors hold efficient portfolioshigher
  expected returns involve higher risk.
• Unlimited borrowing and lending is possible at
  the risk-free rate.
• Investors have homogenous expectations.
• There is a one-period time horizon.
• Investments are infinitely divisible.
• No taxes or transaction costs exist.
• Inflation is fully anticipated.
• Capital markets are in equilibrium.
• Examine CAPM as an extension to portfolio theory

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The Equation of the CML is

• Y b mX
• This leads to the Security Market Line (SML)

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SML risk-return trade-off for individual
securities

• Individual securities have
• Unsystematic risk
• Volatility due to firm-specific events
• Can be eliminated through diversification
• Also called firm-specific risk and diversifiable
  risk
• Systematic risk
• Volatility due to the overall stock market
• Since this risk cannot be eliminated through
  diversification, this is often called
  nondiversifiable risk.

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The equation for the SML leads to the CAPM

• ß is a measure of relative risk
• ß 1 for the overall market.
• ß 2 for a security with twice the systematic
  risk of the overall market,
• ß 0.5 for a security with one-half the
  systematic risk of the market.

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Using CAPM

• Expected Return
• If the market is expected to increase 10 and the
  risk free rate is 5, what is the expected return
  of assets with beta1.5, 0.75, and -0.5?
• Beta 1.5 E(R) 5 1.5 ? (10 - 5) 12.5
• Beta 0.75 E(R) 5 0.75 ? (10 - 5)
  8.75
• Beta -0.5 E(R) 5 -0.5 ? (10 - 5)
  2.5

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CAPM and Portfolios

• How does adding a stock to an existing portfolio
  change the risk of the portfolio?
• Standard Deviation as risk
• Correlation of new stock to every other stock
• Beta
• Simple weighted average
• Existing portfolio has a beta of 1.1
• New stock has a beta of 1.5.
• The new portfolio would consist of 90 of the old
  portfolio and 10 of the new stock
• New portfolios beta would be 1.14 (0.91.1
  0.11.5)

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Estimating Beta

• Need
• Risk free rate data
• Market portfolio data
• SP 500, DJIA, NASDAQ, etc.
• Stock return data
• Interval
• Daily, monthly, annual, etc.
• Length
• One year, five years, ten years, etc.
• Use linear regression Rab(Rm-Rf)

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Problems using Beta

• Which market index?
• Which time intervals?
• Time length of data?
• Non-stationary
• Beta estimates of a company change over time.
• How useful is the beta you estimate now for
  thinking about the future?
• Beta is calculated and sold by specialized
  companies

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CAPM used in the industry

• CAPM plus extra risk premiums

• Rs size premium
• Ri industry premium
• Ru firm specific risk premium

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Multifactor models

• Fama-French Three Factor Model
• Beta, size, and B/M
• SMB, difference in returns of portfolio of small
  stocks and portfolio of large stocks
• HML, difference in return between low B/M
  portfolio and high B/M portfolio
• Kenneth French keeps a web site where you can
  obtain historical values of the Fama-French
  factors,
• mba.tuck.dartmouth.edu/pages/faculty/ken.french/da
  ta_library.html

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Sharpe Ratio

• Reward-to-variability measure
• Risk premium earned per unit of total risk
• Higher Sharpe ratio is better.
• Use as a relative measure.
• Portfolios are ranked by the Sharpe measure.

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Treynor Ratio

• Reward-to-volatility measure
• Risk premium earned per unit of systematic risk
• Higher Treynor Index is better.
• Use as a relative measure.

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Example

• A pension funds average monthly return for the
  year was 0.9 and the standard deviation was
  0.5. The fund uses an aggressive strategy as
  indicated by its beta of 1.7.
• If the market averaged 0.7, with a standard
  deviation of 0.3, how did the pension fund
  perform relative to the market?
• The monthly risk free rate was 0.2.
• Solution
• Compute and compare the Sharpe and Treynor
  measures of the fund and market.
• For the pension fund
• For the market
• Both the Sharpe ratio and the Treynor Index are
  greater for the market than for the mutual fund.
  Therefore, the mutual fund under-performed the
  market.

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Learning objectives
Discuss the CAPM assumptions and model Discuss
the CML and SML Discuss the firm specific versus
market risk Discuss the concepts of correlation
and its relation with diversification Know Alpha
and Beta Know how to calculate the require
return portfolio beta Discuss the industry CAPM
model (slide 16) and Fama-French model Discuss
how Beta is estimated and the problems with
Beta Discuss and know how to calculate Sharpe and
Treynor ratios End of chapter problems 5.1, 5.9,
5.15, 5.16,5.1, 5.19, CFA problems 5.1, 5.3