Week 5

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INVESTMENTS | BODIE, KANE, MARCUS

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Chapter Nine

The Capital Asset Pricing Model

INVESTMENTS | BODIE, KANE, MARCUS

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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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INVESTMENTS | BODIE, KANE, MARCUS

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Assumptions

  • Investors optimize portfolios a la Markowitz
  • Investors use identical input list for efficient frontier
  • Same risk-free rate, tangent CAL and risky portfolio
  • Market portfolio is aggregation of all risky portfolios and has same weights

INVESTMENTS | BODIE, KANE, MARCUS

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Resulting Equilibrium Conditions

  • All investors will hold the same portfolio for risky assets – market portfolio

  • Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

INVESTMENTS | BODIE, KANE, MARCUS

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Figure 9.1 The Efficient Frontier and the Capital Market Line

INVESTMENTS | BODIE, KANE, MARCUS

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Market Risk Premium

  • The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor:


E(RM) = Ᾱσ2M

Where σ2M is the variance of the market portfolio and Ᾱ is the average degree of risk aversion across investors

INVESTMENTS | BODIE, KANE, MARCUS

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Return and Risk For Individual Securities

  • The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio.
  • An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio.

INVESTMENTS | BODIE, KANE, MARCUS

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GE Example

  • Covariance of GE return with the market portfolio:

  • Therefore, the reward-to-risk ratio for investments in GE would be:

INVESTMENTS | BODIE, KANE, MARCUS

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GE Example

  • Reward-to-risk ratio for investment in market portfolio:

  • Reward-to-risk ratios of GE and the market portfolio should be equal:

INVESTMENTS | BODIE, KANE, MARCUS

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GE Example

  • The risk premium for GE:

  • Restating, we obtain:

INVESTMENTS | BODIE, KANE, MARCUS

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Expected Return-Beta Relationship

  • CAPM holds for the overall portfolio because:

  • This also holds for the market portfolio:

INVESTMENTS | BODIE, KANE, MARCUS

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Figure 9.2 The Security Market Line

INVESTMENTS | BODIE, KANE, MARCUS

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Figure 9.3 The SML and a Positive-Alpha Stock

INVESTMENTS | BODIE, KANE, MARCUS

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Single-Index Model and Realized Returns

  • To move from expected to realized returns, use the index model in excess return form:

  • The index model beta coefficient is the same as the beta of the CAPM expected return-beta relationship.

INVESTMENTS | BODIE, KANE, MARCUS

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Assumptions of the CAPM

  • Individuals
  • Mean-variance optimizers
  • Homogeneous expectations
  • All assets are publicly traded
  • Markets
  • All assets are publicly held
  • All information is available
  • No taxes
  • No transaction costs

INVESTMENTS | BODIE, KANE, MARCUS

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Extensions of the CAPM

  • Zero-Beta Model
  • Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks
  • Consideration of labor income and non-traded assets

INVESTMENTS | BODIE, KANE, MARCUS

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Extensions of the CAPM

  • Merton’s Multiperiod Model and hedge portfolios
  • Incorporation of the effects of changes in the real rate of interest and inflation
  • Consumption-based CAPM
  • Rubinstein, Lucas, and Breeden
  • Investors allocate wealth between consumption today and investment for the future

INVESTMENTS | BODIE, KANE, MARCUS

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Liquidity and the CAPM

  • Liquidity: The ease and speed with which an asset can be sold at fair market value
  • Illiquidity Premium: Discount from fair market value the seller must accept to obtain a quick sale.
  • Measured partly by bid-asked spread
  • As trading costs are higher, the illiquidity discount will be greater.

INVESTMENTS | BODIE, KANE, MARCUS

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Figure 9.5 The Relationship Between Illiquidity and Average Returns

INVESTMENTS | BODIE, KANE, MARCUS

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Liquidity Risk

  • In a financial crisis, liquidity can unexpectedly dry up.
  • When liquidity in one stock decreases, it tends to decrease in other stocks at the same time.
  • Investors demand compensation for liquidity risk
  • Liquidity betas

INVESTMENTS | BODIE, KANE, MARCUS

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CAPM and World

  • Academic world
  • Cannot observe all tradable assets
  • Impossible to pin down market portfolio
  • Attempts to validate using regression analysis
  • Investment Industry
  • Relies on the single-index CAPM model
  • Most investors don’t beat the index portfolio

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