Chapter 7: The Capital Asset Pricing Model

1
Chapter 7 The Capital Asset Pricing Model

• Objective To present the model.
• Assumptions
• Resulting Equilibrium Conditions
• The Security Market Line (SML)
• CAPM and Liquidity
• Skip 7.2 pp.262-267
• Understanding the lecture is sufficient for
  section 7.3.

2
7.1 Capital Asset Pricing Model (CAPM)

• Equilibrium model that underlies modern financial
  theory
• The CAPM is based on principles of
  diversification with simplified assumptions
• Markowitz, Sharpe, Lintner and Mossin developed
  the model.

3
Assumptions

• Individual investors are price takers
• Single-period investment horizon
• Investments are limited to traded financial
  assets
• No taxes, and transaction costs
• Information is costless and available to all
  investors
• Investors are rational mean-variance optimizers
• There are homogeneous expectations

4
Recall Capital Market Line
Slope of the CML E(rp)-rf/?p
5
CAPM relation

• All investors will hold the same portfolio of
  risky assets, m, the tangency portfolio CML
  result.
• Market portfolio contains all securities and the
  proportion of each security is its market value
  as a percentage of total market value
• The CAPM says that
• m is the market portfolio
• E(ri) rf ?i E(rm) - rf
• The risk premium on asset i depends on the
  asset is contribution to the risk of the market
  portfolio, i.e., covariance of asset is returns
  with market portfolio return

6
Security Market Line (SML)
? ? Cov(ri,rm) / ?m2 Slope of SML E(rm) rf
market risk premium E(ri) rf ?i E(rm) -
rf BetaM Cov (rM,rM)/sM sM2 /sM2 1
7
Example CAPM

• E(rm) - rf .08 rf .03
• a) ?x 1.25
• E(rx) .03 1.25(.08) .13 or 13
• b) ?y .6
• E(ry) .03 .6(.08) .078 or 7.8

8
Graph of Sample Calculations
9
Disequilibrium Example

• Suppose a security with a ? of 1.25 has expected
  return of 15
• According to SML, it should be 13
• The expected return is too high for its level of
  risk (or equivalently, the stock is underpriced)

10
7.2 Blacks Zero Beta Model

• Absence of a risk-free asset
• Combinations of portfolios on the efficient
  frontier are efficient
• All frontier portfolios have companion portfolios
  that are uncorrelated
• Returns on individual assets can be expressed as
  linear combinations of efficient portfolios

11
Efficient portfolios and zero companions
12
7.3 CAPM Liquidity

• Liquidity cost or ease with which an asset can
  be sold
• Illiquidity Premium
• Research (Amihud and Mendelson) supports a
  premium for illiquidity
• CAPM with liquidity premium
• E(ri) rf ?i E(rm) - rf f(ci)
• f(ci) liquidity premium for security i.
• f(ci) increases at a decreasing rate

13
Illiquidity and Average Returns