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Chapter 9. Capital Market Theory. Learning Objectives. Explain capital market theory and the Capital Asset Pricing Model (CAPM). Discuss the importance and composition of the market portfolio.

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chapter 9

Chapter 9

Capital Market Theory

learning objectives
Learning Objectives
  • Explain capital market theory and the Capital Asset Pricing Model (CAPM).
  • Discuss the importance and composition of the market portfolio.
  • Describe two important relationships in CAPM as represented by the capital market line and the security market line.
  • Describe how betas are estimated and how beta is used.
  • Discuss the Arbitrage Pricing Theory as an alternative to the Capital Asset Pricing Model.
capital asset pricing model
Capital Asset Pricing Model
  • Focus on the equilibrium relationship between the risk and expected return on risky assets
  • Builds on Markowitz portfolio theory
  • Each investor is assumed to diversify his or her portfolio according to the Markowitz model
capm assumptions
All investors:

Use the same information to generate an efficient frontier

Have the same one-period time horizon

Can borrow or lend money at the risk-free rate of return

No transaction costs, no personal income taxes, no inflation

No single investor can affect the price of a stock

Capital markets are in equilibrium

CAPM Assumptions
market portfolio
Market Portfolio
  • Most important implication of the CAPM
    • All investors hold the same optimal portfolio of risky assets
    • The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
    • The portfolio of all risky assets is the optimal risky portfolio
      • Called the market portfolio
characteristics of the market portfolio
Characteristics of the Market Portfolio
  • All risky assets must be in portfolio, so it is completely diversified
    • Contains only systematic risk
  • All securities included in proportion to their market value
  • Unobservable, but proxied by S&P/TSX Composite Index
  • In theory, should contain all risky assets worldwide
capital market line
Capital Market Line
  • Line from RF to L is capital market line (CML)
  • x = risk premium

= E(RM) - RF

  • y = risk = M
  • Slope = x/y

= [E(RM) - RF]/M

  • y-intercept = RF

L

M

E(RM)

x

RF

y

M

Risk

capital market line8
Capital Market Line
  • Slope of the CML is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market
  • Relationship between risk and expected return for portfolio P (Equation for CML):
security market line
Security Market Line
  • CML Equation only applies to markets in equilibrium and efficient portfolios
  • The Security Market Line depicts the tradeoff between risk and expected return for individual securities
  • Under CAPM, all investors hold the market portfolio
    • How does an individual security contribute to the risk of the market portfolio?
security market line10
Security Market Line
  • Equation for expected return for an individual stock similar to CML Equation
security market line11
Security Market Line
  • Beta = 1.0 implies as risky as market
  • Securities A and B are more risky than the market
    • Beta > 1.0
  • Security C is less risky than the market
    • Beta < 1.0

SML

E(R)

A

E(RM)

B

C

RF

0

0.5

1.0

1.5

2.0

BetaM

security market line12
Security Market Line
  • Beta measures systematic risk
    • Measures relative risk compared to the market portfolio of all stocks
    • Volatility different than market
  • All securities should lie on the SML
    • The expected return on the security should be only that return needed to compensate for systematic risk
sml and asset values
SML and Asset Values

Er

UnderpricedSML: Er = rf +  (Erm – rf)

Overpriced

rf

β

Underpriced  expected return > required return according to CAPM

 lie “above” SML

Overpriced  expected return < required return according to CAPM

 lie “below” SML

Correctly priced  expected return = required return according to CAPM

 lie along SML

capm s expected return beta relationship
CAPM’s Expected Return-Beta Relationship
  • Required rate of return on an asset (ki) is composed of
    • risk-free rate (RF)
    • risk premium (i [ E(RM) - RF ])
      • Market risk premium adjusted for specific security

ki = RF +i [ E(RM) - RF ]

    • The greater the systematic risk, the greater the required return
estimating the sml
Estimating the SML
  • Treasury Bill rate used to estimate RF
  • Expected market return unobservable
    • Estimated using past market returns and taking an expected value
  • Estimating individual security betas difficult
    • Only company-specific factor in CAPM
    • Requires asset-specific forecast
estimating beta
Estimating Beta
  • Market model
    • Relates the return on each stock to the return on the market, assuming a linear relationship

Rit =i +i RMt + eit

  • Characteristic line
    • Line fit to total returns for a security relative to total returns for the market index
how accurate are beta estimates
How Accurate Are Beta Estimates?
  • Betas change with a company’s situation
    • Not stationary over time
  • Estimating a future beta
    • May differ from the historical beta
  • RMt represents the total of all marketable assets in the economy
    • Approximated with a stock market index
    • Approximates return on all common stocks
how accurate are beta estimates18
How Accurate Are Beta Estimates?
  • No one correct number of observations and time periods for calculating beta
  • The regression calculations of the true  and  from the characteristic line are subject to estimation error
  • Portfolio betas more reliable than individual security betas
test of capm
Test of CAPM
  • Empirical SML is “flatter” than predicted SML
  • Fama and French (1992)
    • Market
    • Size
    • Book-to-market ratio
  • Roll’s Critique
    • True market portfolio is unobservable
    • Tests of CAPM are merely tests of the mean-variance efficiency of the chosen market proxy
arbitrage pricing theory
Arbitrage Pricing Theory
  • Based on the Law of One Price
    • Two otherwise identical assets cannot sell at different prices
    • Equilibrium prices adjust to eliminate all arbitrage opportunities
  • Unlike CAPM, APT does not assume
    • single-period investment horizon, absence of personal taxes, riskless borrowing or lending, mean-variance decisions
factors
Factors
  • APT assumes returns generated by a factor model
  • Factor Characteristics
    • Each risk must have a pervasive influence on stock returns
    • Risk factors must influence expected return and have nonzero prices
    • Risk factors must be unpredictable to the market
apt model
APT Model
  • Most important are the deviations of the factors from their expected values
  • The expected return-risk relationship for the APT can be described as:

E(Rit) =a0+bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +… +bin (risk premium for factor n)

apt model23
APT Model
  • Reduces to CAPM if there is only one factor and that factor is market risk
  • Roll and Ross (1980) Factors:
    • Changes in expected inflation
    • Unanticipated changes in inflation
    • Unanticipated changes in industrial production
    • Unanticipated changes in the default risk premium
    • Unanticipated changes in the term structure of interest rates
problems with apt
Problems with APT
  • Factors are not well specified ex ante
    • To implement the APT model, the factors that account for the differences among security returns are required
      • CAPM identifies market portfolio as single factor
  • Neither CAPM or APT has been proven superior
    • Both rely on unobservable expectations