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Chapter 9

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

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  1. Chapter 9 Capital Market Theory

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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):

  9. 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?

  10. Security Market Line • Equation for expected return for an individual stock similar to CML Equation

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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)

  23. 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

  24. 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

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