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Chapter 7

Chapter 7. The Capital Asset Pricing Model. Chapter Summary. Objective: To present the basic version of the model and its applicability. Assumptions Resulting Equilibrium Conditions The Security Market Line (SML) Black’s Zero Beta Model CAPM and Liquidity.

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Chapter 7

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  1. Chapter 7 The Capital Asset Pricing Model

  2. Chapter Summary • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

  3. Capital Asset Pricing Model (CAPM) • 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

  4. Assumptions • Individual investors are price takers • Single-period investment horizon • Investments are limited to traded financial assets • No taxes, and transaction costs

  5. Assumptions (cont’d) • Information is costless and available to all investors • Investors are rational mean-variance optimizers • There are homogeneous expectations

  6. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

  7. Resulting Equilibrium Conditions • All investors will hold the same portfolio of 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 • The market portfolio is on the efficient frontier and, moreover, it is the tangency portfolio

  8. Resulting Equilibrium Conditions (cont’d) • Risk premium on the market depends on the average risk aversion of all market participants • Risk premium on an individual security is a function of its covariance with the market

  9. E(r) CML M E(rM) rf  m Capital Market Line

  10. Slope and Market Risk Premium M = The market portfolio rf = Risk free rate E(rM) - rf = Market risk premium = Slope of the CML

  11. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

  12. Expected Return and Risk on Individual Securities • The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio • Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

  13. E(r) SML E(rM) rf ß ß = 1.0 M Security Market Line

  14. SML Relationships  = Cov(ri,rm) / m2 Slope SML = E(rm) - rf = market risk premium E(r)SML = rf + [E(rm) - rf] BetaM = Cov (rM,rM) / sM2 = sM2 / sM2 = 1

  15. Sample Calculations for SML 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%

  16. E(r) SML Rx=13% .08 Rm=11% Ry=7.8% 3% ß .6 1.0 1.25 ß ß ß y m x Graph of Sample Calculations

  17. E(r) SML 15% Rm=11% rf=3% ß 1.25 1.0 Disequilibrium Example

  18. Disequilibrium Example • Suppose a security with a  of 1.25 is offering expected return of 15% • According to SML, it should be 13% • Under-priced: offering too high of a rate of return for its level of risk

  19. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

  20. Black’s 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

  21. Black’s Zero Beta Model Formulation

  22. E(r) Q P E[rz (Q)] Z(Q) Z(P) E[rz (P)] s Efficient Portfolios and Zero Companions

  23. Zero Beta Market Model CAPM with E(rz (M)) replacing rf

  24. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

  25. CAPM & Liquidity • Liquidity – cost or ease with which an asset can be sold • Illiquidity Premium • Research supports a premium for illiquidity • Amihud and Mendelson

  26. CAPM with a Liquidity Premium f (ci) = liquidity premium for security i f (ci) increases at a decreasing rate

  27. Average monthly return (%) Bid-ask spread (%) Illiquidity and Average Returns

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