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Chapter 9

Chapter 9. The Capital Asset Pricing Model. Capital Asset Pricing Model (CAPM). Equilibrium model that underlies all modern financial theory Derived using principles of diversification with simplified assumptions

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Chapter 9

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  1. Chapter 9 The Capital AssetPricing Model

  2. 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

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

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

  5. 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

  6. 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

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

  8. Slope and Market Risk Premium M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk = Slope of the CAPM  M

  9. 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

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

  11. SML Relationships = [COV(ri,rm)] / m2 Slope SML = E(rm) - rf = market risk premium SML = rf + [E(rm) - rf] Betam = [Cov (ri,rm)] / sm2 = sm2 / sm2 = 1

  12. Sample Calculations for SML E(rm) - rf = .08 rf = .03 x = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% y = .6 e(ry) = .03 + .6(.08) = .078 or 7.8%

  13. 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

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

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

  16. 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

  17. Black’s Zero Beta Model Formulation

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

  19. Zero Beta Market Model CAPM with E(rz (m)) replacing rf

  20. CAPM & Liquidity • Liquidity • Illiquidity Premium • Research supports a premium for illiquidity • Amihud and Mendelson

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

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

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