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The Capital Asset Pricing Model

The Capital Asset Pricing Model. Chapter 9. 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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The Capital Asset Pricing Model

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  1. The Capital Asset Pricing Model Chapter 9 Bodi Kane Marcus Ch 5

  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 Problem 9-7,8,9,12; p313

  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 = 1.0 M Security Market Line Problem 9-6,10,11

  11. Bodi Kane Marcus Ch 5 6

  12. Bodi Kane Marcus Ch 5 10

  13. Bodi Kane Marcus Ch 5 11

  14. 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

  15. Sample Calculations for SML RPM=E(rm) - rf = .08rf= .03 x = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% 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 Exercise 9.6 - 9.12

  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% • Underpriced: offering too high of a rate of return for its level of risk

  19. Black’s Zero Beta Model p.301 • 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

  20. Black’s Zero Beta Model Formulation

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

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

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

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

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

  26. Bodi Kane Marcus Ch 5 THank You

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