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Chapter 9

The Capital Asset Pricing Model. Chapter 9. Capital Asset Pricing Model (CAPM). It is the 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. The Capital Asset Pricing Model Chapter 9

  2. Capital Asset Pricing Model (CAPM) • It is the 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. • There are 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 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. Capital Market Line E(r) CML M E(rM) rf  m

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

  10. Security Market Line E(r) SML E(rM) rf b bM = 1.0

  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. Graph of Sample Calculations E(r) SML Rx=13% .08 Rm=11% Ry=7.8% 3% b .6 by 1.0 1.25 bx

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

  15. Disequilibrium Example (cont.) • 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.

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

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

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