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Understanding the Capital Asset Pricing Model (CAPM): Key Concepts and Applications

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This summary explores the Capital Asset Pricing Model (CAPM), an essential framework in modern finance. It outlines the model's foundational assumptions, such as investors being price takers and the existence of a market portfolio composed of all risky assets. The Security Market Line (SML), Black's Zero Beta Model, and the relationship between risk and return are detailed. Additionally, the model's equilibrium conditions highlight how risk premiums depend on individual securities' covariances with market returns. This analysis emphasizes CAPM's relevance in assessing investment risks and returns.

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Understanding the Capital Asset Pricing Model (CAPM): Key Concepts and Applications

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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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