L Pch10

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L Pch10

  1. 1. Investments Chapter 10: The Capital Asset Pricing Model
  2. 2. Two Definitions Explained <ul><li>Asset Pricing Theories </li></ul><ul><li>Asset pricing theories try to explain the expected rates of return of assets and why they differ both among each other and over time. </li></ul><ul><li>Equilibrium Rates of Return </li></ul><ul><li>A market is in equilibrium when all investors hold their optimal portfolio and hence there is no reason for further transactions. </li></ul>
  3. 3. The Basic Question of the CAPM <ul><li>‘ What are the equilibrium rates of return if all investors apply the mean-variance criterion to an identical mean-variance efficient set?’ </li></ul>
  4. 4. Two Additional Concepts Introduced in the CAPM Framework <ul><li>The Risk-free Asset </li></ul><ul><li>The rate of return this asset is known with certainty. (Short-term treasury bills often proxy for the risk-free rate) </li></ul><ul><li>The Market Portfolio </li></ul><ul><li>Includes all available risky capital at their relative market value. </li></ul>
  5. 5. Assumptions Behind the CAPM <ul><li>The capital market is characterized by perfect competition. </li></ul><ul><li>All investors choose their portfolio according to the mean-variance criterion. </li></ul><ul><li>All investors have homogeneous expectations regarding the future in terms of means, variances and covariances. (This implies investors have the same investment horizon.) </li></ul><ul><li>Investors can borrow and lend at the risk-free rate. </li></ul><ul><li>UNDER THESE ASSUMPTIONS ALL INVESTORS FACE IDENTICAL EFFICIENT FRONTIERS. </li></ul>
  6. 6. The Opportunity Line: I <ul><li>Assumptions: </li></ul><ul><li>1. Investor can borrow and lend at the risk-free rate. </li></ul><ul><li>2. Investor can invest in one risky asset. </li></ul><ul><li>Under these assumption the expected return of this portfolio is a linear positive relation of the standard deviation of the risky asset. </li></ul>
  7. 7. The Opportunity Line: II - Illustration Exhibit 10.1 Investment opportunities with risk-free asset Source: From Introduction to Investments , 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
  8. 8. The Capital Market Line: I <ul><li>Opportunity line assumes one available risky asset. The capital market line (CML) drops this assumption. </li></ul><ul><li>Investors can invest in many risky assets, creating many opportunity lines. </li></ul><ul><li>It can be shown that investors will choose the same portfolio of risky assets , maximizing the slopes of the individual opportunity lines, known as the tangency portfolio. </li></ul>
  9. 9. The Capital Market Line: II <ul><li>Since all investors hold the tangency portfolio, this portfolio equals the market portfolio. </li></ul><ul><li>By mixing the market portfolio with borrowing and lending of the risk-free asset one gets a linear positive line analogous to the opportunity line. </li></ul><ul><li>But, note that the market portfolio is not an individual asset. By mixing it with the risk-free rate, we end up holding a portfolio of risky assets and the risk-free asset. </li></ul>
  10. 10. The Separation Principle <ul><li>Given the assumptions behind the CAPM, and the resulting CML, one can separate the investment process into two stages: </li></ul><ul><li>1. Determining the market portfolio </li></ul><ul><li>Because all investors hold the same portfolio, there ’s no need to know investors’ individual preferences at this stage. </li></ul><ul><li>2. Adjusting the return characteristics by mixing the market portfolio with the risk-free asset </li></ul><ul><li>This stage is based on each investor ’s individual preferences. </li></ul>
  11. 11. Separating Systemic from Nonsystemic Risk <ul><li>Under the separation principle all investors hold the market portfolio. </li></ul><ul><li>The relevant risk measure for an individual asset than logically becomes its contribution to the risk of the market portfolio. </li></ul><ul><li>Consequently, investors need to be compensated for bearing systemic risk but not for non-systemic risk. </li></ul>
  12. 12. Definition of Risk When Investors Hold the Market Portfolio <ul><li>Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (  )of the security. </li></ul><ul><li>Beta measures the responsiveness of a security to movements in the market portfolio. </li></ul>
  13. 13. Aggressive, Neutral and Defensive Assets <ul><li>Aggressive Asset </li></ul><ul><li> i > 1, asset i has more (systematic) risk than the market. </li></ul><ul><li>Neutral Asset </li></ul><ul><li> i  1, asset i has the same (systematic) risk as the market. </li></ul><ul><li>Defensive Asset </li></ul><ul><li> i < 1, asset i has less (systematic) risk than the market. </li></ul>
  14. 14. The Security Market Line: I <ul><li>Under the assumptions of the CAPM, only compensating investors for bearing systemic risk, the following linear risk-return relation (for both individual assets and portfolios) should hold: </li></ul><ul><li>E ( R i )  r  [ E ( R m ) – r ]   i </li></ul><ul><li>   </li></ul><ul><li>Expected Rate of Return  Risk-Free Rate  Risk Premium </li></ul>
  15. 15. Expected Return on an Individual Security <ul><li>This formula is called the Capital Asset Pricing Model (CAPM) </li></ul><ul><li>Assume  i = 0, then the expected return is R F . </li></ul><ul><li>Assume  i = 1, then </li></ul>Expected return on a security = Risk-free rate + Beta of the security × Market risk premium
  16. 16. The Security Market Line: II – The Risk Premium <ul><li>The risk premium is the expected return investors require above and beyond what can be earned on the risk-free asset: </li></ul><ul><li> [ E ( R m ) – r ]   i </li></ul><ul><li> </li></ul><ul><li> market risk premium Asset i’s Beta </li></ul>
  17. 17. The Security Market Line: III – Illustration Exhibit 3.4 Security line (SML) Source: From Introduction to Investments , 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
  18. 18. Estimating an Asset ’s Beta: I – The Characteristic Line <ul><li>Besides being an indication of the relative riskiness of an asset, the beta also measures the sensitivity to market movements . </li></ul><ul><li>The regression line describing the relationship between Ri (Return on Asset i ) and Rm (Return on Market Portfolio) is called the characteristic line of Asset i . </li></ul>
  19. 19. Estimating an Asset ’s Beta: II – The Characteristic Line Exhibit 10.4 Examples of the characteristic line Source: From Introduction to Investments , 2nd edn, by Levy. © 1999. Reprinted with permission of South-Western, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730-2215.
  20. 20. Estimating an Asset ’s Beta: III – The Characteristic Line <ul><ul><li>The Characteristic Line can be written as: </li></ul></ul><ul><ul><li>R i – r   i   i  R m – r ]  e i </li></ul></ul><ul><ul><li>  </li></ul></ul><ul><ul><li> i intercept of the regression line </li></ul></ul><ul><ul><li> i slope of the regression line </li></ul></ul><ul><ul><li>e t firm-specific factor with mean E ( e i )=0 and variance  2 e,i </li></ul></ul>
  21. 21. Estimating an Asset ’s Beta: IV – The Characteristic Line <ul><ul><li>Use regression analysis to find the statistically best fit to the relationship between Ri and Rm: </li></ul></ul>Exhibit 10.8 Estimating the characteristic line for Microsoft
  22. 22. Estimates of  for Selected Stocks Stock Beta Bank of America 1.55 Borland International 2.35 Travelers, Inc. 1.65 Du Pont 1.00 Kimberly-Clark Corp. 0.90 Microsoft 1.05 Green Mountain Power 0.55 Homestake Mining 0.20 Oracle, Inc. 0.49
  23. 23. Theoretical Extensions of the CAPM <ul><ul><li>Zero-beta model. </li></ul></ul><ul><ul><li>GCAPM. </li></ul></ul><ul><ul><li>ICAPM. </li></ul></ul><ul><ul><li>CCAPM. </li></ul></ul><ul><ul><li>3M CAPM. </li></ul></ul>
  24. 24. Empirical Validity of the CAPM <ul><li>Two tests: </li></ul><ul><li>Check if the underlying assumptions of the CAPM are realistic. </li></ul><ul><li>Empirically test the degree to which the CAPM predicts actual security prices. </li></ul>
  25. 25. Empirically Testing the Predictions of the CAPM <ul><li>Often-used method: </li></ul><ul><li>Two-Pass Regression Methodology </li></ul><ul><li>Step 1 : Establish sample data. </li></ul><ul><li>Step 2 : Estimate characteristic lines. </li></ul><ul><li>Step 3 : Estimate the security market line. </li></ul><ul><li>Step 4 : Test predictions of the CAPM. </li></ul>
  26. 26. CAPM Anomalies <ul><li>Several phenomena discovered that seem inconsistent with the CAPM: </li></ul><ul><li>1. The size effect. </li></ul><ul><li>2. The value effect. </li></ul><ul><li>3. The momentum effect. </li></ul>
  27. 27. Methodological Problems in Testing the CAPM <ul><li>Benchmark error. </li></ul><ul><li>Time variation of the return distribution. </li></ul><ul><li>Statistical problems with the test methodology. </li></ul><ul><li>Data mining, data snooping and sample selection bias. </li></ul>

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