CAPM - Capital Asset Pricing Model

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CAPM - Capital Asset Pricing Model

  1. 1. THE CAPITAL ASSET PRICING MODEL
  2. 2. THE CAPM ASSUMPTIONS <ul><li>NORMATIVE ASSUMPTIONS </li></ul><ul><ul><li>expected returns and standard deviation cover a one-period investor horizon </li></ul></ul><ul><ul><li>nonsatiation </li></ul></ul><ul><ul><li>risk averse investors </li></ul></ul><ul><ul><li>assets are infinitely divisible </li></ul></ul><ul><ul><li>risk free asset exists </li></ul></ul><ul><ul><li>no taxes nor transaction costs </li></ul></ul>
  3. 3. THE CAPM ASSUMPTIONS <ul><li>ADDITIONAL ASSUMPTIONS </li></ul><ul><ul><li>one period investor horizon for all </li></ul></ul><ul><ul><li>risk free rate is the same for all </li></ul></ul><ul><ul><li>information is free and instantaneously available </li></ul></ul><ul><ul><li>homogeneous expectations </li></ul></ul>
  4. 4. THE CAPITAL MARKET LINE <ul><li>THE CAPITAL MARKET LINE (CML) </li></ul><ul><ul><li>the new efficient frontier that results from risk free lending and borrowing </li></ul></ul><ul><ul><li>both risk and return increase in a linear fashion along the CML </li></ul></ul>
  5. 5. THE CAPITAL MARKET LINE <ul><li>THE CAPITAL MARKET LINE </li></ul>M r P  P CML rfr
  6. 6. THE CAPITAL MARKET LINE <ul><li>THE SEPARATION THEOREM </li></ul><ul><ul><li>James Tobin identifies: </li></ul></ul><ul><ul><ul><li>the division between the investment decision and the financing decision </li></ul></ul></ul>
  7. 7. THE CAPITAL MARKET LINE <ul><li>THE SEPARATION THEOREM </li></ul><ul><ul><li>to be somewhere on the CML, the investor initially </li></ul></ul><ul><ul><ul><li>decides to invest and </li></ul></ul></ul><ul><ul><ul><li>based on risk preferences makes a separate financing decision either </li></ul></ul></ul><ul><ul><ul><ul><li>to borrow or </li></ul></ul></ul></ul><ul><ul><ul><ul><li>to lend </li></ul></ul></ul></ul>
  8. 8. THE MARKET PORTFOLIO <ul><li>DEFINITION: the portfolio of all risky assets which contains </li></ul><ul><ul><li>complete diversification </li></ul></ul><ul><ul><li>a central role in the CAPM theory which is the tangency portfolio (M) with the CML </li></ul></ul>
  9. 9. THE SECURITY MARKET LINE (SML) <ul><li>FOR AN INDIVIDUAL RISKY ASSET </li></ul><ul><ul><li>the relevant risk measure is its covariance with the market portfolio (  i, M ) </li></ul></ul><ul><ul><li>DEFINITION: the security market line expresses the linear relationship between </li></ul></ul><ul><ul><ul><li>the expected returns on a risky asset and </li></ul></ul></ul><ul><ul><ul><li>its covariance with the market returns </li></ul></ul></ul>
  10. 10. THE SECURITY MARKET LINE (SML) <ul><li>THE SECURITY MARKET LINE </li></ul><ul><ul><li>or </li></ul></ul><ul><li>where </li></ul>
  11. 11. THE SECURITY MARKET LINE (SML) <ul><li>THE SECURITY MARKET LINE </li></ul><ul><ul><li>THE BETA COEFFICIENT </li></ul></ul><ul><ul><ul><li>an alternative way to represent the covariance of a security </li></ul></ul></ul>
  12. 12. THE SECURITY MARKET LINE (SML) <ul><li>THE SECURITY MARKET LINE </li></ul><ul><ul><li>THE BETA COEFFICIENT </li></ul></ul><ul><ul><ul><li>of a portfolio </li></ul></ul></ul><ul><ul><ul><ul><li>is the weighted average of the betas of its component securities </li></ul></ul></ul></ul>
  13. 13. THE SECURITY MARKET LINE (SML) <ul><li>THE SECURITY MARKET LINE </li></ul>SML  E(r) r rf r M 
  14. 14. THE MARKET MODEL <ul><li>FROM CHAPTER 7 </li></ul><ul><ul><li>assumed return on a risky asset was related to the return on a market index </li></ul></ul>
  15. 15. THE MARKET MODEL <ul><li>DIFFERENCES WITH THE CAPM </li></ul><ul><ul><li>the market model is a single-factor model </li></ul></ul><ul><ul><li>the market model is not an equilibrium model like the CAPM </li></ul></ul><ul><ul><li>the market model uses a market index, </li></ul></ul><ul><ul><li>the CAPM uses the market portfolio </li></ul></ul>
  16. 16. THE MARKET MODEL <ul><li>MARKET INDICES </li></ul><ul><ul><li>the most widely used and known are </li></ul></ul><ul><ul><ul><li>S&P 500 </li></ul></ul></ul><ul><ul><ul><li>NYSE COMPOSITE </li></ul></ul></ul><ul><ul><ul><li>AMEX COMPOSITE </li></ul></ul></ul><ul><ul><ul><li>RUSSELL 3000 </li></ul></ul></ul><ul><ul><ul><li>WILSHIRE 5000 </li></ul></ul></ul><ul><ul><ul><li>DJIA </li></ul></ul></ul>
  17. 17. THE MARKET MODEL <ul><li>MARKET AND NON-MARKET RISK </li></ul><ul><ul><li>Recall that a security’s total risk may be expressed as </li></ul></ul>
  18. 18. THE MARKET MODEL <ul><li>MARKET AND NON-MARKET RISK </li></ul><ul><ul><li>according to the CAPM </li></ul></ul><ul><ul><ul><li>the relationship is identical except the market portfolio is involved instead of the market index </li></ul></ul></ul>
  19. 19. THE MARKET MODEL <ul><li>MARKET AND NON-MARKET RISK </li></ul><ul><ul><li>Why partition risk? </li></ul></ul><ul><ul><ul><li>market risk </li></ul></ul></ul><ul><ul><ul><ul><li>related to the risk of the market portfolio and to the beta of the risky asset </li></ul></ul></ul></ul><ul><ul><ul><ul><li>risky assets with large betas require larger amounts of market risk </li></ul></ul></ul></ul><ul><ul><ul><ul><li>larger betas mean larger returns </li></ul></ul></ul></ul>
  20. 20. THE MARKET MODEL <ul><li>MARKET AND NON-MARKET RISK </li></ul><ul><ul><li>Why partition risk? </li></ul></ul><ul><ul><ul><li>non-market risk </li></ul></ul></ul><ul><ul><ul><ul><li>not related to beta </li></ul></ul></ul></ul><ul><ul><ul><ul><li>risky assets with larger amounts of   I will not have larger E(r) </li></ul></ul></ul></ul><ul><ul><ul><li>According to CAPM </li></ul></ul></ul><ul><ul><ul><ul><li>investors are rewarded for bearing market risk not non-market risk </li></ul></ul></ul></ul>

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