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					Chapter 9

  The Capital Asset
   Pricing Model
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
               Assumptions

 Individual investors are price takers
 Single-period investment horizon
 Investments are limited to traded financial
  assets
 No taxes, and transaction costs
         Assumptions (cont’d)

 Information is costless and available to all
  investors
 Investors are rational mean-variance
  optimizers
 Homogeneous expectations
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
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
        Capital Market Line
    E(r)

                         CML
               M
E(rM)
   rf


                   m
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
    M
             =   Slope of the CAPM
    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
          Security Market Line
        E(r)


                                 SML

E(rM)

   rf


                                   ß
                ß       = 1.0
                    M
           SML Relationships

= [COV(ri,rm)] / m2
Slope SML = E(rm) - rf
                    = market risk premium
           SML = rf + [E(rm) - rf]
          Betam = [Cov (ri,rm)] / m2
                    = m2 / m2 = 1
   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%
Graph of Sample Calculations
      E(r)
                                           SML

Rx=13%                                       .08
Rm=11%
Ry=7.8%

   3%
                                                 ß
             .6       1.0       1.25
             ß         ß          ß
                  y         m          x
    Disequilibrium Example
     E(r)

                         SML
  15%

Rm=11%


 rf=3%

                               ß
            1.0   1.25
      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
     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
Black’s Zero Beta Model Formulation


                                             Cov(ri , rP )  Cov(rP , rQ )
                    
 E (ri )  E (rQ )  E (rP )  E (rQ )          P  Cov(rP , rQ )
                                                  2
      Efficient Portfolios and Zero
              Companions
            E(r)




                          Q
                   P
E[rz (Q)]          Z(Q)
E[rz (P)]                 Z(P)


                                      
     Zero Beta Market Model



                          
 E (ri )  E (rZ ( M ) )  E (rM )  E (rZ ( M ) )      Cov(ri , rM )
                                                                2
                                                                 M



CAPM with E(rz (m)) replacing rf
          CAPM & Liquidity

 Liquidity
 Illiquidity Premium
 Research supports a premium for illiquidity
   - Amihud and Mendelson
CAPM with a Liquidity Premium

                             
E (ri )  rf   i E (ri )  rf  f (ci )

   f (ci) = liquidity premium for security i
   f (ci) increases at a decreasing rate
            Illiquidity and Average
                     Returns
Average monthly return(%)




                               Bid-ask spread (%)

				
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posted:9/25/2012
language:English
pages:22