Risk Return and Capital Asset Pricing Model by obr30388

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									ee8190f5-f13e-4629-9378-6f657810a299.xls                                                                                   Model
  Ch 03 Mini Case                                                                                            3/8/2001

                                              Chapter 3. Mini Case

  Situation
  To begin, briefly review the Chapter 2 Mini Case. Then, extend your knowledge of risk and return by
  answering the following questions.


  CAPM
  The Capital Asset Pricing Model is an equilibrium model that specifies the relationship between risk and
  required rate of return for assets held in well diversified portfolios.

  Assumptions
  Investors all think in terms of a single holding period.
  All investors have identical expectations.
  Investors can borrow or lend unlimited amounts at the risk free rate.
  All assets are perfectly divisible.
  There are not taxes and transaction costs.
  All investors are price takers, that is, investors buying and selling will not influence stock prices.
  Quantities of all assets are given and fixed.


  FEASIBLE AND EFFICIENT PORTFOLIOS
  The feasible set of portfolios represent all portfolios that can be constructed from a given set of stocks.
  An efficient portfolio is one that offers: the most return for a given amount of risk or the least risk for a
  given amount of return.




              Expected
              Portfolio             Efficient Set
              Return, kp



                                                                      Feasible Set




                                                                          Risk, sp
       Feasible and Efficient Portfolios
          .




  OPTIMAL PORTFOLIOS
  An investor's optimal portfolio is defined by the tangency point between the efficient set and the investor's
  indifference curve. The inderference curve reflect an investor's attitude toward risk as reflected in his or
  her risk/return trade off function.



         Expected
                                              IB2 I
         Return, kp                                B1


Michael C. Ehrhardt                                             Page 1                                                  7/19/2011
         Expected
ee8190f5-f13e-4629-9378-6f657810a299.xls                                                                              Model
                                            IB2 I
         Return, kp                              B1




                                                                     Optimal Portfolio
                      IA2                                               Investor B
                       IA1

                                                                     Optimal Portfolio
                                                                        Investor A


                                                                       Risk sp
                         Optimal Portfolios
              .


  EFFICIENT SET WITH A RISK-FREE ASSET
  When a risk free asset is added to the feasible set, investors can create portfolios that combine this asset
  with a portfolio of risky asset. The straight line connecting krf with M, the tangency point between the line
  and the old efficiency set, becomes the new efficient frontier.




                      Efficient Set with a Risk-Free Asset

              Expected                                   Z
              Return, kp
                                                                   .B
                  ^
                  kM                  .
                                      M

                                                          The Capital Market

              kRF
                             A   .                           Line (CML):
                                                           New Efficient Set


                                      sM                                     Risk, sp
          .




  OPTIMAL PORTFOLIO WITH A RISK-FREE ASSET
  The optimal portfolio for any investor is the point of tangency between the CML and the investors indifference
  curve.



       Expected
       Return, kp
                                                                 CML
                                 I2
                                      I1



                             . .
           ^                          M
           kM
           ^                 R
           k
Michael C. Ehrhardt
                  R                                           Page 2                                               7/19/2011

                                              R = Optimal
         kRF                                   Portfolio
                                                                                CML
                                             I2
                                                        I1
ee8190f5-f13e-4629-9378-6f657810a299.xls
           ^
           kM
           ^
           k   R
                              M

                                       .R
                                         .                                                                                                  Model




                                                               R = Optimal
         kRF                                                    Portfolio




                                       sR          sM                                  Risk, sp
          .



  Capital Market Line
  The capital market line is all linear combinations of the risk free asset and portfolio M.


              khat=                               krf              +            (km-krf)/sm           x                  sp



                                            Intercept                              Slope                         Risk Measure

  The CML gives the risk and return relationship for efficient portfolios
  The SML , also part of CAPM, gives the risk and return relationship for individual stocks.

          SML =                                   ki                +             (RPm)               x                  b


  Beta Calculation
  Run a regression line of past returns on Stock I versus returns on the market


                                             Year                   km               ki
                                              1                    15%             18%
                                              2                    -5%             -10%
                                              3                    12%             16%



                                                                   Beta Calculation

                                                        25%
                                                        20%
                                                        15%
                      Stock Return




                                                        10%                                               beta calculation

                                                         5%
                                                                                                          Linear (beta
                                                         0%                                               calculation)
                                     -10%     -5%-5% 0%            5%    10%      15%      20%
                                                       -10%                                        y = 1.4441x - 0.0259
                                                                                                        R² = 0.9943
                                                       -15%
                                                              Market Return


                                                                              R2 measures the percent of a stock's variance as explained by the market.

  Relationship between stand alone, market, and diversifiable risk


Michael C. Ehrhardt                                                           Page 3                                                    7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                                                                                    Model

           s2j =                 b2j *s2m                 +           s2ej

              s2j =         stand alone risk of stock J
          2       2
        b j *s     m=       market risk of stock J
              s2ej =        diversifiable risk of stock J


  Test to verify CAPM
  Beta stability test and tests based on the slope of the SML.

  Test of the SML indicate a more-or-less linear relationship between realized return and market risk.
  Slope is less than predicted
  Irrelevance of diversifiable risk specified in the CAPM model can be questioned.
  Betas of individual securities are not good estimators of future risk.
  Betas of ten or more randomly selected stocks are reasonably stable.
  Past betas are good estimates of future portfolio volitility.

  Conclusions regarding CAPM
  It is impossible to verify.
  Recent studies have questioned its validity.
  Investors seemed to be concerned with both market and stand alone risk. Therefore, the SML may not produce the correct estimate of kj.
  CAPM/SML concepts are based on expectations, yeta betas are calculated using historical data.

  CAPM and the Arbitrage Pricing Theory
  The CAPM is a single factor model. The APT proposes that the relationship between risk and return is more complex and may be due
  to multiple factos such as GDP, growth, expected inflation, tax rate changes, and dividend yield.

  Required Return for stock I under the Fama-French-3-Factor Model
  Fama and French propose three factors:
  The excess market return, km-krf.
  The return on, S, a portfolio of small firms minus the return on B, a portfolio of big firms. This return is called
  ksmb, for S minus B.
  The return on, H, a portfolio of firms with high book-to-market ratios minus the return on L, a portfolio of firms
  with low book-to-market ratios. This return is called khml, for H minus L.

  Required return for Stock I

              ki =                  krf                   +         (km-krf) b         +              (ksmb) c          +


                        b= Sensitivity of stock I to the market
                        c= Sensitivity of stock I to the size factor
                        c= Sensitivity of stock I to the book-to-market factor

  b=                                         0.9
  krf =                                   6.8%
  RPm =                                   6.3%
  c=                                        -0.5
  value for size factor =                 4.0%
  d=                                        -0.3
  book-to-market factor=                  5.0%

              ki =                        8.97%

         CAPM =                       12.47%




Michael C. Ehrhardt                                              Page 4                                                 7/19/2011
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                             Excess Returns
                              on Wal-Mart,
                                 kS-kRF
                              120%

                              110%

                              100%

                               90%

                               80%

                               70%

                               60%

                               50%

                               40%                         Excess Returns
                                                    on the Market, k M-kRF
                               30%

                               20%

                               10%

                                0%
      -30%     -20%   -10%           0%       10%    20%          30%




Michael C. Ehrhardt                                          Page 15         7/19/2011

								
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