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Unit 5: Risk and Return Analysis



            Portfolio betas are interpreted in the same way as the betas of individual assets. They indicate  Notes
            the degree of responsiveness  of the  portfolio’s return  to changes in the market return.  For
            example, when the market return increases by 10 per cent, a portfolio with a beta of 0.75 will
            experience a 7.5 per cent increase in its return (0.75 × 10%).
            Again since beta measures the relative volatility of a security’s return, in relation to the market
            return, it should be measured in terms of security’s and markets’ covariance and markets variance.
            Thus   can be measured by:
                 1
                                  Cov(K , K )  s s Cor j  s Cor j
                              =       i 2  m  =  1  m  2  m  =  1  m
                             1        s          s m         sm
            Where,          k = The expected return on indiversifiable security
                             i
                            K  = The expected return on market portfolio
                             m
                            s  = Standard deviation of the security
                             1
                            s  = Standard deviation of the market portfolio
                             m
                       Cov     = Covariance of security with regard to market portfolio
                           (kikm)
                         Cor   = Correlation coefficient of the security with the market
                             jm

                   Example: An investor is seeking the price to pay for a security whose standard deviation
            is 3.00 per cent. The correlation coefficient for the security with the market is 0.8 and the market
            standard deviation is 2.2 per cent. The return for government securities is 7.2 per cent and from
            the market portfolio 12.8 per cent. The investors know that, by calculating the required return he
            can determine the price to pay for the security. What is the required return on the security?
            Solution:
                                               ´
                                             0.8 0.03
                            Beta Coefficient =      =  1.0909
                                              0.022
                      Required rate of return = 0.072 + 1.0909 × (0.128 – 0.072)
                                          = 0.072 + 0.061 = 0.133




               Task  An investor holds two equity shares X and Y in equal proportion with the following
              risks and return characteristics:
                        Return of Security X = 24 %; Return of Security Y = 19 %
                     Standard Deviation of X = 28% Standard Deviation of Y = 23 %
              The return of these securities has a positive correlation of 0.6. You are required to calculate
              the portfolio return and risk. Further suppose that the investor wants to reduce the portfolio
              risk to 15 per cent. How much should the correlative coefficient be to bring the particular
              risk to the desired level?

            5.5.3  Limitations of CAPM
            1.   It  is based on unrealistic assumptions that are far from reality. For example, it is very
                 difficult to find a risk-free security, since inflation causes uncertainty about the real rate of
                 return. The assumption of the equality of lending and borrowing rate is also not correct.
                 Further, investors may not hold highly diversified portfolio or the market indices may
                 not be  well-diversified.



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