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Financial Management



                      Notes         Perfect Negative Correlation


                                    If the returns of securities M and N are perfectly negative correlative the portfolio variance will be:
                                                                 2
                                                    6p 2  = 0.04 (0.5)  + 0.04 (0.5) + 2 (0.5)(0.5) (–1.0)(0.2)(0.2)
                                                        = 0.01 + 0.01 –0.02 = 0
                                    The portfolio variance is zero. The combination of securities M and N completely reduces the
                                    risk.
                                    Weak Positive Correlation: The portfolio variance under weak positive correlation (+0.10) is
                                    given below:
                                                                 2
                                                    6p 2  = 0.04 (0.5)  + 0.04 (0.5)  + 2 (0.5)(0.5) (0.1)(0.2)(0.2)
                                                                           2
                                                        = 0.01 + 0.01 + 0.002 = 0.022
                                    The portfolio variance is less than the variance of individual securities.

                                    Weak Negative Correlation

                                    The portfolio variance under weak negative correlation (–0.10) is given below:
                                                    6p 2  = 0.04 (0.5)  + 0.04 (0.5)  + 2 (0.5)(0.5) (–1.0)(0.2)(0.2)
                                                                 2
                                                                           2
                                                        = 0.01 + 0.01 –0.002 = 0.018
                                    The portfolio variance has reduced more than when the returns were weak positive correlated.

                                    5.4.1  Portfolio Risk N-Security Case
                                    We have so far discussed the computation of risk when a two security portfolio is formed. The
                                    calculations of risk becomes quite involved when a large number of securities are combined to
                                    form a portfolio.

                                    Based on the logic of the portfolio risk in a two security case, the portfolio risk (measured as
                                    variance) in N security can be calculated as follows:
                                                                                           2
                                                               2
                                                                                   2
                                                    6p 2  = n(1/n)  × average variance (+n  – n) (1/n)  × average covariance
                                                        = (1/n) × average variance + (1 – 1/n) × average covariance
                                    It may be noted that the first term on the right hand side (1/n) will become insignificant when
                                    n is very large  and thus the positive variance will become approximately  equal to average
                                    covariance.

                                    5.4.2  Systematic and Unsystematic Risk
                                    Risk has two parts. A part of the risk arises from the uncertainties which are unique to individual
                                    securities and which is diversifiable if large number of securities are combined to form well
                                    diversified portfolios. The  unique risk of individual securities in a portfolio cancel out each
                                    other. This  part  of  the  risk  can  be  totally  reduced  through  diversification  and is  called
                                    unsystematic or unique risk. The examples of unsystematic risk are:
                                    1.   The company loses a big contract in a bid.

                                    2.   The company makes a breakthrough in process innovation.
                                    3.   The R&D expert of the company leaves.
                                    4.   Workers declare strike in a company.

                                    5.   A formidable competitor enters the market.



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