a) calculate the expected return for each share(A,B,C) and based on the expected

Question

a) calculate the expected return for each share(A,B,C) and based on the expected return and the risk,how will the investment be ranked?

b) calculate the correlation co efficient and the covariance between each pair of investment, portfolio AB,AC, and BC.

c) if investment A & B are combined in a portfolio in the propotion of 60% and 40% respectively,what is the expected returns and the standard deviation of the portfolio.

d) what is the expected return and the standard deviation of the portfolio made up of 40% in A, 30% in B and 30% in C

market conditions probability A B C Optmistic 0.25 16% 4% 20% Normal 0.50 12% 6% 14% Persmistic 0.25 8% 8% 8%

Explanation / Answer

a)Stock :

A = (.25 * 16) +(.50 *12)+(.25*8)

   = 4 + 6 + 2

= 12%

B = (.25 *4) +(.50 *6) +(.25*8)

    = 1 + 3 +2

   = 6%

C = (.25 *20) +(.50 *14 ) +(.25 *8)

=5 + 7 + 2

= 14%

Ranking Stock C -1

                      A -2

                      B - 3

b)covariance between A and B

covariance of AB= - 4

coefficient of correlation = COV ab / SD A *SD B

                                = -4 / (8*2)

                               = -4 / 16

                               = -.25

Covariance of BC:

Covariance of BC = - 6

coeeficient of correlation = - 6/ (2*18)

                                     = - .167

covariance between AC

covariance of AC = 12

Coeeficient of correlation = 12 /(8*18)

                                      = .0833

c)Expected return = (12*.60 )+(6*.40)

                           = 7.2 + 2.4

                            = 9.6%

SD = (8*.60) +(2*.40)

        = 4.8 + .8

         =5.6%

d)EXpected return = (12*.40)+(6*.30)+(14*.30)

                           =4.8+ 1.8 + 4.2

                             = 10.8%

SD = (8 *.40)+(2*.30)+(18*.30)

          = 3.2 + .6 + 5.4

          = 9.2%

covariance standard deviation Probability Stock A   (x) Stock B (y) (X -average return on A) (y-Average return on B) (x-AR of A)(y-AR of B)P (X-AR of A)^2 *Probability (Y-AR OF B)^2*probability .25 16 4 4    [16-12] -2    [4-6] -2    [4*-2*.25] 4    [4* 4*.25] 1    [-2*-2*.25] .50 12 6 0    [12-12] 0     [6-6] 0 0 0 .25 8 8 -4   [8-12] 2    [8-6] -2    [-4*2*.25] 4    [-4*-4*.25] 1     [2*2*.25] expected return (calculated in a) 12 6 covariance AB = -4 SD of A= 8 SD of B= 2

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