Question

You are given the following data

                       Year            HPR of Stock A      HPR of Stock B      HPR of Stock C

                         2017                12%                            16%                         12%

                        2018                 14%                            14%                         14%

                        2019                 16%                            12%                         16%

(1) Calculate expected rate of return for each stock

(2) Calculate standard deviation for each stock

(3) Calculate coefficient of variation for each stock. If you will choose only one stock for investment, which stock will you choose? Why?

(4) How much is correlation coefficient between A and B? between A and C?

(5) Calculate expected rate of return and standard deviation for the portfolio A + B. Assume you invest equal proportion (50%) in each stock

(6) Calculate expected rate of return and standard deviation for the portfolio A+C. Assume you invest equal proportion (50%) in each stock

(7) Which portfolio do you recommend? Why?

Answer 1

(1) Expected rate of return:

Stock A = (12+14+16)/3 = 14%

Stock B = (16+14+12)/3 = 14%

Stock C = (12+14+16)/3 = 14%

(2) Standard deviation of each stock:

Stock A:

Variance = {1/3 * (12-14)2}+{1/3 * (14-14)2}+ {1/3 * (16-14)2}

= 1/3*4+1/3*4

=8/3

Standard Deviation = (8/3)1/2

=1.63%

Stock B:

Variance = {1/3 * (16-14)2}+{1/3 * (14-14)2}+ {1/3 * (12-14)2}

= 1/3*4+1/3*4

=8/3

Standard Deviation = (8/3)1/2

=1.63%

Stock C:

Variance = {1/3 * (12-14)2}+{1/3 * (14-14)2}+ {1/3 * (16-14)2}

= 1/3*4+1/3*4

=8/3

Standard Deviation = (8/3)1/2

=1.63%

(3) Coefficient of variance = Sd/Expected return*100

Stock A = 1.63/14*100

= 11.64%

Stock B = 1.63/14*100

= 11.64%

Stock C = 1.63/14*100

= 11.64%

(4) Correlation of Coefficient:

rAB = CovarianceAB /SdA * SdB

Covariance between A and B = {1/3*(12-14)(16-14)}+ {1/3*(14-14)(14-14)}+{1/3*(16-14)(12-14)}

= {1/3*(-2)*2}+{1/3*0*0}+{1/3*2*(-2)}

={1/3*(-4)}+ {1/3*0}+{1/3*(-4)}

= (-8/3)

rAB = (-8/3)/(1.63*1.63)

= (-1)

rAC = CovarianceAC /SdA * SdC

Covariance between A and C = {1/3*(12-14)(12-14)}+ {1/3*(14-14)(14-14)}+{1/3*(16-14)(16-14)}

= {1/3*(-2)*(-2)}+{1/3*0*0}+{1/3*2*2}

={1/3*4}+ {1/3*0}+{1/3*4}

= 8/3

rAC = (8/3)/(1.63*1.63)

= 1

(5) Expected rate of return of A and B = (0.5*14)+ (0.5*14)

=14%

Standard deviation of A and B = {(X2A Sd2A)+ (X2B Sd2B )+(2 XA XB(SdA SdB rAB))}1/2

= {(0.52 *1.632)+(0.52*1.632)+(2*0.5*0.5*1.63*1.63*(-1))}1/2

=(0.25*2.66)+ (0.25*2.66)+(2*0.25*2.66*(-1))}1/2

=(0.66+0.67-1.33)

=0

(6) Expected rate of return of A and C = (0.5*14)+ (0.5*14)

=14%

Standard deviation of A and C = {(X2A Sd2A)+ (X2C Sd2C )+(2 XA XC(SdA SdB rAC))}1/2

= {(0.52 *1.632)+(0.52*1.632)+(2*0.5*0.5*1.63*1.63*(1))}1/2

=(0.25*2.66)+ (0.25*2.66)+(2*0.25*2.66*(1))}1/2

=(0.66+0.67+1.33)1/2

=(2.66)1/2

=1.63%

(7) Portfolio consisting stocks A and B having Expected rate of return is 14% with 0% risk and Portfolio consisting stocks A and C having Expected rate of return is 14% with 1.63% risk, since the both portfolio have same return but the risk is low in Portfolio consisting stock A and B, so the Portfolio A and B should be selected.