1. Security A has an expected return of 8%t and a standard deviation of 20%. Sec

Question

1. Security A has an expected return of 8%t and a standard deviation of 20%. Security B has an expected return of 10% and a standard deviation of 50%.

a) If you place half of your money in each stock, what is your expected return?


b) If you place 30% of your money in A and the remaining 70% in B, what is your expected return?

c) If the correlation between the returns of Securities A and B above is-0.5, what are the
variance and the standard deviation of the returns of each of the two portfolios
you found in parts a) and 1 b) above?

Explanation / Answer

a) Expected Return = (Return from security A * Weight of Security A) + (Return form security B * Weight of Security B)

     Expected Return = (8%*0.5) + (10%*0.5)     = 9%

b) Expected Return = (Return from security A * Weight of Security A) + (Return from Security B * Weight of Security B)

    Expected Return = (8%*0.3) + (10%*0.7)     = 9.4%

c) Correlation between secuirities A & B = -0.5

     Standard Deviation of the return of the Portfolio in Part a) = W12* SD12 + W22*SD22 + 2*W1*W2*r12*SD1*SD2           

         0.52*0.2 + 0.52*0.50 + 2*0.5*0.5*(-0.5)*0.2*0.5   = 0.15

Standard Deviation of the return of the Portfolio in Part a) = W12* SD12 + W22*SD22 + 2*W1*W2*r12*SD1*SD2

        0.32*0.2 + 0.72*0.50 + 2*0.3*0.7*(-0.5)*0.2*0.5   = 0.242

Variance of the Portfolio a = Portfolio Standard Deviation2 = 0.152 = 0.0225

Variance of the Portfolio b = Portfolio Standard Deviation2 = 0.2422 = 0.05856

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