Following are the details of a portfolio consisting of three shares: Share Portfolio weight Beta Expected return in % Total variance A 0.20 0.40 14…

(i) Portfolio Beta 0.20 x 0.40 + 0.50 x 0.50 + 0.30 x 1.10 = 0.66 (ii) Residual Variance To determine Residual Variance first of all we shall compute the Systematic Risk as follows: β A 2 × σ M 2 = (0.40) 2 (0.01) = 0.0016 β B 2 × σ M 2 = (0.50) 2 (0.01) = 0.0025 β C 2 × σ M 2 = (1.10) 2 (0.01) = 0.0121 Residual Variance A 0.015 – 0.0016 = 0.0134 B 0.025 – 0.0025 = 0.0225 C 0.100 – 0.0121 = 0.0879 (iii) Portfolio variance using Sharpe Index Model Systematic Variance of Portfolio = (0.10) 2 x (0.66) 2 = 0.004356 Unsystematic Variance of Portfolio = 0.0134 x (0.20) 2 + 0.0225 x (0.50) 2 + 0.0879 x (0.30) 2 = 0.014072 Total Variance = 0.004356 + 0.014072 = 0.018428 (iv) Portfolio variance on the basis of Markowitz Theory = (W A X W A Xσ A 2 ) + (W A X W B XCOV AB ) + (W A X W C XCOV AC ) + (W B X W A XCOV AB ) + (W B X W B Xσ B 2 ) + (W B X W C XCOV BC ) + (W C x W A XCOV CA ) + (W C X W B XCOV CB ) + (W C x W C X σ C 2 ) = (0.20 x 0.20 x 0.015) + (0.20 x 0.50 x 0.030) + (0.20 x 0.30 x 0.020) + (0.20 x 0.50 x 0.030) + (0.50 x 0.50 x 0.025) + (0.50 x 0.30 x 0.040) + (0.30 x 0.20 x 0.020) + (0.30 x 0.50 x 0.040) + (0.30 x 0.30 x 0.10) = 0.0006 + 0.0030 + 0.0012 + 0.0030 + 0.00625 + 0.0060 + 0.0012 + 0.0060 + 0.0090 = 0.0363