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: βA² × σM² = (0.40)²(0.01) = 0.0016 βB² × σM² = (0.50)²(0.01) = 0.0025 βC² × σM² = (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 = (WA x WA x σA²) + (WA x WB x COVAB) + (WA x WC x COVAC) + (WB x WA x COVAB) + (WB x WB x σB²) + (WB x WC x COVBC) + (WC x WA x COVCA) + (WC x WB x COVCB) + (WC x WC x σC²) = (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