A portfolio manager is analysing four equity securities to construct an optimal risky portfolio using Sharpe's Single Index Model. The securities…

(i) Securities whose excess-return to risk ratio is above the cut-off ration of 7.95 are selected and all whose ratios are below are rejected. Security Calculation [E(r)-RF]/β; Ratio C* = Cut off Rate Decision Rule A (17-6) / 1.40 7.86 7.95 Ratio below C*, Rejected B (15-6) / 1.10 8.18 7.95 Ratio above C*, Selected C (13-6) / 0.90 7.77 7.95 Ratio below C*, Rejected D (11-6) / 0.60 8.33 7.95 Ratio above C*, Selected Select Security D & B in the optimal portfolio and reject Security A & C from the optimal portfolio selection. (ii) Calculation of percentage to be invested in each security: Using the formula: Zi = (Ri - Rf) / βi - C* σei² βi Zi values for Security D = 0.60 / 0.0100 x (8.33 – 7.95) = 60 x 0.38 = 22.80 Zi values for Security B = 1.10 / 0.0196 x (8.18 – 7.95) = 56.12 x 0.23 = 12.91 Weight of D in the Portfolio = 22.80 / (22.80 + 12.91) = 22.80 / 35.71 x 100 = 63.8% Weight of B in the Portfolio = 12.91 / (22.80 + 12.91) = 12.91 / 35.71 x 100 = 36.2% (iii) CAPM expected return and Valuation: Security Return as per CAPM Expected Return Status B 6% + 1.1 x 8% = 14.80% 15% Undervalued (Buy) D 6% + 0.6 x 8% = 10.80% 11% Undervalued (Buy) (iv) The portfolio constructed using Sharpe's Single Index Model is fully consistent with CAPM, as it included only securities offering superior risk-adjusted returns.