The following details are given for TC Limited and PC Limited stocks and Nifty Index for a period of one year: TC Limited PC Limited Nifty Index…

(i) Calculation of Systematic Risk and Unsystematic Risk of TC Ltd. Systematic Risk = β²σm² = (0.8)²(2.10) = 1.344 Unsystematic Risk = Total Risk – Systematic Risk = 5.80 – 1.344 = 4.456 PC Ltd. Systematic Risk = β²σm² = (0.7)²(2.10) = 1.029 Unsystematic Risk = Total Risk – Systematic Risk = 4.80 – 1.029 = 3.771 (ii) Portfolio Risk Covariance of returns between any two stocks = β1β2σm² Accordingly, Covariance of returns between TC Ltd. and PC Ltd. shall be: = 0.8 x 0.7 x 2.10 = 1.176 and the Portfolio Risk shall be: σp² = (0.50)²(5.80) + (0.50)²(4.80) + 2 x 1.176 x 0.50 x 0.50 σp² = 1.45 + 1.20 + 0.588 = 3.238 σp = √3.238 = 1.80 (iii) If Fund allocation is changed to 60% and 40% then Portfolio Risk shall be σp² = (0.60)²(5.80) + (0.40)²(4.80) + 2 x 1.176 x 0.60 x 0.40 σp² = 2.088 + 0.768 + 0.565 = 3.421 σp = √3.421 = 1.85 Exiting Return (50:50) = 0.50 X 0.12 +0.50 X 0.18 = 0.06 + 0.09 = 0.15 or 15% New Proportion Return (60:40) = 0.60 X 0.12 +0.40 X 0.18 = 0.072 + 0.072 = 0.144 or 14.40% It is not advisable to change the allocated fund ratio as return is decreased from 15% to 14.40% and portfolio risk is increased from 3.238 (or 1.80) to 3.421 or 3.420 (or 1.85). Alternatively, it can also be advised based on Coefficient of Variation as follows: Exiting = (Standard Deviation/ Mean) x 100 = (1.80/ 15) x 100 = 12% Proposed = (Standard Deviation/ Mean) x 100 = (1.85/14.40) x 100 = 12.85% Since volatility for per unit of return is higher in case of proposed allocation it is not advised.