An investor has decided to invest - 1,00,000 in the shares of two companies, namely, ABC and XYZ. The projections of returns from the shares of the…

(i) Probability ABC (%) XYZ (%) 1 X2 (%) 1 X3 (%) (1) (2) (3) (4) (5) 0.20 12 16 2.40 3.20 0.25 14 10 3.50 2.50 0.25 -7 28 -1.75 7.00 0.30 28 -2 8.40 -0.60 Average return 12.55 12.10 Hence the expected return from ABC = 12.55% and XYZ is 12.10% Probability (ABC-ABC) (ABC-ABC) 2 1 X3 (XYZ-XYZ) (XYZ-XYZ) 2 (1)X(6) (1) (2) (3) (4) (5) (6) 0.20 -0.55 0.3025 0.06 3.9 15.21 3.04 0.25 1.45 2.1025 0.53 -2.1 4.41 1.10 0.25 -19.55 382.2025 95.55 15.9 252.81 63.20 0.30 15.45 238.7025 71.61 -14.1 198.81 59.64 167.75 126.98 σ 2 ABC = 167.75(%) 2 ; σ ABC = 12.95% σ 2 XYZ = 126.98(%) 2 ; σ XYZ = 11.27% (ii) In order to find risk of portfolio of two shares, the covariance between the two is necessary here. Probability (ABC-ABC) (XYZ-XYZ) 2 X3 1 X4 (1) (2) (3) (4) (5) 0.20 -0.55 3.9 -2.145 -0.43 0.25 1.45 -2.1 -3.045 -0.76 0.25 -19.55 15.9 -310.845 -77.71 0.30 15.45 -14.1 -217.845 -65.35 -144.25 σ 2 P = (0.5 2 x 167.75) + (0.5 2 x 126.98) + 2 x (-144.25) x 0.5 x 0.5 σ 2 P = 41.9375 + 31.745 – 72.125 σ 2 P = 1.5575 or 1.56(%) σ P = √1.56 = 1.25% E (R P ) = (0.5 x 12.55) + (0.5 x 12.10) = 12.325% Hence, the return is 12.325% with the risk of 1.25% for the portfolio. Thus, the portfolio results in the reduction of risk by the combination of two shares. (iii) For constructing the minimum risk portfolio, the condition to be satisfied is X ABC = (σ XYZ - r AX σ A σ XYZ ) / (σ 2 A + σ 2 XYZ - 2r AX σ A σ XYZ ) or = (σ 2 XYZ - Cov. AX ) / (σ 2 A + σ 2 XYZ - 2Cov. AX ) σ XYZ = Std. Deviation of XYZ σ A = Std. Deviation of ABC r AX = Coefficient of Correlation between XYZ and ABC Cov. AX = Covariance between XYZ and ABC. Therefore, % ABC = (126.98-(-144.25)) / (126.98+167.75-[2×(-144.25)]) = 271.23 / 583.23 = 0.4650 or 46.50% % XYZ = (1 – 0.4650) = 0.5350 = 53.50%