An investor has decided to invest - 1,00,000 in the shares of X Ltd. and Y Ltd. The desired returns from the shares of the two companies along with…

(i) Probability X Ltd. (%) Y Ltd. (%) 1 X2 (%) 1 X3 (%) (1) (2) (3) (4) (5) 0.20 -5 15 -1.00 3.00 0.50 10 25 5.00 12.50 0.30 15 -10 4.50 -3.00 Average return 8.50 12.50 Hence the expected return from X Ltd. = 8.50% and Y Ltd. is 12.50% Probability (X-X) (X-X)² 1 X3 (Y-Y) (Y-Y)² (1)X(6) (1) (2) (3) (4) (5) (6) 0.20 -13.50 182.25 36.45 2.50 6.25 1.25 0.50 1.50 2.25 1.125 12.50 156.25 78.125 0.30 6.50 42.25 12.675 -22.50 506.25 151.875 50.25 231.25 σ² x = 50.25(%)² ; σ x = 7.09% σ² y = 231.25(%)²; σ y = 15.21% (ii) In order to find risk of portfolio of two shares, the covariance between the two is necessary here. Probability (X-X) (Y-Y) 2 X3 1 X4 (1) (2) (3) (4) (5) 0.20 -13.50 2.50 -33.75 -6.75 0.50 1.50 12.50 18.75 9.375 0.30 6.50 -22.50 -146.25 -43.875 -41.25 σ² p = (0.5² x 50.25) + (0.5² x 231.25) + 2 x (-41.25) x 0.5 x 0.5 σ² p = 12.563 + 57.813 - 20.625 σ² p = 49.751 or 49.75(%) σ p = √49.75 = 7.053% or 7.05% E (R p ) = (0.5 x 8.50) + (0.5 x 12.50) = 10.50% Return Risk Return to Risk Ratio Ranking of CV X Ltd. 8.50% 7.09 1.20 2 Y Ltd. 12.50% 15.21 0.82 3 Portfolio 10.50% 7.05 1.48 1 Risk of the portfolio is reduced by combining two shares. (iii) For constructing the minimum risk portfolio the condition to be satisfied is Y = (σ² x - r xy σ x σ y ) / (σ² x + σ² y - 2r xy σ x σ y ) or = (σ² x - Cov xy ) / (σ² x + σ² y - 2Cov xy ) σ x = Std. Deviation of X Ltd. σ y = Std. Deviation of Y Ltd. r xy = Coefficient of Correlation between X Ltd. and Y Ltd. Cov. XY = Covariance between X Ltd. and Y Ltd. Therefore, % Y Ltd. = (50.25 - (-41.25)) / (50.25 + 231.25 - [2×(-41.25)]) = 91.50 / 364 = 0.2514 or 25.14% or 25% Y Ltd. = 25.14% or 25% X Ltd. = 74.86% or 75% Alternatively, it can also be computed as follows: For constructing the minimum risk portfolio the condition to be satisfied is X = (σ² y - r xy σ x σ y ) / (σ² x + σ² y - 2r xy σ x σ y ) or = (σ² y - Cov xy ) / (σ² x + σ² y - 2Cov xy ) σ x = Std. Deviation of X Ltd. σ y = Std. Deviation of Y Ltd. r xy = Coefficient of Correlation between X Ltd. and Y Ltd. Cov. xy = Covariance between X Ltd. and Y Ltd. Therefore, % X Ltd. = (231.25 - (-41.25)) / (50.25 + 231.25 - [2×(-41.25)]) = 272.50 / 364 = 0.7486 or 74.86% or 75% Y Ltd. = 25.14% or 25% X Ltd. = 74.86% or 75%