Consider the following information on two stocks, X and Y: Year Return on X (%) Return on Y (%) 2024-25 10 12 2025-26 16 18 Required: (i) Determine…

(i) Stock X: Average Return E(X) = (10 + 16) / 2 = 13% Variance = 0.5(10 - 13) 2 + 0.5(16 - 13) 2 = 9 Standard deviation = √9 = 3% Stock Y: Average Return E(Y) = (12 + 18) / 2 = 15% Variance = 0.5(12 - 15) 2 + 0.5(18 - 15) 2 = 9 Standard deviation = 3% (ii) Covariance of stocks X and Y Cov XY = 0.5(10 - 13)(12 - 15) + 0.5(16 - 13)(18 - 15) = 9 Correlation of coefficient R XY = Cov XY / (σ X σ Y ) = 9 / (3 × 3) = 1 (iii) Since Coefficient of Correlation between the Securities is 1 there will no risk reduction through diversification. (iv) Expected return of the portfolio X and Y E(X) = (10 + 16) / 2 = 13% E(Y) = (12 + 18) / 2 = 15% R p = Σ X i R i = 0.4(13) + 0.6(15) = 14.2% Portfolio Risk σ P = √[W X 2 σ X 2 + W Y 2 σ Y 2 + 2W X W Y (σ X σ Y R XY )] = √[(0.4) 2 (3) 2 + (0.6) 2 (3) 2 + 2(0.4)(0.6)(3)(3)(1)] = √[1.44 + 3.24 + 4.32] = 3% (v) Since the two securities have identical standard deviations and a perfect positive correlation of +1, there is no unique optimal weight. Every combination of X and Y has the same portfolio risk of 3%. However, since Security Y has higher expected return, but same risk is should be opted for.