Mr. X is interested in investing - 4,00,000 for which he is considering following three alternatives: (i) Invest - 4,00,000 in Security A (ii)…

Working Notes: (1) Beta of each Security β = Cov(Security, Market) / Variance of Market β A = 3.370 / 3.100 = 1.087 β B = 2.800 / 3.100 = 0.903 (2) Weight of Security A in portfolio = 2,40,000 / 4,00,000 = 0.60 Weight of Security B in portfolio = 1,60,000 / 4,00,000 = 0.40 (3) Portfolio Beta 0.60 x 1.087 + 0.40 x 0.903 = 1.013 (i) Expected Return Security A Return = 10% + 1.087(12% - 10%) = 12.17%. Security B Return = 10% + 0.903(12% - 10%) = 11.81%. Portfolio Return = 10% + 1.013(12% - 10%) = 12.03%. (ii) Variance of Returns Cor i,j = Cov (i, j) / (σ i σ j ) Accordingly, for Security A 1 = Cov (A,A) / (σ A σ A ) σ A 2 = 4.800 Accordingly, for Security B 1 = Cov (B,B) / (σ B σ B ) σ B 2 = 4.250 Accordingly, for Market Return 1 = Cov (M,M) / (σ M σ M ) σ M 2 = 3.100 Alternatively, by referring diagonally the given Table these values can identified as follows: Variance A = 4.800 Variance B = 4.250 Variance M = 3.100 (iii) Variance and Standard Deviation of Portfolio Variance σ P 2 = w A 2 σ A 2 + w B 2 σ B 2 + 2w A w B Cov A,B = (0.60) 2 (4.800) + (0.40) 2 (4.250) + 2(0.60) (0.40) (4.300) Variance = 4.472 Standard Deviation σ P = √4.472 = 2.115 (iv) Systematic and Unsystematic Risks of Security A, Security B and Portfolio Systematic Risk = β 2 σ M 2 Accordingly, Systematic Risk of Security A = (1.087) 2 x 3.10 = 3.663Systematic Risk of Security B = (0.903) 2 x 3.10 = 2.528Systematic Risk of Portfolio = (1.013) 2 x 3.10 = 3.181 Unsystematic Risk = Total Risk – Systematic Risk Accordingly, Unsystematic Risk of Security A = 4.80 – 3.663 = 1.137Unsystematic Risk of Security B = 4.250 – 2.528 = 1.722Unsystematic Risk of Portfolio = 4.472 – 3.181 = 1.291