Mr. Abhishek is interested in investing - 2,00,000 for which he is considering following three alternatives: (i) Invest 2,00,000 in Mutual Fund X…

(i) Variance of Returns Cor i,j = Cov (i, j) / (σi σj) Accordingly, for MFX 1 = Cov (X,X) / (σX σX) σX² = 4.800 Accordingly, for MFY 1 = Cov (Y,Y) / (σY σY) σY² = 4.250 Accordingly, for Market Return 1 = Cov (M,M) / (σM σM) σM² = 3.100 Alternatively, by referring diagonally the given Table these values can identified as follows: Variancex = 4.800 Variancey = 4.250 VarianceM = 3.100 (ii) Portfolio return, beta, variance and standard deviation Weight of MFX in portfolio = 1,20,000 / 2,00,000 = 0.60 Weight of MFY in portfolio = 80,000 / 2,00,000 = 0.40 Accordingly, Portfolio Return 0.60 × 15% + 0.40 × 14% = 14.60% Beta of each Fund β = Cov (Fund,Market) / Variance of Market βX = 3.370 / 3.100 = 1.087 βY = 2.800 / 3.100 = 0.903 Portfolio Beta 0.60 x 1.087 + 0.40 x 0.903 = 1.013 Portfolio Variance σXY² = WX²σX² + WY²σY² + 2 WXWY CovX,Y = (0.60)² (4.800) + (0.40)² (4.250) + 2(0.60) (0.40) (4.300) = 4.472 Or Portfolio Standard Deviation σXY = √4.472 = 2.115 (iii) Expected Return, Systematic and Unsystematic Risk of Portfolio Portfolio Return = 10% + 1.0134(12% - 10%) = 12.03% MF X Return = 10% + 1.087(12% - 10%) = 12.17% MF Y Return = 10% + 0.903(12% - 10%) = 11.81% Systematic Risk = β² σ² Accordingly, Systematic Risk of MFX = (1.087)² x 3.10 = 3.663 Systematic Risk of MFY = (0.903)² x 3.10 = 2.528 Systematic Risk of Portfolio = (1.013)² x 3.10 = 3.181 Unsystematic Risk = Total Risk – Systematic Risk Accordingly, Unsystematic Risk of MFX = 4.80 – 3.663 = 1.137 Unsystematic Risk of MFY = 4.250 – 2.528 = 1.722 Unsystematic Risk of Portfolio = 4.472 – 3.181 = 1.291 (iv) Sharpe and Treynor Ratios and Alpha Sharpe Ratio MFX = (15% - 10%) / √4.800 = 2.282 MFY = (14% - 10%) / √4.250 = 1.94 Portfolio = (14.6% - 10%) / 2.115 = 2.175 Treynor Ratio MFX = (15% - 10%) / 1.087 = 4.60 MFY = (14% - 10%) / 0.903 = 4.43 Portfolio = (14.6% - 10%) / 1.0134 = 4.54 Alpha MFX = 15% - 12.17% = 2.83% MFY = 14% - 11.81% = 2.19% Portfolio = 14.6% - 12.03% = 2.57%