You are given the following information related to the return from various securities: Effective Annual Return Probability LMN Ltd. XYZ Ltd. Risk…

8. (i) Expected Return of different Portfolios To calculate expected return of different Portfolios first we shall calculate the expected return each security as follows: Share of LMN E(R L ) = 5% x 0.40 + 25% x 0.60 = 17% Share of XYZ E(R X ) = 15% x 0.40 + 5% x 0.60 = 9% Risk Free Bond = 4% Expected Returns from Portfolios Portfolio A = 0.75 X 17% + 0.25 x 9% = 15% Portfolio B = 0.75 x 17% + 0.25 x 4% = 13.75% Portfolio C = 17% To calculate risk of each Portfolio, first we shall calculate risk i.e. Variance and Standard Deviations of each security and covariance between LMN & XYZ and LMN & Risk Free Bonds as follows: Variance of LMN Ltd. = 0.40 x (5 - 17)² + 0.60 x (25 - 17)² = 0.40 x 144 + 0.60 x 64 = 96 Variance of XYZ Ltd. = 0.40 x (15 – 9)² + 0.60 x (5 – 9)² = 0.40 x 36 + 0.60 x 16 = 24 Variance of Risk free Bond = 0 Covariance between LMN and XYZ Scenario Prob. (P) (R L – R L ) (R X – R X ) (R L – R L ) (R X – R X ) P Situation I 0.40 (5%-17%) (15%-9%) 28.80% Situation II 0.60 (25%-17% (5%-9%) -19.20% 48.00% Covariance between share of LMN and Risk Free Bond shall be Zero. Variance of Portfolio = (w 1 )² (σ 1 )² + (w 2 )² (σ 2 )² + 2 w 1 w 2 Cov 12 Variance of Portfolio A = (0.75)² (96) + (0.25)² (24) + 2 (0.75) (0.25) (- 48) = 54 + 1.50 – 18 = 37.50 Risk of Portfolio A (σ A ) = √37.50 = 6.12 Variance of Portfolio B = (0.75)² (96) + (0.25)² (0) = 54 Risk of Portfolio B (σ B ) = √54 = 7.35 Risk of Portfolio C (σ C ) = √96 = 9.80 (ii) (I) Since a Risk neutral investor judges the portfolio only by expected return and ignore the risk factor and hence will choose Portfolio C having maximum return and that too without any risk. (II) Risk Seeker investor chooses the portfolio taking into account both risk and return. Though greater return is penalized depending on how much extra risk is taken considering return achieved. There can be two ways to select the Portfolio one on the basis of covariance as due to negative covariance he may opt for Portfolio A as return is bit higher than Portfolio B. Alternatively, Portfolio can also be chosen based on Coefficient of Variation as follows: Portfolio A = 6.12/15 = 0.408 Portfolio B = 7.35/13.75 = 0.535 Portfolio C = 9.80/17 = 0.576. Since CV is best in case of Portfolio A it should be opted for as it results better risk- return trade off.