As an Investment manager, you are given the following information: Investment in equity share of Expected Return (%) Standard Deviation (%) Beta A Ltd. 22% 40% 0.86 B Ltd. 24% 38% 1.24 The correlation coefficient between

(i) Is investing in B Ltd. better than A Ltd.? Expected return of B Ltd. is 24% as compared to 22% of A Ltd. Standard deviation of B Ltd. is 24% as compared to 40% of A Ltd. In view of the above, A Ltd. has lower return and carried higher risk as compared to B Ltd. Hence, investing in B Ltd. is better than investing in A Ltd. but investing in both A Ltd. and B Ltd. will cause to yield the advantage due to diversification of portfolio. (ii) If you invest 70% in A Ltd. and 30% in B Ltd., what is your expected rate of return and standard deviation? R AB = (R A × W A ) + (R B × W B ) = (0.22 × 0.7) + (0.24 × 0.3) = 22.6% σ AB = √[(σ A W A )² + (σ B W B )² + 2 σ A σ B W A W B ρ AB ] = √[(0.40² × 0.7²) + (0.38² × 0.3²) + (2 × 0.7 × 0.3 × 0.72 × 0.40 × 0.38)] = √[(0.16 × 0.49) + (0.144 × 0.09) + 0.0459648] = √[0.0784 + 0.012996 + 0.0459648] = √0.1373608 = 0.370622 = 37.06% (iii) What is the rate of return on market portfolio and what is risk-free rate? The risk-free rate will be the same for A and B Ltd. Their rates of return are given as follows: R A = R f + (R m - R f ) β A => 22 = R f + (R m - R f ) 0.86 (Equation-1) R B = R f + (R m - R f ) β B => 24 = R f + (R m - R f ) 1.24 (Equation -2) Subtracting Equation 1 from Equation 2: R B - R A = (R m - R f ) (1.24 - 0.86) 24 - 22 = (R m - R f ) (0.38) 2 = (R m - R f ) (0.38) R m - R f = 2 / 0.38 = 5.26% Substituting the value of (R m - R f ) in equation 1: 22 = R f + (5.26) 0.86 22 = R f + 4.5236 R f = 22 - 4.5236 = 17.4764% ≈ 17.48% R m = R f + 5.26 = 17.48 + 5.26 = 22.74% (iv) What is beta of portfolio, if weights of A Ltd. and B Ltd. are 70% and 30% respectively? β AB = (β A × W A ) + (β B × W B ) = (0.86 × 0.7) + (1.24 × 0.3) = 0.602 + 0.372 = 0.974