Question

QUESTION 2: The returns on shares A and B in four equally likely states at the end of next year are summarized below. 30 State Probability Rates of Rates of Return of Return of Share A Share B 0.3 -25 10.4 50 25 0.2 5 -40 0.1 40 30 a. Calculate the expected return, variance and standard deviation for each share. b. Compute the coefficient of correlation for the returns to these shares. c. Calculate the expected return, variance and standard deviation on a portfolio with 60 per cent invested in share A and 40 per cent in share B. Compute the diversifi- cation effect for this portfolio. . d. Derive the standard deviation for the return to the minimum variance portfolio and compute the diversification effect. c. Explain what factors determine the risk premium paid on any security. QUESTION 3: Assume a mean-variance opportunity set is constructed from two risky shares, A and B, with the variance covariance matrix for their returns of Share A has an expected return of 25 per cent and share B an expected return of 15 per cent. (0.0064 0 0 0.0016) Suppose investor I chooses a 'market portfolio' which consists of 80 per cent in share A and 20 per cent in share B, whereas investor J chooses a different 'market portfolio with 50 per cent in each share. Calculate the beta coefficient (BA) of share A for each investor. Explain why they differ.

Answer 1

Sol a Calculation of Expected Retior for Share A E(R) - (-250:3) + (50X0.4) + (5X0.2) & (40x0.1) - 17.5% Calculation of expected Return for Share &. E(R) - Box0.3 ) +(25x0.4) +(-40x0:2) + (30 x00 A Shared Share & U Formula Used : E(R) - (P,* R) + ({X R2 ) + XR3) + (Pyx Ru) where E(R) - Expected retur P - Probability R- Return Calculation of Variance and standard Deviation. Prob. Y px py (x-7)(y-7) P(x - x * P(x-7) P(x-7)(y-7) | 0.3 -25 30 7.5 9 -42.5 16 541.875 76.8 – 204 0.4 50 25 20 10 32.5 11 422.5 48.4 143 0.2 5 40 I -8 -12.5 -54 31.25 583.2 135 40 30 4 3 22.5 16 50.625 25.6 36 1 7.5% 14% 1046:25 734 110 X = 17.5% Note : Assume 7 = 14% Share A-X Share B =Y 1

Variance of Share A = ex - {P(x-x)² = 1046.25 (36) Standard Deviation of Share A - x = SEP(x-x)? N1046.25 - 32.35% Variance of Share B 67 - Elly-7)2 = 734 1%)2 Standard Deviation of Share B- by = SEP (x-7) ² - 1734 = 27.09% b. Coefficient of Correlation. (8) r = Covarianca (x,y) 6xxy Note: Covariance = EP (X-) (Y-Y) Y = 32.35 X 27.09 8 = 0.13

c Calculation of Exfeted Return of portfolio ElRp) = ( Wtc XRx) + (wity XRy) - (0.6 X1705) + (0.4714) = 16.1% Wt= Weights R = Return Calculation of variance and standard Deviation: 68 p = (With o xo x) + (Why xoy) #2 wit outy) x x x x xory] Covariance. - (0.36 X1046.25) +(0.16x734) + (2x0,6X0.4 x 110) = 376.65 + 117.44 +52.8 = 546.89 (%)² Standard Deviation (ap) - Poze = √546.89 - 23.39% Diversification effect Share A Mean Standard Donation Coefficient of Variation. 17.5 32.35% 184.86% Share B 14 27.09% 193.5% Portfolio 16.1 23.39% 145.28% SD X100 Mean

( Diversification has given us a return between Share A and share B. Also, this return is closer to share B (which is good) because investment in share A is higher. It has reduced the rück (S.D) to 23:39% which is lower the better. Coefficient of variation is lower the better and diversification has done it by reducing it to 145.28% d. Computation of Minimum Variance Portfolio - who = By - Cov(x, y) toy - 2 CU.(x, y) 734 - 110 1046.25+ 734 - (2x110) = 0.4 Wty = 0.6 op = (wt x 3 ) + (wity by) + 2 x Wt ₂ x W ty x Cow. (x, y) = 0.16 X104625) + (0-36x734) + (2x0.6x0.4x 110) = $167.4 +264.24 + 52.8 -√484.44 - 22.01%

Diversification Effect : e Diversification has reduced our rusk to minimum which is 22.01% e. Factors that determine disk premium paid on any Security : (i) The amount or percentage of return the security generates. cii) coefficient of Variation. - 80 x 100 OD 0 Mean This shows the risk as a kercentage of man. ģt is lower the better. There may be other non-quantitative factors too. 11)