Question

There are only two risky assets A and B with expected returns r A = 30 % and r The covariance matrix of their returns is = 20 % [0.0576 0.0288] 0.0288 0.0256 (a) Solve for the minimum-variance portfolio of the two risky assets, as well as the expected rate of return and standard deviation of the portfolio. (9 marks) (b) Solve for an efficient portfolio with expected return 29.25 %. (8 marks) (c) Explain how the returns of the two portfolios derived in (a) and (b) are correlated. (3 marks)

Answer 1

TIA = 30% diß = 20% o Variance of A. - SD of A: S of B : 0.05 76 Jo.0576 50.0256 = 0.24 0.16 Covariance Correlation - a 0.0 288 Covariance SDAX SDB 0.0288 = 0:24 X0.16 0.75 - (a) Minimum WA : Variance portfolio SDR² - Cordriare AR SDA? + SD² - 2 Covariare AB 10.1672 – 0.0288 70-24)? +0:1672 - 12X0.0288) 0-0256 -0.0288 0.0576+ 0.0256 -0.0576 E = = - 0.125 0.0032 0.0256 1 +0.125 - 1:125-

Expected Standard Retusn of Portfolio 0-30x60:125)+0-2001-128 - 0.1875 ie 18.757. deviation of portfolio SD p = J SDP SDp² = (S.DA X WA²+ (SDQ x W p ) ² + -2X15DA X WA) X (SDR XW13) x Casselation AB = 0.24x(-0.125)] + (0-16 X 1-12522+ 2 x 0:24 x 1-0-125) x 0.16 x 1.125 x 0-75_ -0.0087 SDp² 0.0009 to.0324 = 0.0252 SDP = 0.0252 = 0.1587 ie 15.87% (6) ERP = 29.25%. = MAX WA + iB WB 0.2925 = 0.308 WA + 0.2ox(1-WA) 0.2925 & 0.30 WA +0.20 0.20 WA 0-10WA = 0.0925 - WA : 0.925. WB = -0.925 = 0.075

(c) Portfolio Return is weighted average of the returns of individual securities. W_A and W_B are proportions invested in risky assets A and B respectively. Thus expected return will be R_A*W_A + R_B*W_B. This is how returns of the two portfolios are derived.