Question

Bosco has an investment portfolio comprised of shares in three companies: Abacus, Baracus, and Cerberus (A B, and C for short). The returns for shares A, B, and C have expected values 5%, 4%, and 8% respectively The covariance matrix for these retums is 0.0025 0.0003 -0.00161 0.0003 0.0001 -0.0004 -0.0016 -0.0004 0.09 Bosco has invested 50%, 30%, and 20% of his portfolio in shares A, B, and C respectively a) Calculate the correlations paB, PAC, and psc for the returns. b) Calculate the expected return on Bosco's portfolio c) Calculate the variance and standard deviation of the returm on Bosco's portfolio. d) John, another investor, also has an investment portfolio consisting of the same three shares. However John tends to take more investment risk than Bosco. Name one way that John's portfolio might differ from Bosco's? You do not have to give any explanation

Answer 1

a.From the matrix, std deviation of AA = sqrt (variance of AA) = 0.0025^(0.5) = 0.05

similarly, std deviation of BB = 0.01, std deviation of CC = 0.3

correlation (rho) of AB = (covariance of AB)/(std deviation of A)*(std deviation of B)

using the formula, rho AB = +0.0003/(0.05*0.01) = 0.6

rho BC = -0.0004/(.01*0.3) = -0.13333

rho AC = -0.0016/(0.3*0.05) =-0.10667

b. Expected return of a protfolio = wt A * expected return A + wt B * expected return B + wt C * expected return C = =0.5*0.05+0.3*0.04+.2*.08 = 0.053 = 5.3%