Question 1 Consider the following data: Assets E(r) A 0.05 0.10 B 0.10 0.20 C 0.15 0.30 The risk-free rate is If = 0.035. The correlation matrix for the assets is given by: Correlation matrix: (for risky assets) D B C 0.5 O 0.5 0.5 0.5 1 Solver (in Excel) yields two portfolios on the minimum variance frontier: Global minimum variance (GMV) portfolio: WA = 0.887 WB = 0.287 Wc= -0.174 E[I'MV] = 0.047 OMV= 0.079 (MV = minimum variance) * A portfolio with expected return = 0.10; we will denote it by ri (Portfolio 1) WA = 0.294 WB = 0.412 Wc = 0.294 E[ri] = 0.10 61= 0.159 For this set of data: a) Calculate the covariance of the GMV portfolio with portfolio 1. Hint: The covariance between two portfolios is an extension of the covariance formulas in class. Suppose there are 3 assets (r; with i=1, 2, and 3). Let portfolio i have weights wi, i=1, 2, 3 in each asset. Let portfolio j have weights wj, j=1, 2, 3 in each asset. The covariance of portfolio i and portfolio j is given by: cov(li,nj) = wi Wi var(ri) + w1 w2 cov(11,r2) + WI W3 cov(11,13) + W2 WI cov(11,12) + W2 W2 var(12) + W2 W3 Cov(12,13) + W3 WI Cov(1 1,13) + W3 W2 cov(12,13) + W3 W3 var(13)