In an attached file, A257_A2_T2_covmatrix.xlsx, you'll find a 5x5 matrix representing the var-cov matix of five assets (we might think of them as asset classes, eg US equities, Asian equities, small cap stocks, long-term corporate bonds, T-bills). You are running an asset-allocation fund, and you need to decide on portfolio weights among these five classes, for which decision you want to compute the portfolio variance with various weights. Call the assets x1 to x5, with variances var(xi) given on the main diagonal. 1. Compute the portfolio variance for the equally weighted portfolio (20% of the portfolio in each asset class). 2. Now consider keeping the 20% weight on assets x2-x4, but varying the weight on assets x1 and x5. Compute the portfolio-variance-minimizing weight on each of these assets, subject to the no-short-sales constraint (weight cannot be negative). Note that the total weight on these two assets together must be 40% as the other three add to 60%. 3. Optional, if you know how to use numerical minimization in your computing software: obtain the answer to this problem using numerical methods, ie get the computer to figure it out without calculus. If you don't know how to do this, no worries, but look into it just to get some familiarity; for example you might look up the Powell optimization algorithm. You could (again not necessary, just think about how you might do this) then extend this to higher dimensions to get the overall optimal portfolio weight distribution subject to weight(i) being non-negative. A B C D E 1 9.599563 1.695803 3.374805 -2.03629 -1.91209 2 1.695803 22.49015 2.451654 9.799176 7.078781 3 3.374805 2.451654 12.074 1.904627 -3.80415 4 -2.03629 9.799176 1.904627 6.270434 4.070652 -1.91209 7.078781 -3.80415 4.070652 5.320049 5 6 7 8 9 10 11 12 13 14 15 16 17 18