This is your only non-group homework assignment. Answer the questions below neatly. You will have to use Excel (or something cooler) to answer questions 4 and 5 1. Write out the algebraic formula for the variance of a three-ass portfolio, , with Var w1 r1 w 2 r2 w3 r3 and , and is a portfolio weight. wi i j Cov ri , r j i2 Var ri 2. Show that w w yields the same answer as you got in problem 1, for , w1 12 w w2 12 w 13 2 3. , and 12 22 23 13 23 32 is the transpose of w. w Given a vector of Expected ReturnsNOT Excess Returns R n1 , and covariance matrix nn , find the formula for the utility maximizing portfolio that solves Max w w R 1 2 for A = risk aversion coefficient and e = an A w w n 1 vector of 1's. s.t. w e 1 4. Assume an investor has a coefficient of risk aversion, A = 2, then use the information in the table below, along with Excel (and your formula you derived in question 3), to find i) ii) iii) Asset AAA BBB CCC DDD EEE 5. the utility maximizing portfolio weights the expected return of the portfolio the volatility of the portfolio E(R) 3.00% 7.00% 15.00% 14.00% 20.00% AAA BBB CCC DDD EEE AAA Covariance Matrix BBB CCC DDD EEE 0.30 0.10 0.20 0.08 0.10 0.10 0.25 0.10 0.10 0.20 0.20 0.10 0.36 0.10 0.22 0.08 0.10 0.10 0.60 0.20 0.10 0.20 0.22 0.20 0.40 How do your answers change for an investor with a risk-aversion coefficient A = 10? (Compare portfolio weightings, expected returns, and volatility.) Do these changes make economic sense? How