1. The goal of this problem is to determine the optimal portfolio weights across risky and risk free assets. Suppose your risky universe consists of CAT, C, JPM and MMM, and their annualized expected returns, variances, covariances are described in excel template sheet question 2.1. The risk-free rate is described in excel template sheet question 2.2. Re- turns, variances and covariances have been annualized already. Complete the optimization problems by filling in tables in sheet question 2.1 and question 2.2.

   • Step 1: Assume you your objective function is minimum risky portfolio variance subject to i) fully invested, ii) an annual target return of 29.8% and iii) leverage and short selling are both allowed. Find the optimal weights of each asset in the risky portfolio, the expected return and variances of the risky portfolio. (Excel sheet question 2.1)

   • Suppose you follow a standard two moment utility function with risk aversion param- eter equal to 5, also assuming that tangency risky portfolio on the efficient frontier is the portfolio in step 1. Find the weights of each assets in the complete portfolio, expected return and variances of the complete portfolio. (Excel sheet question 2.2)

Table 2.1: CAT C 0.030 0.070 Exp Return Exp Variance Weights JPM 0.041 0.145 0.112 0.071 MMM 0.147 0.033 Risky Portfolio Target Return 0.298 0.298 0.000 Covariance CAT JPM CAT 0.030 0.070 0.054 0.041 0.030 0.054 0.112 0.077 0.037 0.041 0.077 0.071 0.030 0.037 0.030 C JPM 0.033 Table 2.2: Risky Portfolio Exp Return Exp Variance 0.298 0 A 5 Risk Free 0.024 Return Complete Var Complete Utility Weights in Risky 0 CAT C JPM MMM COOOO Weights in Complete CAT JPM MMM Risk Free Total 0 Table 2.1: CAT C 0.030 0.070 Exp Return Exp Variance Weights JPM 0.041 0.145 0.112 0.071 MMM 0.147 0.033 Risky Portfolio Target Return 0.298 0.298 0.000 Covariance CAT JPM CAT 0.030 0.070 0.054 0.041 0.030 0.054 0.112 0.077 0.037 0.041 0.077 0.071 0.030 0.037 0.030 C JPM 0.033 Table 2.2: Risky Portfolio Exp Return Exp Variance 0.298 0 A 5 Risk Free 0.024 Return Complete Var Complete Utility Weights in Risky 0 CAT C JPM MMM COOOO Weights in Complete CAT JPM MMM Risk Free Total 0