2. Portfolio Selection Problem. An individual with $100,000 to invest has identified three mutual funds as attractive opportunities. Over the last five years, dividend payments (in cents per dollar invested) have been as shown in Table 5, and the individual assumes that these payments are indicative of what can be expected in the future. This particular individual has three requirements: (1) the combined expected yearly return from her/his investments must be no less than $2,000, i.e., the amount $100,000 would earn at 2 percent interest, and (2) the variance in future, yearly, dividend payments should be as small as possible, and (3) the amount invested in Investment 1 must be at least the amount invested in Investment 3. How much should this individual fully invest her/his $100,000 in each fund to achieve these requirements? Table 5: Dividend Payments Years 1 2 3 4 5 Investment 1 58831 Investment 243620 Investment 3 56432 [Hint: Let x, i = 1,2,3, designate the amount of funds to be allocated to investment i, and let ik denote the return per dollar invested from investment i during the kth time period in the past (k = 1, 2,..., 5). If the past history of payments is indicative of future performance, the expected return per dollar from investment i is Ei Tik- k=1 The variance in future payments can be expressed as 3 3 f(x1, x2, x3)= {xx = xCx, i=1 j=1 where the covariances are given by 5 5 1 TikXjk 5 -+-)) ] (a) Using the following table, calculate the covariance matrix C = [}}]. Table 6: Intermediate Calculations k 21k 12k 3k 1 4 5 25 16 25 20 25 20 2 8 3 6 64 36 24 48 18 3 6 4 64 36 16 48 32 24 4 3 2 3 9 4 9 6 9 6 1 0 2 1 0 4 0 0 total 25 15 20 163 65 90 98 116 68 (b) Set up a standard form optimization problem (i.e. quadratic optimization problem) that will deter- mine the best investment mix. (c) Solve the problem using the MATLAB quadratic programming routine quadprog. Interpret your results in plain English.