A speculator in the futures market for corn, wheat, and sugar would like to construct a marketing portfolio. Assume that the cost of each position is $20 (corn), $10 (wheat), and $12 (sugar) per share respectively. The investor has a total of $100,000 to invest. The investor has observed the following rates of return for each commodity over the past four years:
|
Year
|
Corn
|
Wheat
|
Sugar
|
|
1
|
-5%
|
10%
|
25%
|
|
2
|
15%
|
0%
|
12%
|
|
3
|
-2%
|
1%
|
2%
|
|
4
|
15%
|
2%
|
-30%
|
a. Compute the variance-covariance matrix for this problem.
b. Formulate this problem as a quadratic risk programming problem, where the objective function is to minimize the total variance-covariance matrix subject to a minimum expected return constraint, which should be parametrically varied.
c. Formulate a MOTAD model to maximize return (where the expected return is the four-year simple average).