Question

A customer is interested in investing and has been tracking the following stocks over time: Stock Mean Return Standard Deviation Variance 12% 11% 10% 28% 0.0432 19% 0.0325 6% 0.0164 The customer wishes to develop a strategy that will provide an expected return of 11.5% The expected return is the return on each stock weighted by the percentage invested in each If the customer placed 40% in A, 20% in B, and 40% in C then the return would be calculated: 40%(12%) + 20%(11%) + 40%(10%) 11% Based on the same data the customer also determined that the stock performances are correlated with the other. These are helpful in determining risk: Correlation Std. Dev of First Pairs A and B A and C B and C 0.5 0.4 0.3 20% 10% 5% Std. Dev of Second Covariance 0.029 15% 0.0053 15% 0.0095 18% Portfolio risk is measured based on the standard deviation of the portfolio The standard deviation is a function of the variance of the individual stocks, the investment percentage in those stocks and a covariance measure for stock pairs This would be computed as Var-(40%)2 Var(A) + (20%)2 Var(B) + (40%)2 Var(C) + 2 (40%)(20%)Cov(A, B) + 2 (40%) (4096)Cou(A, C) + 2 (20%) (40%) Cou(B, C) - (. 16)(0432) +(.04)(.0325) + (.16) (.0164) +2( 08) (.029) + 2(.16)( 0053) + 2(.08)( 0095) 0.018692 The standard deviation is the square root: 0.018692 0.1367186893 The customer is interested in determining an investment strategy such that they have an expected of at least 11.5% while minimizing risk Generally formulate this problem as a mathematical programming problem. Identify and label all decision variables, parameters, and sets. Write the objective function. Write and label all constraints