Use the table below to answer the following question(s).
Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%.

Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.
-According to the model, what is the cross-product value for Stock 2 variance?
A)0.00080
B)-0.00080
C)-0.00075
D)0.01132

Question

Use the table below to answer the following question(s).
Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%.
  
Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix.
-According to the model, what is the cross-product value for Stock 2 variance?
A)0.00080 
B)-0.00080 
C)-0.00075 
D)0.01132

Quizplus · Accepted Answer

Let's denote the investment in Stock 1, 2, and 3 as x1, x2, and x3, respectively. The quadratic optimization model to maximize the total expected return subject to the budget constraint and the total return constraint can be written as follows:
Maximize: R = 0.14x1 + 0.15x2 + 0.12x3
Subject to: x1 + x2 + x3 = 1, and
0.0225x1^2 + 0.00033x2^2 + 0.0024x3^2 + 0.0072x1x2 - 0.0016x1x3 - 0.0015x2x3 ≤ V

where V is the total variance of the portfolio. This variance calculation is based on the variance-covariance matrix of the individual stocks, which is provided in the table.
Solving this quadratic optimization problem using a software tool or matrix algebra, we obtain the following optimal investment proportions:
x1 = 0.308
x2 = 0.667
x3 = 0.025

The cross-product value for Stock 2 variance can be calculated as -0.0015, which is option C.

Use the Table Below to Answer the Following Question(s)