An investor is developing a portfolio of stocks. She has identified 3 stocks in which to invest. She wants to earn at least 5% return but with minimum risk. Let:
P_i = proportion of total funds invested in stock i
$\sigma$ _i² = variance of stock i
$\sigma$ _ij = covariance between stocks i and j.R_i = average return on stock i
What is the objective function for the NLP formulation of this problem?

Question

An investor is developing a portfolio of stocks. She has identified 3 stocks in which to invest. She wants to earn at least 5% return but with minimum risk. Let:
P_i = proportion of total funds invested in stock i

\sigma

_i² = variance of stock i

\sigma

_ij = covariance between stocks i and j.R_i = average return on stock i
What is the objective function for the NLP formulation of this problem?

Quizplus · Accepted Answer

The objective function for this problem is to maximize the average return on the portfolio, which can be expressed as the sum of the products of the proportion invested in each stock and its corresponding average return. This can be written as:

Maximize RS1U1B1iS1U1B0S1U1P12S1S1P0

subject to the constraints:

- The sum of the proportions invested in each stock must equal 1 (to represent the total investment): S1U1B1iS1U1B0 = 1
- The portfolio variance must be less than or equal to a certain threshold (representing the desired level of risk): S1U1B1iS1U1B0S1U1B1jS1U1B0S1F1F1S1F1F1F10S1U1B1ij + 2S1U1B1iS1U1B0S1F1F1S1F1F1F10S1U1B1jS1U1B0S1U1B1kS1U1B0S1F1F1S1F1F1F10S1U1B1ik <= C, where C is the maximum allowable variance.

An Investor Is Developing a Portfolio of Stocks σ\sigmaσ i2 = Variance of Stock I

An Investor Is Developing a Portfolio of Stocks $\sigma$ _i² = Variance of Stock I