Computation - Operations Management/Industrial Engineering

Computation

Equity

Portfolio Selection

Examples

Mathematics

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	Equity
	- Portfolio Selection

Harry Markowitz presented a theory for selecting financial securities for an investment portfolio in the paper "Portfolio Selection", in the Journal of Finance, Vol. VII, No. 1, March 1952. The paper is widely referenced. Two generally conflicting measures evaluate the portfolio, the expected return and the variance of the return. The latter represents the risk of the portfolio. The investor desires a portfolio that has a high return and low risk. Since the goals of maximizing return and minimizing risk are usually conflicting, we create a model that minimizes variance while satisfying a constraint on the target return. By solving the model for a series of returns we obtain an efficient frontier of solutions. Depending on the investor's risk tolerance, he or she should choose one of these solutions. We compute the variance of a portfolio using a Correlation matrix.

Data

The Equity add-in creates a worksheet to hold data describing the one-period return statistics for a collection of candidate securities, constructs the nonlinear programming programming model and provides buttons to solve the model for a specified target return or to find the sequence of solutions that comprise the efficient frontier. Three different assumptions are accommodated by the model:

The returns are independent random variables.
The returns are correlated random variables with the correlation matrix given by the analyst.
The mean and standard deviations of the returns and the correlation matrix are estimated by data included directly on the worksheet.

Click the icon below to see a sequence of pages describing how to use the add-in for independent returns.

Independent Returns

Click the icon below to see a sequence of pages describing how to use the add-in for correlated returns.

Correlated Returns

Click the icon below to see a sequence of pages describing how to use the add-in when security statistics are computed directly from data.

Security Statistics from Data

The examples are described more carefully in the following pages.