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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. |
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.
Click the icon below to see a sequence of pages describing
how to use the add-in for 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.
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Security
Statistics from Data |
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The examples are described more carefully in the following
pages. |
