The Mathematics of Financial Modelingand Investment Management

16-Port Selection Mean Var Page 485 Wednesday, February 4, 2004 1:09 PM

Portfolio Selection Using Mean-Variance Analysis 485

EXHIBIT 16.5 Optimal Portfolio and the Capital Market Line

hold portfolios consisting of combinations of the risk-free asset and the

tangency portfolio M on the Markowitz efficient frontier.

EXTENSION OF THE MARKOWITZ MEAN-VARIANCE MODEL TO

INEQUALITY CONSTRAINTS

The earlier optimization model introduced by Markowitz is useful from

a theoretical point of view, but it is insufficient from the point of view of

a portfolio manager who wants to optimize a real portfolio. In fact, the

above model has a number of serious shortcomings. In the next chapter

we will introduce the notion of systematic risk and nonsystematic risk.

A limitation of the Markowitz model presented above is that it only

minimizes systematic risk given a target expected return, but it does not

set any objectives for systematic risk. The latter can be set by constrain-

ing the portfolio exposure to selected risk factors. We will discuss these

risk factors in the next chapter.