ABSTRACT
In all the theoretical developments so far, we have used the model problem
min{ − tµ′x + 1 2 x′Σx | l′x = 1}, (7.1)
or its extension to include a risk free asset. The parameter t ≥ 0 quantifies the risk aversion of the investor. Although (7.1) is very useful for developing the basic concepts for portfolio optimization, it is not particularly suitable in practice. There are two main reasons for this. First, the solution of (7.1) may result in excessive long and short selling. An example of this is an optimal solution of (7.1) with x1 = 1000, x2 = −1000, x3 = 1, x4 = 0, . . . , xn = 0. This means that the investor would sell 1000 times his wealth in asset 2 in order to purchase 1000 times his wealth in asset 1. This is a completely unrealistic position. Furthermore, there are generally legal requirements restricting short sales. One way of precluding short sales is to impose nonnegativity restrictions (x ≥ 0) on the problem. Note that these constraints are a special case of the general linear inequality constraints considered in the previous chapter.
