ABSTRACT
In previous chapters, we have used a model portfolio optimization problem with only a budget constraint. Practical portfolio problems may have nonnegativity constraints (x ≥ 0) on the asset holdings to preclude the possibility of short sales. These are lower bound constraints. Portfolio managers may also include upper bound constraints so that any change in asset holdings is not too large. Practitioners may also impose sector constraints which require that the portfolio’s holdings in particular industry sectors, for example oil related sectors, does not exceed a certain percentage. Transaction costs may also be included by introducing new variables which are restricted to be nonnegative. Thus a realistic portfolio optimization problem must include general linear inequality constraints.
