Chapter 6
A QP Solution Algorithm
In previous chapters, we have used a model p ortfolio optimization prob-
lem with o nly a budget constraint. Practical portfolio problems may
have nonnegativity constraints (x ≥ 0) on the asset holdings to pre-
clude 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 a lso
impose sector constraints which require that the portfo lio’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 ...