Experiments with robust asset allocation strategies: classical versus relaxed robustness
Many
optimization problems involve parameters which are not known in advance, but
can only be forecast or estimated. This is true, for example, in portfolio
asset allocation. Such problems fit perfectly
into the framework of Robust Optimization that, given optimization problems with uncertain
parameters, looks for solutions that will achieve good objective function
values for the realization of these parameters in given uncertainty sets.
Aim of this paper is to compare alternative
forms of robustness in the context of portfolio asset allocation. Starting with
the concept of convex risk measures, a new family of models, called norm-portfolio
models, is firstly proposed where not only the values of the uncertainty
parameters, but also their degree of feasibility are specified. This relaxed
form of robustness is obtained by exploiting the link between convex risk
measures and classical robustness.
Then, we
test some norm-portfolio models, as well as various robust strategies from the
literature, with real market data on three different data sets. The objective
of the computational study is to compare alternative forms of relaxed
robustness - the relaxed robustness characterizing the norm portfolio models,
the so-called soft robustness and the CVaR robustness. In addition, the models
above are compared to a more classical robust model from the literature, in
order to experiment similarities and dissimilarities between robust models
based on convex risk measures and more