  Signals coming from multivariate higher order conditional moments as well as
the information contained in exogenous covariates, can be effectively exploited
by rational investors to allocate their wealth among different risky investment
opportunities. This paper proposes a new flexible dynamic copula model being
able to explain and forecast the time-varying shape of large dimensional asset
returns distributions. Moreover, we let the univariate marginal distributions
to be driven by an updating mechanism based on the scaled score of the
conditional distribution. This framework allows us to introduce time-variation
in up to the fourth moment of the conditional distribution. The time-varying
dependence pattern is subsequently modelled as function of a latent Markov
Switching process, allowing also for the inclusion of exogenous covariates in
the dynamic updating equation. We empirically assess that the proposed model
substantially improves the optimal portfolio allocation of rational investors
maximising their expected utility.
