  A relationship between the growth-rate of logoptimal portfolios and capacity
of fading single-input multiple output (SIMO) channels are established. Using
this relation, stock vector stochastic processes that model the investment
environments are stochastically ordered using different criteria. The presence
of side information (SI) is considered, and a bound on the gains in the
growth-rate due to SI is derived along with data processing inequality and
convexity properties. A statistical test on the usefulness of SI that does not
require the computation of the optimal portfolio vector in the presence of SI
is introduced and its several variants are discussed.
