The study of Dirichlet-weighted universal portfolios with side information was initiated by Cover and Ordentlich (1996) with emphasis on the (1, 1,..., 1) and (1/2,1/2,.…, 1/2) universal portfolios.Bounds on the ratio of wealths achievable were derived for the parametric class of Dirichlet-weighted universal portfolios by Tan (2002).Two-stock beta-weighted universal portfolios were studied by Tan (2004) with respect to a discretized market.We extend this study to the parametric class of Dirichlet-weighted universal portfolios with side information in a discretized market.Bounds on the ratio of wealths achievable in the discretized and non-discretized markets will be compared.