A general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. Inference is Bayesian and the computation is carried out using Markov chain Monte Carlo simulation. To enable model parsimony, a variable selection prior is used in each set of covariates and among the covariates in the mixing weights. The model is used to analyze the distribution of daily stock market returns, and shown to more accurately forecast the distribution of returns than other widely used models for financial data.