It is well-known in empirical finance that virtually all asset returns, whether monthly, daily, or intraday, are heavy-tailed and, particularly for stock returns, are mildly but often significantly negatively skewed. However, the tail indices, or maximally existing moments of the returns, can differ markedly across assets. To accommodate these stylized facts when modeling the joint distribution of asset returns, an asymmetric extension of the meta-elliptical t distribution is proposed. While the likelihood is tractable, for high dimensions it will be impractical to use for estimation. To address this, a fast, two-step estimation procedure is developed, based on a saddlepoint approximation to the noncentral Student's t distribution. The model is extended to support a CCC-(I)GARCH structure and demonstrated by modeling and forecasting the return series comprising the DJIA. The techniques of shrinkage, time-varying tail dependence, and weighted likelihood are employed to further enhance the forecasting performance of the model with no added computational burden.