A mean–variance heterogeneous tails mixture distribution is proposed for modeling financial asset returns. It captures, along with the obligatory leptokurtosis, different tail behavior among the assets. Its construction allows for joint maximum likelihood estimation of all model parameters via an expectation–maximization algorithm and thus is applicable in high dimensions. A useful and unique feature of the model is that the tail behavior of the individual assets is driven by asset-specific news effects. In the bivariate iid case, the model corresponds to the standard CAPM model, but enriched with a filter for capturing the news impact associated with both the market and asset excess returns. An empirical application using a portfolio of highly tail-heterogeneous cryptocurrencies and realistic transaction costs shows superior out-of-sample portfolio performance compared to numerous competing models. A model extension to capture asset-specific asymmetry is also discussed.