The aim of this paper is to propose a portfolio selection methodology capable to take into account asset tail co-movements as additional constraints in Markowitz model. We apply the methodology to the observed time series of the 10 largest crypto assets, in terms of market capitalization, over the period 20 September 2017–31 December 2020 (1200 daily observations). The results indicate that the portfolios selected considering tail risk are more diversified and, therefore, more resilient to financial shocks.