In this paper, we use vine copula approaches to model the co-dependence and portfolio value-at-risk (VaR) of six cryptocurrencies using data of daily periodicity from September 2015 to June 2018. We establish evidence of strong dependencies among the virtual currencies with a dynamic dependency structure. We find that among the class of cryptocurrencies examined, Ethereum offers the best optimal and economically risk-reward trade-off subject to a no-shorting constraint for portfolio investors using the efficient frontier. Given the paucity of empirical research on the cryptocurrency markets, this paper provides new insights, which could be useful in developing dependence and risk strategies for investment and hedging purposes, especially during more volatile periods in the markets.