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Cryptocurrencies (CCs) have risen rapidly in market capitalization over the last years. Despite striking price volatility, their high average returns have drawn attention to CCs as alternative investment assets for portfolio and risk management. We investigate the utility gains for different types of investors when they consider cryptocurrencies as an addition to their portfolio of traditional assets. We consider risk-averse, return-seeking as well as diversificationpreferring investors who trade along different allocation frequencies, namely daily, weekly or monthly. Out-of-sample performance and diversification benefits are studied for the most popular portfolio-construction rules, including mean-variance optimization, risk-parity, and maximum-diversification strategies, as well as combined strategies. To account for low liquidity in CC markets, we incorporate liquidity constraints via the LIBRO method. Our results show that CCs can improve the risk-return profile of portfolios. In particular, a maximum-diversification strategy (maximizing the Portfolio Diversification Index, PDI) draws appreciably on CCs, and spanning tests clearly indicate that CC returns are non-redundant additions to the investment universe. Though our analysis also shows that illiquidity of CCs potentially reverses the results.