This research explores the effects of adding bitcoin to an optimal portfolio (naïve, long-only, semi-constrained with and without bitcoin shorting) by relying on the mean-CVaR approach. We explore bitcoin's role in portfolios of U.S., European and Chinese assets. We back-test to compare the performance of portfolios with and without bitcoin for each scenario. The results show that by adding bitcoin, the portfolio performance improves; but this is due more to the increase in returns than in the reduction of volatility. In addition, the improvement is linked to bitcoin's performance in 2013. We conclude that bitcoin may have a role in portfolio diversification even though our analysis confirms bitcoin speculative characteristics.