The authors examine the relation between price returns and volatility changes in the Bitcoin market using a daily database denominated in US dollar. The results for the entire period provide no evidence of an asymmetric return-volatility relation in the Bitcoin market. The authors test if there is a difference in the return-volatility relation before and after the price crash of 2013 and show a significant inverse relation between past shocks and volatility before the crash and no significant relation after. This finding shows that, prior to the price crash of December 2013, positive shocks increased the conditional volatility more than negative shocks. This inverted asymmetric reaction of Bitcoin to positive and negative shocks is contrary to what one observes in equities. As leverage effect and volatility feedback do not adequately explain this reaction, the authors propose the safe-haven effect (Baur, Asymmetric volatility in the gold market, 2012). They highlight the benefits of adding Bitcoin to a US equity portfolio, especially in the pre-crash period. Robustness analyses show, among others, a negative relation between the US implied volatility index (VIX) and Bitcoin volatility. Those additional analyses further support the findings and provide useful information for economic actors who are interested in adding Bitcoin to their equity portfolios or are curious about the capabilities of Bitcoin as a financial asset.