<p>Despite its importance, there has been little research on the relationship between Bitcoin’s risk and returns. Therefore, it is necessary to investigate the risk–return trade-off of Bitcoin. In the existing limited literature, a negative risk–return relationship in Bitcoin for high-frequency intraday time-series data has been reported. In this paper, we use lower time–frequency data and suitable models for the data frequency to examine the risk–return trade-off of Bitcoin. Specifically, this paper examines the time-series volatility risk–return trade-off of Bitcoin using standard Markov switching (MS) and MS–GARCH models with weekly Bitcoin data from 2010 to 2024. Consequently, the study reveals several new findings. Firstly, the volatility risk–return trade-off relationship is identified for Bitcoin’s log returns. Secondly, the risk–return trade-off is also found for Bitcoin’s simple returns. Thirdly, the risk–return trade-off is uncovered for Bitcoin’s risk premiums as well. Fourthly, the study shows that the risk–return trade-off relationships for Bitcoin’s log returns, simple returns, and risk premiums hold true for all business days from Monday to Friday, indicating the robustness of the results. Furthermore, the study presents significant interpretations, implications, and discussion. We emphasize that we have discovered positive weekly risk–return relationships for Bitcoin using Markov switching models for the first time. This demonstrates the novelty of our work.</p>