Market turmoil, such as that induced by Covid-19, tends to create huge pressure on financial markets, forcing decision-makers and investors to analyze risks and manage their investment portfolios. Taking the market turmoil induced by Covid-19 as an example, this study addresses the question of whether Bitcoin exhibits a hedging and safe haven property during the period of turmoil. We employ the TVP-VAR approach to investigate return spillovers and interconnectedness among Bitcoin and stock, money, and bond markets. In addition, we employ three portfolio techniques, including minimum variance portfolios, minimum correlation portfolios, and minimum connectedness portfolios, to evaluate the Sharpe ratios of the portfolios as well as the cumulative return before and during the epidemic. The results demonstrate that incorporating Bitcoin decreases total connectedness across markets, and Bitcoin provides stronger hedging and safe haven capabilities. Notably, the portfolio with minimum connectedness approach reaches the highest Sharpe ratio during the pandemic.