*4.1. Criteria for Distinguishing an Asset's Risk Diversification, Hedging and Safe-Haven Properties*

We first established the criteria by which bitcoin is considered a diversifier, hedge or a safe haven. We followed Baur and Lucey [40] and Ratner and Chiu [37] to define a diversifier, hedge and safe haven, as these have become standard in the literature. Following Baur and Lucey [40] and Ratner and Chiu [37], we then distinguished bitcoin's risk diversification, hedging and safe-haven properties. The risk diversification property means that bitcoin is positively (but not perfectly) correlated with the returns of other assets. The hedging property includes a weak hedge, which means that bitcoin is uncorrelated with the returns of other assets, and a strong hedge, which means that bitcoin is negatively correlated with the returns of other assets. The safe-haven property includes a weak safe haven, which means that bitcoin is uncorrelated with the returns of other assets in times of market turmoil, and a strong safe haven, which means that bitcoin is negatively correlated with the returns of other assets in times of market turmoil. It is worth noting that our definition of a safe haven is ex post facto; that is, an asset (such as bitcoin) is considered a safe haven if investors show a preference for it during a market stress, which is of course only a necessary but not sufficient condition for an asset to be a safe-haven asset.
