*4.2. Identification Approach*

The DCC coefficient between bitcoin and each asset is regressed on the lower quantile dummy variables of the corresponding asset returns to specifically identify the diversification, hedging and safe-haven properties of bitcoin for that asset. The regression equation is as follows:

$$D\mathbb{C}\mathbb{C}\_{l} = m\_{0} + m\_{1}D(r\_{\text{other\ asset}}q\_{10}) + m\_{2}D(r\_{\text{other\ asset}}q\_{5}) + m\_{3}D(r\_{\text{other\ asset}}q\_{1}) + \varepsilon\_{l} \tag{11}$$

where *rother asset* is the return on the corresponding asset, and *D*(*rother assetq*10), *D*(*rother assetq*5) and *D*(*rother assetq*1) denote the 10%, 5%, and 1% lower quartile dummy variables for the return on that asset, respectively. Figure 3 shows the 10%, 5% and 1% lower quartile values of daily returns for 14 traditional financial assets. The observations below the lower quartile values comprise the analysis period for our test of bitcoin's safe-haven properties. For observations below the 10% lower quantile value, we set *D*(*rother assetq*10) = 1; for observations below the 5% lower quantile value, we set *D*(*rother assetq*5) = 1; and for observations below the 1% lower quantile value, we set *D*(*rother assetq*1) = 1.

If *m*<sup>0</sup> is significantly positive, then bitcoin has risk diversification capability for that asset; if *m*<sup>0</sup> is equal to 0, then bitcoin has weak hedging capability for that asset; if *m*<sup>0</sup> is negative, then bitcoin has strong hedging capability for that asset. If *m*1, *m*<sup>2</sup> and *m*<sup>3</sup> are not significantly nonzero, then bitcoin has a weak safe-haven capability for that asset; if *m*1, *m*<sup>2</sup> and *m*<sup>3</sup> are significantly negative, then bitcoin has a strong safe-haven capability for that asset.

**Figure 3.** The 10%, 5% and 1% lower quartile values of 14 traditional asset returns (daily frequency). The three horizontal lines from top to bottom in each graph indicate the 10%, 5% and 1% lower quartile values, respectively.
