*4.3. Regression Results*

We extracted the pairwise DCC series between bitcoin and other assets from the ADCC-GARCH estimation results and then regressed the DCC series based on Equation (11) to assess the diversification, hedging and safe-haven properties of bitcoin for each asset. For example, by regressing the DCC series between bitcoin and the MSCI world index on a constant (*m*0) and three dummy variables (*m*1, *m*<sup>2</sup> and *m*3), we can assess the diversification or hedging capability of bitcoin for the global stock market based on the value and significance level of *m*<sup>0</sup> and the safe-haven capability of bitcoin for the global stock market based on the values and significance levels of *m*1, *m*<sup>2</sup> and *m*3. Tables 5–7 report the regression results for the daily, weekly and semi-monthly DCC series, respectively.

**Table 5.** Regression results for the risk diversification, hedging and safe-haven properties of bitcoin for other assets (daily frequency).


Note: *p* values are in parentheses. \*\*\*, \*\* and \* indicate significance at the 1%, 5% and 10% levels, respectively.

**Table 6.** Regression results for the risk diversification, hedging and safe-haven properties of bitcoin for other assets (weekly frequency).



**Table 6.** *Cont.*

Note: *p* values are in parentheses. \*\*\*, \*\* and \* indicate significance at the 1%, 5% and 10% levels, respectively.

**Table 7.** Regression results for the risk diversification, hedging and safe-haven properties of bitcoin for other assets (semi-monthly frequency).


Note: *p* values are in parentheses. \*\*\*, \*\* and \* indicate significance at the 1%, 5% and 10% levels, respectively.

The regression results for the daily frequency sample (Table 5) show that bitcoin cannot be considered a strong safe haven for all financial assets, implying that investors holding bitcoin cannot protect against extreme volatility in the prices of those assets. For the S&P 500, FTSE 100, DAX30, U.S. bond index, non-U.S. bond index, emerging markets bond index, S&P GSCI, oil and gold, the coefficients of the dummy variables characterizing the lower quartile values of their returns (*m*1, *m*<sup>2</sup> and *m*3) are all significantly positive in at least one case, which can only mean that bitcoin is an effective risk diversifier at the corresponding lower quartile levels of these asset returns. In terms of hedging properties, only the constant term (*m*0) of the U.S. dollar index is significantly negative across all assets, implying that bitcoin is an effective tool to hedge against the movement of the USD exchange rate and that USD investors in the FX market tend to use bitcoin to hedge their currency portfolios. This is consistent with the findings of Dyhrberg [21], who also shows that bitcoin can be

used as a hedge for the USD/EUR and USD/GBP exchange rates. All assets other than the U.S. dollar have significantly positive *m*0, so for these assets, bitcoin is only an effective risk diversifier. The main reason why bitcoin has risk diversification capabilities for most assets is that the mechanism of bitcoin price formation is more influenced by the bitcoin market's own supply and demand and investors' preferences for cryptocurrencies and less correlated with global macroeconomic and financial developments.

The regression results for the weekly frequency sample (Table 6) showed that in terms of hedging properties, only the U.S. dollar index had a significantly negative *m*0, while all other assets had a significantly positive *m*0. This suggests that in the weekly frequency dimension, bitcoin is still only a strong hedge against the U.S. dollar exchange rate and only an effective risk diversifier for other assets. In terms of safe-haven properties, *m*<sup>3</sup> was significantly negative for the S&P 500, and *m*<sup>1</sup> was significantly negative for crude oil, suggesting that bitcoin can be viewed to some extent as a safe haven against extreme volatility in the U.S. stock market (at the lower 1% quartile) and crude oil market (at the lower 10% quartile). This also means that investors have a tendency to put their money into the bitcoin market when there is a crisis in the U.S. stock market and the crude oil market. A possible explanation for why investors choose bitcoin as a safe haven in some cases, is that bitcoin operates as a decentralized cryptocurrency that is completely independent of any central institution. When traditional financial markets are under downward pressure, investors choose to seek shelter in the bitcoin market, which is independent of the traditional financial system and its underlying technical architecture.

The regression results for the semi-monthly frequency sample (Table 7) were similar to those for the weekly frequency samples. However, there were two differences. First, in terms of hedging properties, on the semi-monthly frequency, bitcoin not only had the ability to hedge the U.S. dollar index but also had a significant hedging effect on the SSEC. This suggests that bitcoin has the ability to hedge against declines in China's stock market in the long term. Moreover, the observation that bitcoin can hedge the Chinese stock market in the long term is also mentioned in the literature; for example, Chan et al. [24] found that bitcoin could serve as an effective hedge for the Chinese stock market in the monthly frequency dimension over the period 2010–2017. The likely reason is, that due to the existence of cross-border capital flow controls in China, when its domestic stock market is under long-term downward pressure, investors may seek to enter the bitcoin market to hedge against declines in the domestic stock market, as they have limited access to foreign investment. Second, in terms of safe-haven properties, on the semi-monthly frequency, bitcoin no longer has a strong hedging effect on the crude oil market but can still be considered to some extent as a safe haven against the risk of extreme volatility in the U.S. stock market at the low 1% quartile. Combining the weekly and semi-monthly frequency regression results, it was found that among the global stock markets, bitcoin had a significant safe-haven effect only for the U.S. stock market, which echoed the results found by Wang et al. [25] that the safe-haven properties of cryptocurrencies are more pronounced in developed markets or markets with larger market capitalization and higher liquidity.

In summary, bitcoin's risk diversification, hedging and safe-haven properties vary across time frequency dimensions, so distinguishing the holding period matters to bitcoin holders. For example, bitcoin does not have hedging ability against the Chinese stock market on the daily and weekly frequencies, but starts to produce a significant hedging effect on the semi-monthly frequency. In addition, bitcoin has no safe-haven properties for all assets on the daily frequency, but is starting to exhibit safe-haven properties for some assets (i.e., S&P 500 and crude oil) on the weekly and semi-monthly frequencies. One explanation for the differences in bitcoin's hedging and safe-haven properties at different time frequencies is that bitcoin's high short-term volatility and its strong speculative properties undermine its hedging and safe-haven properties in the short term and may even compromise its hedging and safe-haven properties in the long term. Another explanation is that bitcoin's hedging and safe-haven properties at different frequencies may be driven by different factors, as price formation of bitcoin may be influenced by different factors in the long and short term.
