*4.4. Further Discussion*

One major distinction between measuring risk with volatility and anomaly score is that anomaly scores based on MD accounts for correlation among assets. Figure 5 plots cross-correlations among 15 cryptocurrencies for various rolling windows. The average cross-correlation is greater than 0.4 for most of the period in Panel (a), and a relatively high cross-correlation seems to be the norm due to inherent similarities among cryptocurrencies. In Panel (b), which plots the average among the top 50 cross-correlation values among 15 cryptocurrencies, the average cross-correlation is above 0.6 for most of the period. Nonetheless, there are noticeable drops in early 2021 for all the plots in Figure 5. In other words, cross-correlations among cryptocurrencies are relatively stable until late 2020 but inconsistency is observed in early 2021, which coincides with high anomaly scores. Even though average cross-correlations were more volatile when computed with daily returns as shown in Figure 6, lower cross-correlations in early 2021 are still observed, and it is especially evident from Panel (b) that the highest correlations show a significant drop in early 2021.

**Figure 5.** Rolling cross-correlations of weekly returns (rolling windows = 26, 39, 52, 104 weeks).

(b) Average of top 50 rolling cross-correlations among 15 cryptocurrencies

**Figure 6.** Rolling cross-correlations of daily returns (rolling windows = 30, 60, 90, 120 days).
