*4.3. Anomaly Scores from Risk Factors*

Next, anomaly scores of the cryptocurrency market were further observed using the risk factors of the crypto market. Among several studies on cryptocurrency factors, Liu and Tsyvinski [20] performed comprehensive experiments to show the significance of network factors. While network factors do not provide a complete factor model for explaining the returns and risks of cryptocurrencies, it is worth analyzing with the factors that have been identified so far as being significant.

Weekly growths of four network factors (address, transaction, transfer, and wallet) were used for computing anomaly scores, and minimum covariance determinant (MCD) was chosen for robust MD calculations. The main idea of MCD is to find a sub-sample without outliers and the sub-sample is used for computing the sample mean and covariance [43]. Shrinkage estimators are often applied when the number of variables is large, so MCD was used in our experiment for estimating robust anomaly scores when there were only a few factors [44].

Here, returns were calculated for every week ending Sunday, following [20], and also because Figure 3 shows no substantial disparity among the seven graphs. In Figure 4, the anomaly scores either based on the entire period or only based on the last 104 weeks are almost identical; the robustness of MCD is also evident, similar to the robustness of shrinkage estimators in Figure 3. Additionally, the high volatility from March to May 2020 in Figures 1 and 2 is not noticeable in Figure 4, which matches the anomaly results in Figure 3. While there is a large spike in March 2019 in Figure 4, this is due to a sudden decrease in the numbers of transactions and transfers (see Figure A1). Even though these factors are not able to fully describe cryptocurrency returns or risks, the main purpose of the analysis using risk factors is to demonstrate its use in scenario analysis, as demonstrated in Section 5.2.

**Figure 4.** Anomaly scores from network factors (with MCD).
