**6. Conclusions**

Overall, we have uncovered nuanced similarities and differences between the cryptocurrency and equity markets. These mathematical properties signal increased signatures of maturity in the collective dynamics and diversification benefit of different portfolio spreads and provide concrete suggestions to retail investors seeking a relatively lowcomplexity exposure to the cryptocurrency market. Cryptocurrency decile sectors have been shown to share several properties, but not all, with industry sectors of the equity markets, and the most relevant findings for small-scale investors interested in limited-size portfolios are shared.

There are a variety of opportunities for future research building upon the methodologies we have developed and the insights highlighted in this paper. First, it would be interesting to test how the cryptocurrency market compares with other more mature and better-established asset classes with respect to various statistical properties. A thorough inspection of metrics such as drawdowns, peak-to-trough analysis, changepoint propagation, intra and inter-asset correlations, etc., could reveal information as to how cryptocurrencies can complement a multi-asset investment portfolio. An additional avenue of future research could be studying the data at a higher sampling rate than daily data. Given the significant

composition of day traders in the cryptocurrency market, we may see patterns that deviate from what we see intra-day within the equity market. In a somewhat-related manner, studying these securities in a longer time horizon may highlight regime shifts in dynamics or optimal portfolio construction. One of the key assumptions in this work is our separating cryptocurrencies into size deciles. Further work could look into alternative bucketing criteria such as sector allocation, volatility or other measures of risk. Finally, given the number of quantitative investment firms with burgeoning high-frequency cryptocurrency trading operations, one could examine the effectiveness of frequency-based trading strategies to see if there is greater "power" with certain trading windows. This could reveal typical holding periods for investment firms that trade in the cryptocurrency market.

**Author Contributions:** Both authors contributed equally to every aspect of the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data analyzed in this article are publicly available at [87]. A cached copy of the data and code are available at https://github.com/nickjamesgithub/Cryptocurrency\_Entropy.

**Conflicts of Interest:** The authors declare no conflict of interest.
