**5. Discussion**

This paper has investigated the cryptocurrency market with a focus on collective correlation dynamics and portfolio diversification benefits across different market capitalization size deciles. We choose to investigate deciles as an analog of industry sectors in the equity market motivated by the vagueness of existing cryptocurrency sectors and the hypothesis that many retail investors use size as a primary means of diversifying across highly different cryptocurrencies. Throughout the paper, we consistently observed signatures of maturity in the cryptocurrency market with nuanced differences relative to established patterns in the (much) more mature equity market.

In Section 3, we analyzed the collective dynamics of the cryptocurrency market, focusing on collective correlation strength and market uniformity summarized in the leading eigenvalue and eigenvector of the correlation matrix, examining both the full market and individual deciles. Our first finding is that collective correlations spike during market crises connected to cryptocurrency exchange crashes; this occurs in every decile and closely resembles analogous behavior in the more mature equity market. Other findings of this section portray a more nuanced picture of the differences between the cryptocurrency and equity markets. While collective correlations spike across every decile during a crisis, it is not the case that correlations within each decile sector are uniformly higher than collective correlations across the whole market, as we previously observed for the equity market. In addition, the uniformity *h*(*t*) of different deciles over time exhibited a finding highly dissimilar from the equity market. This was the most significant difference relative to the equity market observed in this paper. While the uniformity (measuring the uniformity of different assets contributing toward the first principle component) was close to maximal 1 for every sector in the equity markets, that finding was not at all observed for the deciles of the cryptocurrency market. Curiously, it was observed for just two deciles consistently over time, but not the others. In addition, uniformity within deciles dropped during market crises, the opposite finding for the equity market.

These findings have significant implications for the alpha generation in the cryptocurrency market. The fact that collective correlations are so pronounced during market crises implies that alpha-generating opportunities based on systematic market movements would be more predictable and successful if performed on the short side. During market crises, correlations translate upward and cryptocurrencies of all sizes tend to decline. This would suggest that fundamentally-driven investment strategies may be more successful when implemented during buoyant equity markets, where there is less correlation among underlying securities. By contrast, during market crises (which are typically coincident among the equity and cryptocurrency asset classes) the collective strength of the market is so strong that the weight of underlying security investments driven by bottom-up analysis may be washed away by the sheer weight of money.

In Section 4, our portfolio sampling experiment investigated the diversification benefit of portfolios of total size *mn* spread evenly across *m* separate deciles. In a greedy experiment, we demonstrated that greater diversification benefit is generally obtained by increasing the number of decile sectors rather than the number of cryptocurrencies per decile, a result analogous to that observed for the cryptocurrency market. We followed this up with a careful experiment clustering different temporal trajectories of median normalized eigenvalue functions *λ*˜ *<sup>m</sup>*,*n*(*t*). A large majority cluster showed a similar result as observed for the equity market, that a portfolio of spread (4,4) had near-identical diversification benefit as our maximal size (10,4) cryptocurrency collection.

Our findings in this section may drive decision-making for optimal portfolio construction for cryptocurrency investors. First, the emergence of a low-cardinality highly diversified portfolio implies that retail investors may gain exposure to high-quality diversification at low-cost. When contrasting this analysis with that of the equity market, if we were to assume equivalent transaction costs and equivalent periodicity of portfolio rebalancing, the cryptocurrency may be a more retail-friendly market for easy access and portfolio diversification. Of course, given that the equity market is so sophisticated, there

is a large number of index-tracking and factor-based investment strategies that may benefit retail investors. This could be an opportunity for asset managers and large investment firms who are looking to create cryptocurrency investment products and is certainly a signature of the market's maturity. Finally, our analysis supports the notion that the cryptocurrency market may be a suitable environment for skillful stock pickers. We have highlighted that a portfolio of just 16 stocks produces low correlation and significant diversification benefits. This would indicate that an investment portfolio built upon a smaller number of high-conviction ideas could thrive in the cryptocurrency market.

There are several insights contained within concerning the cryptocurrency market's levels of maturity. First, the overall structure of the aforementioned hierarchical clustering is highly similar to that of the equity market. We have identified heterogeneous clusters of diversification benefit, and highlight the existence of a "best value" cryptocurrency portfolio where comparable diversification benefit is attained with relatively fewer securities held in a portfolio. Second, a crucial corollary of this finding is that retail investors with limited ability to hold complex portfolios of many cryptocurrencies may be sufficiently diversified with a relatively small portfolio across just 16 cryptocurrencies. However, there are some key differences in the equity market. First, the link between underlying cryptocurrencies' business functions (at least those coins that have a business function) and various business cycles is far less clear than in the equity market. Perhaps when the market becomes more sophisticated and such technological understanding becomes more mainstream knowledge, this could change the landscape of cryptocurrency investing. This could lead to the development of better-understood and widely disseminated cryptocurrency investment principles, which may drive more predictable investment patterns during different market cycles. Such dynamics are likely to drive further differentiation in cryptocurrency price patterns in varying market cycles and may lead to further diversification benefits as the market approaches greater levels of maturity.

No analysis is without its limitations. There are several limitations in our work. First, we have only looked at a collection of 40 cryptocurrencies. This could be extended, and include a much wider variety of cryptocurrency securities. The difficulty here is that many smaller coins do not have sufficient time windows for us to analyze. However, as time goes on, doing such analysis on a larger number of coins will become easier and may provide more robust insights. Furthermore, we could extend our portfolio sampling analysis to explicitly study diversification benefits during various market conditions. In the near future, we may be able to compare a short and intense market crisis such as the COVID-19 market crash or the Bitmex crash with that of the Russian financial crisis—or something more protracted and systemic. At present, the data is most likely insufficient.
