**Importance of Asset Correlations **

Many investors subscribe to Modern portfolio theory (MPT). MPT provides a model for how risk-averse investors can construct portfolios that maximize risk-adjusted returns (Sharpe ratio). It’s a widely known approach that characterizes the investment decisions of some of the largest asset managers. **Roughly, the goal is to have a high Sharpe ratio.** Importantly, MPT focuses on portfolio-level measures of risk and return rather than the performance of individual assets.

The term **“risk” **in the MPT context refers to a function of the variances of each asset and the correlations of each pair of assets. Measures of asset correlations are thus an input of Sharpe ratio, of which maximization is the investment goal. Intuitively, the relationships between price movements of assets in a portfolio contribute to the volatility of the portfolio, and adding assets that are uncorrelated with the rest of the portfolio might reduce volatility and increase Sharpe ratio.

Asset correlations among portfolio holdings matter.

**Crypto motivations**

In the cryptoasset context, this article covers two topics.

**1) Bitcoin’s correlations with Traditional Finance (TradFi) to evaluate its diversification benefits**

While the store of value/macro safe-haven thesis for Bitcoin has proven compelling for some institutions, others remain weary of Bitcoin exposure. Investors that aren’t gripped by a value approach might instead consider Bitcoin an investable asset due to its diversification benefits. This article assesses Bitcoin’s correlations with important TradFi metrics to qualify the diversification argument.

**2) Within-crypto correlations to study the network of price associations within the cryptoasset space. **

It’s no secret that most cryptoassets move together. Bull markets are (mostly) token agnostic and general sell-offs render the vast majority of assets in the red. This article looks beyond basic interrelationships that are already well-known to those familiar with the space and analyzes the price movements of over 100 cryptoassets. Do tokens that belong to a specific sector, like payment or privacy, tend to move together? Can a post-hoc analysis of price movements reveal relationships between seemingly disparate tokens? What does a visual depiction of the network of price movements look like?

Defining this landscape of relationships furthers understanding of the cryptoasset marketplace. This research can also serve as a benchmark from which future results can be compared. As this space rapidly evolves and innovation drives both iterative and qualitative change, the price relationships between tokens will no-doubt mutate as well. Additionally, this analysis is useful to investors since it deals in the type of investigation required to evaluate the concept of diversification in cryptoasset portfolios.

**Section 1: Assess correlations between Bitcoin and TradFi **

Throughout most of its history, Bitcoin has remarkably maintained a low correlation to traditional asset classes, including broad market equity/bond indices and commodities like oil and gold. However, the year 2020 revealed record high Bitcoin correlations that some believe signal a departure from digital gold’s uncorrelated past.

**Data note: **Unless otherwise specified, correlations refer to Pearson correlations of log-return time series. Price data do not tend to be normally distributed, so their correlations are meaningless. Log-return data are the standard inputs for financial correlations. Additionally, TradFi prices were carried forward for weekends and holidays.

From 2013 to 2019, Bitcoin was essentially uncorrelated with everything. In 2020, the correlation between Bitcoin and the S&P 500 was 0.22. Despite this figure being a record high, Bitcoin’s correlations remain low compared to those between traditional asset classes. For example, the S&P 500 and U.S. Real Estate index boasted a correlation of 0.73 for the same time period.

To obtain an updated assessment of Bitcoin correlations, let’s look at the 6 month period from October 2020 to March 2021. After all, Q2 and Q3 2020 were weird.

Despite the continued economic impact of the coronavirus and the cryptoasset space pulling a 4x since the first of the year, Bitcoin’s last six months correlations remain in line with the figures for the calendar year 2020. Bitcoin’s correlation with Tesla was lower than its corresponding linear association with the broader S&P 500, which might be surprising to those that consider retail interest and activity a driving force in both Bitcoin and Tesla.

In order to get a clearer picture of how Bitcoin’s correlations vary over time, let’s look at 90-day rolling correlations with data beginning in January 2018.

Bitcoin’s correlations with broader equities and U.S. real estate spiked in March 2020, and have remained higher than their historical levels since. Why, in the past 12-14 months, have Bitcoin’s correlations with TradFi been markedly higher than their historical levels? This is unfortunately a tough question to answer reliably, and the best we can do is informed speculation. Some thoughts on the topic are next briefly discussed.

To some degree, institutional involvement in Bitcoin renders it to behave more like other asset classes. In Q4 2020, only 36% of Coinbase volume was attributed to retail activity. But on the other hand, some institutions view Bitcoin as a safe-haven asset, of which demand would not intuitively align with broader equities. Bitcoin’s relationship with TradFi remains largely unclear, and future correlations will depend in part on how institutions view Bitcoin.

And likely to a much smaller degree, retail traders are playing an increasingly important but quantitatively unknown role in equities markets. This is likely not moving the needle on a broader scale, but will be an interesting trend to watch going forward

**Bitcoin and TradFi correlations: takeaways **

Overall, from a correlation perspective, Bitcoin is recently behaving more like traditional asset classes. **The diversification thesis for Bitcoin appears to be weakening, but it is still a relevant and potentially compelling narrative.**

Many diversification benefits remain intact. Adding Bitcoin to an all-stock portfolio could temper volatility. Bitwise, a crypto index fund provider, conducted a more substantive review of the topic, and concluded that “adding bitcoin to a diversified portfolio of stocks and bonds would have consistently and significantly increased both the cumulative and risk-adjusted returns of that portfolio over any meaningful time period in bitcoin’s history, provided a rebalancing strategy is in place.” Interestingly, the above benefits were retained even for hypothetical investors who first allocated to Bitcoin at its all time high.

Bitcoin’s correlations with TradFi are important relationships to follow going forward. Not only are they interesting metrics with which to assess market behavior, but also barometers for investability from a diversification perspective. Only time will tell whether Bitcoin’s correlations will remain uncharacteristically high.

**Section 2: Correlations between cryptoassets; Diversified cryptoasset portfolios **

Raising the concept of diversification in the context of cryptoassets might seem incongruous to some. After all, it’s all crypto and it’s all correlated. But such a take is a superficial treatment of a topic deserving further nuance and detailed study. And for investors, it’s flat out irresponsible. At a time in adoption when Bitcoin is a trillion dollar asset class and multiple ecosystems are gaining genuine traction, diversification in cryptoasset portfolios has never been more important. At the very least, investors should have a rough idea of how price movements of their assets are historically related. And serious investors ought to employ more nuanced diversification practices.

Google and TradFi experience indicate a number of general diversification strategies, each offering intuitive reasoning for why its implementation will mitigate risk. These include, but are not limited to, sector diversification and geographical diversification. While both sector and geographical diversification *seem *like good options, I’m not aware of analysis that justifies their efficacy as risk-mitigation strategies for cryptoassets. At face value, the practices appear to be xeroxed from TradFi portfolio theory and assumed to be applicable to crypto. **This level of scrutiny simply isn’t anywhere near adequate for a two trillion dollar asset class. **

This short article is of course not an exhaustive treatment of the subject, but merely a starting point in understanding the price relationships between cryptoassets.

Before jumping into the methodology or data, it’s useful to discuss a couple intuitive models that elucidate the problems with a high-level, superficial approach to portfolio diversification for cryptoassets. Let’s consider cryptoasset sectors, in which I see at least two reasonable theoretical models for price movements.

**Theory 1: A rising tide lifts all boats**

Generally, as in TradFi equities, sectors move as a group. When DeFi is up, most DeFi tokens will do well.

**Theory 2: Winner take all and network effects**

For a given problem or crypto use-case, network effects might be a fundamental driver of value and utility. That is, a reasonable end-game for a given crypto use-case is a single, well-scaled platform that everyone uses. It’s the best platform because everyone uses it. And users use it because everyone else uses it. A potential example of this notion is the relationship between Sushiswap and Uniswap. It’s a reasonable argument that one community will pull ahead, and the resulting deepening in liquidity will attract all the users.

It’s not in scope to strictly define specific cryptoasset sectors for this section. Rather it’s important to realize that both of the above theories are valid.

Whether you sway towards 1) or 2) above, or even a third reasonable approach, isn’t important for our purposes. What’s paramount to realize is that there are multiple reasonable approaches to crypto correlations that lead to opposite results. It makes sense that tokens from the same sector move in concert. It also makes sense that tokens fulfilling the same use case (a subset of tokens in the same sector) might move inversely.

Cryptoasset investing is new territory. Looking backward to TradFi for risk-mitigation strategies or relying on theoretical guesswork are irresponsible approaches to a serious question.

**Crypto correlations: Data**

Finally we can start getting some real answers. **We consider the universe of Bitcoin and Ethereum denominated cryptoassets traded continuously on Binance between January 1, 2019 and March 31, 2021.** While this criteria does exclude some important DeFi projects that were launched more recently, it incorporates a reasonable universe of cryptoassets and avoids additional data assumptions or complications. As before, correlations refer to Pearson correlations of log-returns time series.

**Crypto correlations: High-level results**

Unsurprisingly, and as we guessed before, it’s all crypto and it’s all correlated. All 5,578 cryptoasset pairs revealed a positive Pearson correlation. No single pair of cryptoassets divulged a log-return series with a negative correlation.

The measured correlations are unimodal and symmetric, and interestingly appear normally distributed with around a mean of 0.50 (median also 0.50) and standard deviation of 0.1.

Of the 30 least correlated pairs of cryptoassets, which sported Pearson correlations that ranged from 0.09 to 0.21, only two did not include DOGE. DOGE’s involvement in these pairs is not surprising given the meme token’s exponential rise driven in part by the Elon-fueled retail craze.

The most highly correlated pairs, which reported Pearson correlations above 0.8, tended to feature cryptoassets that could be reasonably characterized by their focus on scalability and transaction speed. Tokens such as BCH, LTC, ZEC, DASH, EOS, were included in pairs with the highest correlations.

While descriptive analysis like the above can sometimes be helpful, a more in-depth treatment of cryptoasset correlations is necessary. In the sections that follow, we transform our correlations such that we can use network analysis to investigate the space.

**Crypto correlations: High-level methodology**

The end goal is to produce a network of cryptoassets with associated groups of tokens that are mathematically linked by their historical price movements. Analyzing this graphic will hopefully reveal interrelationships between cryptoassets. The following steps are followed to obtain our cryptoasset network.

- Obtain historical prices Bitcoin or Ethereum denominated tokens on Binance. Convert BTC and ETH prices to their equivalent value in USD-Tether. And as before, convert prices to log returns so that Pearson correlations can be calculated.
- Administer applicable statistical techniques (described in more detail below) such that we can treat our correlationships like vectors and capture network features like group clustering.
- Utilize a community detection algorithm to construct network groups

**Crypto correlations: More detailed methodology**

Below we describe in more detail the statistical methodology we apply to create our network graphic. This section is helpful and potentially interesting, but not necessary to interpret the results.

Unfortunately, correlation estimates between two asset log-return series are notoriously misleading. Spurious correlation (linear association but no causal relationship) or the existence of confounding variables (unseen factors that affect both time series) are but two examples of risks incurred in citing correlation analysis.

To reduce the uncertainty and hopefully discover structure in the data, we apply a technique called **regularization, where we replace models with different (read: simpler) but related structures designed to reduce the influence of noise on our output.** Here, we apply a simple form of regularization based on an eigen decomposition of the sample correlation matrix. Eigen decomposition involves calculating eigenvectors and their corresponding eigenvalues. Eigenvectors are special vectors that represent linear transformations, which when applied only change the matrix by a scalar factor. We refer to the values of the scalar factors as eigenvalues. In our case, for example, the first two eigenvectors represent an orthogonal projection of the sample correlation matrix onto a 2-d plane (and so on). After computing the eigenvalues of the sample correlation matrix, we note that most of the information in this matrix is contained in the first few eigenvectors (yes, I checked).

In this analysis, we consider the first 10 eigenvectors. This decision greatly simplifies our computations and is an effective form of regularization in part because our problem of establishing groups of cryptoassets involves inverting matrices. If we invert matrices with very small eigenvectors, we are effectively amplifying to a large degree any noise in the data. Dividing noise by tiny values will obfuscate the analysis and provide misleading results, so our regularization strategy is preferable.

Put concisely, we regularize the sample correlation matrix by approximating it by a low-rank matrix that substantially reduces the influence of noise on the precision matrix. Given our precision matrix, we consider it as an undirected network of associations between cryptoassets. We look at the top 5% of associations, and apply the Louvain community detection algorithm to produce clusters of cryptoassets.

See below for our final result, which is a network graph that contains all cryptoassets denominated in Bitcoin or Ethereum traded continuously on Binance between January 1, 2019 and March 31, 2021.

The algorithm creates clusters of cryptoasset groups. Given that we already know all our pairs are positively correlated (most above 0.3), it’s unsurprising that clusters are not defined in an unconnected manner. Bridges fasten links between several loosely bound groups. No clusters are unconnected with the rest of the network, and there is considerable overlap between many groups.

At a closer look, the lower green cluster seems to capture the group of assets discussed above for featuring very high correlations. Security and scalability are certainly themes in this grouping.

Other clusters don’t reveal an obvious fundamental reason for being grouped. The gold cluster, for example, despite featuring a relatively well-defined and closely connected group of cryptoassets, includes tokens that span across location, use-case, and consensus mechanism. “Gold tokens” broadly cover several important cryptoasset sectors: payment, security, DeFi, ecosystem, and governance, to name a few.

One takeaway is clear, though. **Traditional methods of diversification do not extend – at least not exhaustively – to the cryptoasset space.** Judging by our network, it’s evident that sector or geographical diversification do not reliably define the interrelationships in price movements between cryptoassets.

Larger investors with more exhaustive portfolios should not accept half-baked, surface-level measures of diversification. More rigorous analysis is needed to accurately quantify risk and dependence among cryptoasset portfolios.

**Conclusion **

Bitcoin’s roll in modern portfolios: While Bitcoin in the past 12-16 months has behaved more like traditional asset classes, the diversification argument is still relevant and potentially compelling. Especially on a relative basis, diversification benefits remain intact. In fact, adding Bitcoin to institution grade portfolios, even when allocating at the top, “significantly increased both the cumulative and risk-adjusted returns of that portfolio over any meaningful time period in bitcoin’s history.” Institutions, take note.

Cryptoasset correlations and diversification in cryptoasset investing: Our network analysis shows that price relationships between cryptoassets is a complex space. Intuitive reasoning like use-case diversification holds true in some cases. But in others, fundamental features are defied and cryptoassets that move together don’t seem to be linked by underlying attributes. Larger investors with more exhaustive portfolios should not accept half-baked, surface-level measures of diversification. More rigorous analysis is needed to accurately quantify risk and dependence among cryptoasset portfolios.