Introduction
One of the more difficult questions to answer within the cryptocurrency space is what is the appropriate allocation for institutional investors to the asset class, if any. Most of the work done to address this has been predominantly empirical in nature, concentrating on the divergent return profiles between portfolios with or without crypto assets. In part, that is because the premise of the question is optimisation oriented, based on investors’ relative objectives and constraints. Consequently, most analysts practice mean-variance optimisation to estimate crypto asset allocations that maximise expected returns in the context of risk aversion.
But the tradeoff between expected volatility and returns looks very different depending on which market regime these assets trade under - risk-on or risk-off, reflationary vs deflationary, expansionary or recessionary. Historically, the correlation between cryptocurrency and US stock returns has tended to be low. But the coefficient rose sharply in late 2021 and early 2022 due to stressed market conditions as the Federal Reserve raised rates and reduced the size of its balance sheet. In fact, we show in Exhibit 1 how the risk-adjusted performance of digital assets converged to other asset classes during this period, despite idiosyncratic deleveraging among some key crypto-related entities. This is a notable deviation from cryptocurrencies’ performance during the previous “crypto winter” of 2018-2019 when digital assets sold off compared to peers, under comparably tight macroeconomic conditions.
Source: Coinbase, Bloomberg, Venn by Two Sigma.
Comparing the distribution of daily returns back to 2018, we see how much wider the range of outcomes can be for crypto assets. Specifically, the Coinbase Core Index and S&P Cryptocurrency Top 10 Equal Weight Index exhibited 99 and 142 days of +/-8% returns respectively, whereas a 60/40 equity and bond portfolio experienced daily returns of between -6% to -5% and 4% to 5% only one time each1 (See Exhibit 2).
Understanding this difference can help us better address the original question of portfolio allocation from a fundamental perspective. The challenge is that cryptocurrencies can represent a diverse set of projects that are in varying stages of development (often early), such that the spectrum of utility value can be wide or in some cases, not yet fully realised. While asset allocations under mean-variance optimisation appear to be diversified, we think that this approach crucially does not offer any insight into the diversification benefits in the sources of risk. Alternatively, we will show using a multi-factor risk model that adding cryptocurrencies to a portfolio can increase the diversification benefits from a systematic risk perspective.
Source: Coinbase, Bloomberg, Venn by Two Sigma.
Benchmark selection
When it comes to cryptocurrencies, many investors focus less on the competing investment approaches available to them and more on what percentage of a portfolio they should allocate to digital assets in the first place. This perspective tends to ignore the nuances that can distinguish the thousands of crypto assets that comprise the US$1.2 trillion asset class, including use cases, differentiated architectures and/or growth dynamics. In fact, the higher fluctuations of crypto returns within the distribution curve suggest allocations can be sensitive to small changes in inputs. This makes benchmark selection particularly important in order to limit estimation error.
It is worth noting that, when rewarded, higher fluctuations of crypto assets can also introduce the opportunity for capital efficiency. For example, adding 1% exposure to cryptocurrencies may be more beneficial from an asset allocation perspective than adding 1% exposure to a US large-cap fund, particularly given the long right tail in the distribution of crypto returns historically.2
Source: Coinbase, Bloomberg, Venn by Two Sigma.
We choose two cryptocurrency benchmarks to serve as a reference for our portfolio construction analysis based on an asset-only approach: the Coinbase Core Index (COINCORE) and the S&P Cryptocurrency Top 10 Equal Weight Index (SPCC10).3 Both indices track the largest cryptocurrencies by market capitalisation. We believe this is representative of the current investable universe for the asset class, considering the top ten (non-stablecoin) digital assets alone account for over 73% of total crypto market capitalisation (as of April 2023). Notably, the composition of the overall crypto market today is still disproportionately dominated by Bitcoin and ether, comprising 63% of the market.
With that in mind, COINCORE is a market cap-weighted index that is rebalanced quarterly with an almost 94% combined allocation to Bitcoin (65.3%) and ether (28.7%) among eight constituents total. We think that this can provide greater insight into the concentrated performance characteristics of those two large-cap digital assets. Meanwhile, SPCC10 is an equally weighted index that is also rebalanced quarterly, which we believe better captures the return profile of alternative crypto assets (colloquially known as altcoins) alongside Bitcoin and ether.
Notably, the smaller market cap proportion of digital assets outside of bitcoin and ether, particularly prior to 2017 means that there is a much shorter history with which to evaluate variations in returns. For example, available returns data for the SPCC10 index begins on March 19, 2018, which is what we use as the start date of our common period. Hougan and Lawant (2021) have written that large overlapping factors like “evolving regulation, emerging education, liquidity, and new entrants” tend to drive high correlations among digital assets.4 Historically, this means that the returns of these benchmarks can trend directionally in tandem despite having different return distribution profiles. In fact, the one-year correlation of these indices currently suggests a strong relationship with a coefficient of 0.89 – although it’s still too early in our view to judge the stability of this relationship without a long history. For reference, the lowest one-year correlation between the two indexes was 0.74 in April 2021.
So far, the longest periods of relative upside in risk-adjusted returns for the SPCC10 versus the COINCORE happened in H2 2020 and H2 2021 (see Exhibit 4). We believe that these periods reflected (1) a supportive global liquidity environment due to the pandemic, and (2) the launch of many new altcoin projects at the time that were competing for market share.5 We should note that the equally weighted SPCC10 index has unsurprisingly offered consistently higher risk (both in terms of general volatility as well as higher maximum drawdowns) while practically being more difficult for investors to fully replicate given available supply constraints on some altcoins.
Source: Coinbase, Bloomberg, Venn by Two Sigma
The optimisation problem
We evaluate the marginal impact of incremental cryptocurrency allocations to a traditional 60% equity and 40% fixed-income portfolio starting with a 1% exposure and going up to a maximum of 5%, adjusting our equity and bond positions proportionally. Our simulations are also rebalanced quarterly to limit the risk of outsized exposure increases (decreases) over time. We also consider the fixed five-year period between March 2018 and March 2023 selected based on available data, which encompassed two major cycles of price depreciation and two major cycles of price appreciation for crypto assets. Note that digital assets still represent a small part of many investment portfolios’ value because of concerns over price volatility.
Source: Coinbase, Bloomberg, Venn by Two Sigma. Calmar ratio (return divided by absolute maximum drawdown) shown in the table is over the most recent 3-year period. Using returns and drawdowns over the full 5-year period, Calmar ratios for portfolios with a 1-5% allocation to COINCORE are: 0.23, 0.25, 0.27, 0.29, 0.30. For SPCC10 they are 0.23, 0.24, 0.26, 0.27, 0.28. The full period Calmar ratio for the 60/40 ACWI & US AGG is 0.21.
The results are consistent with previous studies that suggest adding crypto assets to a portfolio can increase the relative return in both absolute and risk-adjusted terms.6 For example, adding a 2% exposure to COINCORE would have increased the return on our base portfolio by 1.20pp, while adding a 2% exposure to SPCC10 would have increased the return on our base portfolio by 1.05pp over the five-year period under consideration. Adding crypto exposure would have increased the volatility of these portfolios as well, but by proportionally less than the accumulated return benefits – 0.25pp and 0.49pp higher respectively.
In other words, crypto exposure ostensibly improved the risk-adjusted performance of a traditional portfolio, expanding the arithmetic Sharpe Ratio7 from 0.35 to 0.45 in the case of a 2% COINCORE allocation and to 0.43 in the case of a 2% allocation to SPCC10. See exhibits 5 and 6 above for our full compiled results. These tables show that the Sharpe Ratio also increases for every 1% increase in our cryptocurrency allocation. For example, using the portfolio with COINCORE, a 1% exposure to digital assets increases the Sharpe Ratio of a 60/40 portfolio by 14% compared to a 63% increase for a 5% exposure, irrespective of the cyclical downturns during our observation period.
The higher risk and reward tradeoff for digital assets tends to put greater scrutiny on their potential for large drawdowns, although the Calmar ratio helps to contextualise such concerns. More precisely, if we measure the average compounded returns of our portfolios against their respective maximum drawdowns, we still see that adding more crypto exposure provides a higher (i.e., better) Calmar ratio even over a longer-term time horizon. Consequently, we believe that this analysis provides added perspective on the risks of higher maximum drawdowns in crypto with respect to the extra returns earned on these assets.
Diversification from known sources of systematic risk
Thus far we have evaluated the risk and reward tradeoff of adding crypto to a standard 60/40 portfolio and shown that empirically this has been beneficial. However, such discourse treats all risk as equal, thus defining outcomes in a binary way (i.e., more risk is “worse” and less risk is “better”), rather than analysing whether a particular set of adopted risks is common or unique.
Venn by Two Sigma is a returns-based multi-factor risk analysis tool that uses 18 systematic risk factors across and within asset classes to identify risk. Risk analysis using Venn helps to not only understand how levels of risk change, but also how that risk is composed and what each component contributes to return. Any risk that cannot be explained by these 18 factors (see exhibit 7) is labelled as residual.
Exhibit 7: The Two Sigma Factor Lens
Source: Venn by Two Sigma. For Illustration Purposes Only.
Residual (or unexplained) risk can represent a variety of things depending on the asset being analysed. For a hedge fund manager, it may represent their unique alpha that cannot be captured by these systematic risk factors. It could also represent unknown factors or factors that are not included in the Two Sigma Factor Lens.8 Many institutional investors welcome a higher residual as it represents a unique risk that may diversify their overall portfolio. This is especially true when that residual has been contributing positively to performance.
Of note, the Two Sigma Factor Lens aims to consolidate risk to the factor generating said risk, even if that risk is found somewhere else. For example, when analysing an emerging market equity fund in Venn, you would expect Venn analysis to separate any risk attributable to Venn’s Equity Factor from any risk attributable to a statistically independent Emerging Market Factor. This lens of independent factors is achieved through a process called residualisation.9 Residualisation is the method by which the influence of higher tier factors is attempted to be removed from lower tier factors, resulting in the consolidation of that risk to higher tiers.10 In the Two Sigma Factor Lens, Equity and Interest Rates represent the highest tier.
Exhibit 8: The Residualisation Process of the Two Sigma Factor Lens
Source: Venn by Two Sigma. For Illustration Purposes Only.
We would expect that the majority of risk in a traditional 60/40 portfolio would be explained by the Two Sigma Factor Lens as the 60% equity and 40% bond allocation closely represents the two highest tier factors, respectively. We found that this expectation was met with roughly 98.99% of risk being explained, leading to 1.01% of risk as an unidentifiable residual. This highly explainable base portfolio provides a good foundation for analysing the impact of crypto allocations on unique sources of risk.
With a 1% allocation to crypto, residual contribution to risk rises to 1.53% and 1.65% for COINCORE and SPCC10 respectively, indicating the introduction of more unique and unexplainable risk. At 5% allocations to these crypto indexes, the residual risk contribution rises to 9.19% and 12.54% of total risk respectively, suggesting these contributions to factor diversification tend to rise at a faster than linear pace.
Source: Coinbase, Bloomberg, Venn by Two Sigma
Additionally, we can observe how the higher residual risk of portfolios that include crypto has contributed positively to return. This is despite this shorter five-year period under examination, which does not capture the significant rise in bitcoin prices before March 2018. Specifically, the portfolios including 5% allocations to each crypto index had their residual components contribute an annualized 2.53pp (COINCORE) and 1.65pp (SPCC10) to total returns. For the 60/40 portfolio (without crypto), the residual return was virtually zero. This helps to illustrate how the addition of crypto can not only increase exposure to residual risk but how that unique risk directly led to positive return contributions in this example. To put it more plainly, crypto has been different in a positive way.
Source: Coinbase, Bloomberg, Venn by Two Sigma
Further areas of study
It is worth noting that much like an Equity Factor can help explain the systematic risk of individual stocks and even other assets, it may be that a Crypto Market Factor can help explain the systematic risk of individual cryptocurrencies. In fact, Venn by Two Sigma has already found evidence that a Crypto Market Factor may be systematic and is currently researching the possibility of implementing it as a 19th factor in the Two Sigma Factor Lens. Adding a 19th factor is not a trivial matter. Added risks must be researched and determined to be sufficiently differentiated and capable of explaining broad and persistent systematic risks in the market. That said, if a Crypto Market Factor is added, we would expect some of the residual risk introduced by digital assets to a 60/40 portfolio to instead be captured in part by this Crypto Market Factor. The introduction of a 19th factor would still be a testament to crypto’s unique nature, even if it does mean that crypto risk contains a systematic component.
Conclusions
Empirical studies of the volatility-adjusted performance of portfolios holding digital asset allocations can be useful for weighing the tradeoffs between maximising wealth and minimising volatility. However, they fail to capture the utility of those allocations from a diversification perspective and offer only a limited framework for optimal allocation size that is contingent on return expectations. In practice, correlations between crypto and other assets tend to be dynamic and the relationships observed during phases of rapid growth may look different from the recent past or post-adoption periods.
Our findings suggest that crypto allocations can diversify fund managers’ exposure to uncommon sources of risk in traditional “balanced” equity vs bond portfolios. Residual risk is everything that the Two Sigma Factor Lens cannot explain, and within that structure, it represents a unique risk which may be desired as a data point to signify that crypto is capturing something that the rest of a portfolio does not. We believe that quantifying this should allow fund managers to determine the merits of different crypto allocations according to their diversification benefits in a measurable way.
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References
1 That is, a portfolio allocated 60% to the MSCI All Country World Index (ACWI) and 40% to the Bloomberg US Aggregate Bond Index (AGG).
2 Andrew Ang, Tom Morris, and Raffaele Savi. “Asset Allocation with Crypto: Application of Preferences for Positive Skewness.” Published 22 February 2022.
3 The factsheets for the COINCORE and SPCC10 indices can be found here and here. Note that the number of constituents in the COINCORE index is variable, based on whether the constituents satisfy fundamental criteria, whereas the number of constituents in the SPCC10 is fixed at ten.
4 Matt Hougan and David Lawant.. “Cryptoassets: The Guide to Bitcoin, Blockchain, and Cryptocurrency for Investment Professionals.” (CFA Institute Research Foundation.) Published 7 January 2021.
5 David Duong, CFA. “Monthly Outlook: It’s Cyclical, Not Structural.” (Coinbase Research.) Published 1 February 2022.
6 Weiyi Liu. "Portfolio diversification across cryptocurrencies." (Finance Research Letters.) Published June 2019.
7 Throughout this piece arithmetic sharpe is used, not geometric. Notably, geometric and arithmetic sharpe will be more differentiated among higher volatility assets such as cryptocurrencies. This is because geometric returns are compounding and introduce volatility drag.
8 More information about the Two Sigma Factor Lens can be found here.
9 More information about residualisation found in the Two Sigma Factor Lens can be found here.
10 More information about the formulas and methodologies used in this paper can be found here
