Correlation, covariance and event risk - Technical article accompanying Portfoliothese | Issue 2

Five building blocks of a digital asset portfolio compared over 54 months

At a glance

Research question and study design

The practical question behind it is familiar. A factsheet shows a correlation of 0.59 for a new strategy to exactly the risk it is meant to diversify. Is that already too high to count as a sensible addition, or does a correlation figure alone say too little about the actual portfolio effect?

The starting point of this study was a widespread rule of thumb: in stress phases all correlations go to one, so a correlation measured over the whole period is of little use for assessing a building block with a diversification function. The plan was therefore to estimate conditional correlations within negative market phases.

This plan was dropped because the subsamples are too small. Depending on the delimitation, only 21 to 26 monthly observations remain within the regimes.

Three levels of analysis were defined in advance: the overall correlation including its estimation uncertainty; behaviour in negative market regimes, that is, in phases of falling markets, based on average return and share of positive months; and three predefined stress events. A qualitative decision rule under which the thesis would be regarded as weakened was likewise defined in advance.

Volatility, beta, the portfolio volatility calculation and the scaled cross-check were not part of this plan. They are downstream explanatory analyses with which we interpret a pattern that the predefined evaluation made visible. This separation is maintained in what follows.

Data basis

Five economically distinct building blocks were examined over a common window from January 2022 to June 2026, that is 54 monthly returns: Bitcoin via the Galaxy Bitcoin Series, the altcoin index via the S&P Cryptocurrency BDA Ex-MegaCap Index, the market-neutral index via the Galaxy VisionTrack Market Neutral Index, and two anonymised individual strategies for stablecoin income and DeFi income. The Ex-MegaCap index covers the broad digital asset market excluding Bitcoin and Ethereum; S&P’s methodology explicitly defines MegaCap as the combination of these two assets. The designations correspond to those of the accompanying LinkedIn newsletter PORTFOLIOTHESE, which you are welcome to subscribe to via the following link: PORTFOLIOTHESE.

The two anonymised series are not segment benchmarks. For these narrowly defined segments, no sufficiently suitable broad benchmark was available for the study. Both stand as examples of the respective return driver and were selected from the available strategy universe for their suitability to represent this return driver, not for the level of their historical returns. For them, monthly net histories after fees are used; market and index series enter as index returns without assumed product costs.

The market-neutral index series needs a qualification that is essential for the robustness of the core finding. The Galaxy VisionTrack Market Neutral Index is based on returns that participating managers contribute voluntarily, and Galaxy states explicitly that this information is not independently verified. Such a database construction is potentially susceptible to selection, survivorship and backfill effects. The direction and magnitude of these effects cannot be quantified from the data used here. The limitation is particularly relevant because the index’s low standalone volatility is essential for part of the portfolio effect that follows.

The individual volatilities, annualised, are 54.1% for Bitcoin, 67.2% for the altcoin index, 4.4% for the market-neutral index, 4.5% for DeFi income and 1.1% for stablecoin income. The correlations with Bitcoin are 0.85 for the altcoin index, 0.59 for the market-neutral index, 0.27 for DeFi income and −0.08 for stablecoin income.

The portfolio volatility calculation

The starting point is a pure Bitcoin portfolio. In each case half of it is replaced by one of the other building blocks. A cash allocation serves as the reference, modelled as a 0% return and 0% fluctuation.

The half-and-half split is deliberately not a client allocation but a comparison measure. It holds weight and starting risk constant across all five cases, so that only the properties of the building block added create the difference. What this means for a real mandate is covered under Limitations of the study.

The second and third columns are the ones to compare: the correlations lie far apart, the resulting volatilities of the first three additions do not.

The correlations clearly distinguish the three building blocks. Their effect on portfolio volatility does not: the resulting values lie 1.4 percentage points apart, and all three are in the range of the plain cash allocation of 27.1%.

With the altcoin index the picture reverses. A correlation of 0.85 meets a standalone volatility that is above that of Bitcoin. Adding it does not lower portfolio volatility; it raises it by just under 8%.

What this calculation does not isolate

A self-correction is needed at this point, which we do not want to conceal. The portfolio volatility calculation does not isolate the diversification effect at all. What it shows is the total portfolio effect, including the effect of replacing a highly volatile building block with a less volatile one (the replacement effect). A large part of the measured reduction arises not from diversification but simply from replacing half of a very volatile building block with a much less volatile one. That is precisely why the cash reference, whose covariance term is zero under assumed zero volatility, achieves almost the same result.

Whether any diversification contribution lies behind the three almost identical values is not answered by this calculation. That requires a cross-check.

The scaled cross-check

The following step is a deliberately unrealistic thought experiment. It answers the question of what remains of the measured effect when the volatility difference disappears.

To isolate the contribution of the correlation, each building block is arithmetically normalised to Bitcoin’s volatility of around 54%. With equal weighting and equal range of fluctuation, only the correlation then determines the difference. The underlying relationship is given in the methodology section.

The result sharpens the picture considerably. Unscaled, the three building blocks lay within 1.4 percentage points. At the same range of fluctuation, the correlation makes the difference between a volatility reduction of around 32% and around 11%, almost a factor of three.

A high correlation therefore does not mean that a building block is worthless. At the same range of fluctuation, it means that it contributes considerably less to reducing portfolio volatility. In the unscaled world, this difference disappears behind the much larger replacement effect.

How large this replacement effect is can be quantified exactly. The calculation is given under Deep dive: Where the effect arithmetically comes from, because it is no longer needed for the finding itself.

Beta and its limits

For portfolio work, the same question arises in a more familiar metric: how much Bitcoin market risk is actually contained in the individual building blocks? Translated into this classic measure, correlation and volatilities yield the beta to Bitcoin.

For stablecoin income, both perspectives point in the same direction: the correlation is close to zero, and owing to the very low standalone volatility the Bitcoin beta is also practically zero. These betas, too, are based on the same 54 observations and are sample estimates, not stable properties of the building blocks.

Estimation uncertainty

Up to this point we have worked with the measured correlations. How robust are these figures in the first place? All correlations mentioned so far are point estimates from 54 months. Their uncertainty is considerable and not visible in the tables.

For stablecoin income, a noticeably negative relationship would be as compatible with this history as a slightly positive one. The statement that this series is uncorrelated with Bitcoin claims more than the data can support. With such a history, the second decimal place suggests a precision that does not exist.

The same uncertainty was the reason not to estimate the originally planned conditional correlations. A correlation of 0.40 measured within a regime would, with around twenty observations, have an approximate 95% interval of −0.04 to +0.71. Such an estimate would look precise without being so.

Behaviour in negative market regimes

For a building block that is meant to spread risk, what counts is not only how strongly two series are related over the whole period, but whether their distinct return behaviour persists precisely when diversification is needed. Within the regimes we calculate no new correlations, for the reason given under Estimation uncertainty, but look at average return and the share of positive months.

The regime indicator for the digital asset market is the market-cap-weighted S&P BDA. Its high Bitcoin weighting is deliberately accepted because it reflects the actual concentration of the market. Because the regime is therefore strongly shaped by Bitcoin, the S&P 500 is added as an external cross-check.

In the 26 months in which the broad digital asset market fell, Bitcoin lost 10.75% on average. In the same regime the market-neutral index achieved plus 0.35% on average and was positive in 23 of 26 months, despite an overall correlation of 0.59. DeFi income stood at plus 0.47%, and stablecoin income was positive in all 26 months. In the 21 negative months of the S&P 500, these three building blocks likewise remained positive on average.

Two qualifications belong here. First, these regime averages already include the shock months. Second, the finding does not prove a general independence from traditional markets. It shows that the three building blocks behaved markedly differently from Bitcoin and the altcoin index on average, both in negative digital asset months and in negative equity market months.

The three stress events

In November 2022, FTX collapsed, at the time one of the largest crypto exchanges in the world, where customer funds were not held separately from the exchange’s own assets. Bitcoin lost 16.80%. With a Bitcoin beta of around 0.05, that corresponds to a computed contribution of around −0.8 percentage points for the market-neutral index. In fact the series lost 4.60% and DeFi income 4.81%.

Measured against their respective monthly volatility, derived from the full history, that corresponds to roughly 3.6 and 3.7 times respectively. A single common event thus hit two previously very smooth building blocks by a multiple of their normal range of fluctuation.

Beta describes the average linear market sensitivity. A Bitcoin beta, however, does not identify counterparty, liquidity or market-structure risks and does not say how a strategy reacts to such a shock. The FTX shock hit exactly those dimensions: exchange, counterparty, liquidity and market-structure risks. That the market-neutral index lost 4.60% that month shows that a low market beta does not rule out these risks.

The rule of thumb mentioned at the outset, that all correlations go to one in stress phases, can be neither confirmed nor refuted from these data; conditional correlations were deliberately not estimated. What the evaluation shows is a different mechanism: a single event can hit several building blocks simultaneously via a risk dimension that is not visible in the full-period correlation.

The two other predefined events stand for different channels. Terra/Luna, the collapse of an algorithmic stablecoin together with the ecosystem built on it, was a protocol shock with Bitcoin at minus 15.75% and the altcoin index at minus 40.80%. In the USDC depeg of March 2023, the stablecoin USDC temporarily lost its dollar peg because part of its reserves were held at Silicon Valley Bank, which regulators had closed shortly before; here a classic banking risk was transferred into a supposedly purely digital structure.

Bitcoin rose 23.08% that month; of the four other building blocks only the altcoin index closed in the red, with a loss of 4.03%. There was no loss on the scale of Terra/Luna or FTX.

The peg, however, was restored within a few days. Monthly data can completely conceal an interim drawdown and its recovery within the same month. What becomes visible here is the month-end, not the path to get there. Which risk dimension a shock hits has a major influence on which building blocks are affected.

Robustness check

A downstream check without the three predefined stress months leaves 51 observations and changes DeFi income in particular. The correlation with Bitcoin falls from 0.27 to 0.13, and at the same time the annualised standalone volatility falls from around 4.5 to 3.3%. For the market-neutral index and for stablecoin income, by contrast, the correlations remain almost unchanged.

This does not change the basic thesis. Rather, the check shows how strongly individual stress observations can shape both a correlation and a volatility estimate from only 54 months. Three of 54 observations halve a point estimate and at the same time reduce a standalone volatility by more than a quarter.

The central portfolio effect remains: without the stress months, the three mixes stand at 26.6 to 27.7% and thus remain close together. The complete recalculation of all inputs is given under Deep dive: The full robustness check.

What it depends on

Before the evaluation, a qualitative decision rule was set that the rule of thumb described at the outset should be regarded as weakened if regime and event analysis provided no additional insight compared with an assessment based on the overall correlation alone. The rule was tested exclusively on the three predefined levels and was not triggered. It is deliberately formulated qualitatively and was not tied to a threshold value.

The assessment differs from case to case, and that is the more honest result. For the market-neutral index and for DeFi income, regime and stress analysis change the judgement markedly. For stablecoin income, the thesis rests mainly on the risks that cannot be read from a smooth series. For Bitcoin and the altcoin index, the additional analysis initially confirms the basic direction of the high overall correlation: both react predominantly negatively in negative digital asset regimes. Individual stress events, however, show that the extent of the losses can differ considerably.

What the history does not show

The stablecoin income strategy was positive in all 54 months, with annualised volatility of around 1.1%. On the basis of volatility and correlation alone, such a series can appear almost ideal for a diversification task.

For income-oriented strategies, however, historical volatility may mainly reflect the variation of the current income. Credit, platform, smart contract or liquidity losses, on the other hand, can fail to appear for a long time and materialise abruptly when an event occurs. A smooth return series is therefore no proof that the underlying risks are low or independent of one another. Some risks do not show up as fluctuation but as events.

Deep dive: Where the effect arithmetically comes from

This section quantifies what was already established above. It is not needed for the finding itself; it shows the mechanics behind it.

Unlike volatility, variance can be decomposed additively: into Bitcoin’s weighted variance term, the weighted variance term of the added building block, and the covariance term that links the two.

For the three low-volatility building blocks, Bitcoin’s weighted variance term accounts for more than 90% of the mixed portfolio’s variance. Specifically, it accounts for around 91% of the resulting portfolio variance for the market-neutral index and around 95% for DeFi income. For stablecoin income, the arithmetic share is even just above 100% owing to the slightly negative covariance term. This explains the finding of the portfolio volatility calculation: the predominant part of the risk reduction here does not come from the diversification effect but from replacing a highly volatile building block with a low-volatility one. The covariance term, in which the correlation takes effect in the first place, accounts for less than 10% in absolute terms for these three building blocks.

Deep dive: The full robustness check

Complete recalculation of all inputs without the months May 2022, November 2022 and March 2023, that is, on the basis of 51 instead of 54 observations.

Limitations of the study

All metrics are based on 54 monthly observations and are sample estimates, not properties of the building blocks and not a statement about the future. The findings remain limited by the short history, by specific individual strategies instead of segment benchmarks, by possible selection, database and smoothing effects, and by the monthly frequency.

The portfolio volatility calculations take account of neither returns nor costs, liquidity or implementability. They answer a risk question, not an allocation question. The fifty-fifty arrangement is a segment view within a digital asset exposure and expressly not a model allocation for a client portfolio. For such a portfolio, what decides is not the correlation with Bitcoin but the covariance of the building block with the existing portfolio and with the position that is reduced to make room for it. The same test applies unchanged outside digital assets, for example for a market-neutral fund alongside an equity core or for a credit strategy alongside a bond portfolio.

One further question remains open and is the subject of a separate study: what happens when several supposedly diversifying return drivers are combined with one another. The FTX month suggests that diversification between strategies is not the same as diversification between risk factors.

Methodology

All empirical volatilities are calculated from the 54 monthly returns and annualised with the square root of twelve. This annualisation presupposes serially uncorrelated monthly returns. For smoothed or less liquid building blocks, volatility annualised in this way can underestimate the economic risk.

The portfolio volatility calculation assumes monthly rebalancing to 50/50. The simplified cash reference is set with an assumed monthly return of zero per cent and thus zero per cent volatility; ongoing income is not modelled. The scaled cross-check is purely analytical and follows the relationship sigma times the square root of 0.5 plus 0.5 times r. A single principle applies to the whole report: all derived metrics are calculated from the unrounded final series; rounding is applied solely for presentation. Back-calculating from the rounded values shown in the tables can therefore deviate in the last digit shown.

Betas are calculated as correlation times the ratio of the volatilities and are based on the same observations as the correlations. The beta approximation for a Bitcoin decline reflects solely the estimated linear market sensitivity and contains neither an intercept nor a residual term.

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Boris Jurczyk is the founder of 21Nexus Capital and is therefore economically connected to the topic of digital assets. Previously he was responsible for equity and quant selection at Berenberg and for liquid investments at AURETAS family trust. There are currently no business relationships with the two fund companies behind the anonymised income strategies; in particular, 21Nexus is not invested there.

This article is for information purposes only and constitutes neither investment advice nor a recommendation to buy or sell financial instruments or crypto assets. Crypto assets are subject to substantial price fluctuations; a total loss of the capital invested is possible. Past performance is not a reliable indicator of future results.