Portfoliothese (Issue 2): What a correlation figure doesn’t tell you

Five questions for every diversification claim

A factsheet lies on the table. A new strategy, a solid track record, a correlation of 0.59 to the very risk it is meant to diversify. Is that a sensible addition or not?

A correlation can range between −1 and +1. At zero there is no discernible linear relationship; the closer it is to +1, the more strongly two return series tend to move in the same direction. A value of 0.59 therefore already indicates a clearly positive co-movement. For a strategy that is meant to diversify exactly this risk, that looks unconvincing at first.

When a new strategy is justified by its diversification effect, correlation is usually among the first metrics examined. It is often shown in the factsheet, is available immediately and seems to make different strategies quickly comparable. Why the figure alone is not sufficient for this is the subject of this issue. We show it using an example from the digital assets space.

Why there in particular? At 21Nexus we are concerned with how different sources of return and risk within this investment universe can be combined into a portfolio. Bitcoin in particular makes the challenge visible: its high volatility can make integration into conventional risk budgets difficult. All the more interesting is the question of whether the risk of a digital asset portfolio can already be spread across different sources of return and risk within this universe, and how such a diversification effect can be recognised.

To this end we examined Bitcoin and four further building blocks: a broad altcoin index, a stablecoin income strategy, a DeFi income strategy and an index of market-neutral hedge fund strategies. The analysis yields five questions that also transfer to other asset classes.

The findings

The 0.59 from the introduction is the correlation of the market-neutral hedge fund strategies index with Bitcoin. The common window is January 2022 to June 2026, that is 54 monthly returns. The two income strategies are not segment benchmarks but two specific anonymised individual strategies that stand as examples of their respective source of return. They were selected from the available strategy universe for their suitability to represent the respective return driver, not for the level of their historical returns.

The starting point is a pure Bitcoin portfolio with annualised volatility of around 54%. In each case we replace half of it:

Three building blocks whose correlations range from −0.08 to +0.59 lead to almost the same portfolio volatility: 27.0%, 27.7% and 28.4%. All three therefore lie in the range of a plain cash allocation at 27.1%.

The reason is not a hidden property of these building blocks but arithmetic. How strongly two building blocks jointly contribute to portfolio risk depends on their weights and their covariance, that is, on the correlation together with both volatilities. The market-neutral index fluctuates at around 4% a year, Bitcoin at around 54%. With a volatility difference of roughly twelve to one, even a pronounced directional relationship can achieve little. Most of the measured reduction does not come from diversification in the first place, but from replacing a highly volatile building block with a low-volatility one.

With the altcoin index, both effects work in the same direction. Its linear Bitcoin sensitivity, with a beta of around 1.05, is close to one, and at the same time its standalone volatility is higher than that of Bitcoin itself. Adding it therefore does not reduce portfolio volatility; it raises it by just under 8%.

That contains everything essential for the variance calculation. For the risk assessment of the building block, it does not. And the calculation answers only a risk question, not an allocation question: returns, costs, liquidity and implementability are not part of it. The table shows volatility because it can be derived directly from correlations, volatilities and weighting. What a building block can lose in a stress phase does not follow from it. Questions four and five lead exactly there.

That brings us to the five questions.

1. How robust is the figure?

The measured correlation of the stablecoin income strategy with Bitcoin is −0.08, seemingly practically uncorrelated. However, the −0.08 is only an estimate from 54 monthly observations. An approximate 95% confidence interval shows how large the statistical uncertainty of this estimate is: the wider the interval, the less precisely the true correlation can be determined from the available history. For the same reason, a survey with few participants does not deliver an exact election result. Here the interval runs from −0.34 to +0.19. The data are therefore compatible with both a noticeably negative and a slightly positive relationship with Bitcoin. The statement that the two are uncorrelated claims more than the data can support.

2. What really drives the portfolio effect?

The table above is deliberately a segment view. It shows what happens when, within a highly volatile digital asset exposure, Bitcoin is replaced by another building block. For a client portfolio the question is different. There, what matters 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. Whether an addition is funded from cash, from equities or pro rata leads to different results.

With more similar volatilities, correlation gains relative importance. The effect shown here is therefore not a general law but a consequence of the extreme volatility difference between Bitcoin at around 54% and the three building blocks considered at only around 1 to 4.5%.

3. What happens when diversification is needed?

For a building block that is meant to spread risk, it is not only a matter of how closely two series are related over the whole period. What matters is whether their distinct return behaviour persists precisely when diversification is needed.

Within negative market regimes we deliberately do not calculate new correlations. The samples become too small for that: even a correlation of 0.40 measured there would, with around twenty observations, have an approximate interval from −0.04 to +0.71. Instead we look at the average return and the share of positive months.

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 returned +0.35% on average and was positive in 23 of 26 months, despite a correlation of 0.59. The DeFi income strategy stood at +0.47%, and the stablecoin income strategy was positive in all 26 months.

Owing to market-capitalisation weighting, this regime is strongly shaped by Bitcoin. We therefore also examine the 21 negative months of the S&P 500 as an external cross-check. There too, the three building blocks mentioned remained positive on average. This does not prove a general independence from traditional markets. It shows that the three building blocks behaved markedly differently on average, both in negative digital asset months and in negative equity market months.

4. What happens during a specific stress event?

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% that month. 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 index lost 4.60%, and the DeFi income strategy 4.81%.

That is roughly 3.6 times the monthly volatility of the index and roughly 3.7 times for the DeFi income strategy, in each case derived from the full history. A single common event thus hit two building blocks that had previously run very smoothly by a multiple of their normal range of fluctuation. The FTX shock hit exchange, counterparty, liquidity and market-structure risks, that is, exactly those risk dimensions that a Bitcoin beta does not identify.

The familiar rule of thumb that all correlations go to one in stress phases can be neither confirmed nor refuted from these data. What we see is not the conditional correlation but behaviour: in the negative regimes, both series remained positive on average. FTX shows 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.

That the risk dimension hit is what decides is also shown by the two other predefined events. Terra/Luna, the collapse of an algorithmic stablecoin together with the ecosystem built on it, was a protocol shock (Bitcoin −15.75%, altcoins −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. Bitcoin rose 23.08% that month, and of the four other building blocks only the altcoin index closed in the red, with a loss of 4.03%. None suffered losses on the scale of Terra/Luna or FTX. The peg, however, was restored within a few days. What monthly data show is the month-end, not the path to get there.

5. Which risks are invisible in the history?

The stablecoin income strategy examined 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.

What remains

Two levels of insight lie in these five questions. Correlation alone is not enough to quantify the normal portfolio effect; that requires at least individual volatilities and weights. And even correlation plus volatility is not enough to understand behaviour under specific stress; that requires a look at regimes, events and the risks behind a smooth series.

Anyone who adds a building block to a portfolio for its diversification effect should therefore ask not only whether its correlation is high or low, but also whether these five questions can be answered convincingly.

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Three levels were defined in advance: overall correlation including estimation uncertainty, behaviour in negative market regimes and three predefined stress events. Volatility, beta and the portfolio volatility calculation are downstream explanatory analyses with which we interpret a pattern that the predefined evaluation made visible. All metrics are based on 54 monthly observations and are therefore sample estimates, not properties of the building blocks, and certainly 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.

On the data basis: 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. For the two income strategies, monthly net histories after fees are used; market and index series are treated as index returns without assumed product costs. The regime indicator for the digital asset market is the market-cap-weighted S&P BDA.

A note on our approach at 21Nexus: We use the return drivers described here as different building blocks of our work in the digital assets investment universe. On this basis, our portfolio construction aims to combine different sources of return and risk systematically. There are currently no business relationships with the two fund companies behind the anonymised income strategies; in particular, we are not invested there.

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.

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.