Bitcoin and equities: The diversification contribution is not a fixed property

The claim and the data

Bitcoin diversifies the portfolio, it is often said. That is only sometimes true. The diversification contribution of an investment does not follow from the investment alone but from its dependence on the other positions, and this dependence changes with the market environment. How large the contribution is also depends on the weight and the stand-alone volatility of the investment; this episode focuses on how dependence changes across market environments. The data show this in two phases. In 2022, Bitcoin and the S&P 500 fell together, with a correlation of daily returns of +0.57. During the US banking turmoil in March 2023, Bitcoin rose by 28.6% and the S&P 500 by 3.1%, and the correlation over the most recent 60 trading days stood at +0.26 on 31 March, after +0.54 on 24 January.

Both phases are examples, not a test. They show that the co-movement is not constant, and they contain no forecast. What follows from this for assessing an investment within a portfolio is set out in the section on portfolio context. This page accompanies episode 2 of the topic series “Volatilität im Portfoliokontext” in the format “21Nexus | Portfoliofragen” (video in German) and can be read without the video.

Data and methodology

The basis is daily closing prices. Bitcoin against the US dollar is available for every calendar day without gaps from 1 January 2012; the S&P 500, as a price index excluding dividends, is available on trading days and is used in this analysis from February 2013. The reference date is 27 October 2026; later prices are disregarded so that all episodes of the topic series rest on the same cut-off. All figures are based on our own calculations from these closing prices; ready-made metrics from third parties are not used.

Return and correlation. For the correlation, return means the logarithmic daily return from closing prices. Correlation is the correlation coefficient of the daily returns of Bitcoin and the S&P 500, calculated exclusively on common trading days. A return on a Monday spans the weekend for both series. The annual figures use all common trading days of the calendar year. The period returns quoted below are simple cumulative returns between two closing prices and are not logarithmic.

Rolling correlation. The 60-trading-day correlation uses the returns of the most recent 60 common trading days up to and including the stated day. The rolling correlation over 252 trading days is formed in the same way.

Period returns. For Bitcoin the closing price on the calendar day applies; for the S&P 500 the last closing price on or before that day. The calendar year 2022 runs from the closing price of 31 December 2021 to the closing price of 31 December 2022. For the banking turmoil, the closing price of 7 March 2023, the last price before the event window, to the closing price of 31 March 2023 applies.

All price data are denominated in US dollars. For 2026 the values run to 27 October and are incomplete.

Two phases compared

The table compares the two phases.

In 2022, Bitcoin lost 64.4% and the S&P 500 19.4%. The correlation of daily returns calculated over the calendar year was +0.57, the highest annual value in the series. In calendar year 2022, Bitcoin therefore did not offset the losses of the S&P 500 but fell further. How Bitcoin behaved in individual equity market sell-offs is not shown by this analysis; a statement on that requires a separate study. Hedging and diversification should therefore be considered separately: a positive co-movement does not rule out a diversification contribution, but on its own says nothing about protection in loss phases.

In March 2023 the development was different. Between the closing prices of 7 and 31 March, Bitcoin rose by 28.6% and the S&P 500 by 3.1%. The correlation over 60 trading days stood at +0.26 on 31 March, after +0.54 on 24 January. The co-movement therefore eased but remained positive: correlation weakened, and the data do not show that the relationship disappeared. The later development lies after the event window and is to be read separately: on 26 June the value was +0.06.

Correlation over time

The two phases do not stand alone. The annual correlation values show that the dependence has changed over the entire common history. In 2013 to 2019 the annual values lay between −0.11 and +0.09, since 2020 between +0.16 and +0.57. The years 2025 and 2026, at +0.42 and +0.46, are again clearly above 2023 at +0.16. The differently measured values prove neither a structural break nor its cause, and these observations alone do not establish how correlation will behave in future.

The rolling correlation over 252 trading days has also ranged widely since 2013: the lowest value was −0.17 (16 December 2019), the highest +0.58 (13 February 2023).

Limits of the conclusion

Every historical metric depends on period, window and convention. Five points matter for the interpretation.

Selection of phases. The banking turmoil and the year 2022 were chosen as examples of two clearly different market environments. They are not a representative sample, and no statistical test of the differences was carried out. The annual values and the rolling correlation show that the change does not depend on these two events alone. They do not replace a systematic study.

Window length. The same event looks different depending on the window. Over 252 trading days, the correlation on 31 March 2023 stood at +0.54, close to its maximum, because the trailing window still contained the year 2022. Only over 60 trading days (+0.26) does the easing become visible. Windows of 20, 30 and 45 trading days were also tested. In the event window from 8 to 31 March 2023 the values lay between +0.07 and +0.27 for 20 days, between +0.14 and +0.34 for 30 days, between +0.20 and +0.39 for 45 days and between +0.23 and +0.41 for 60 days. In none of these windows was negative territory reached. Shorter windows react more strongly to individual observations, longer ones smooth more and react more slowly. The choice of 60 trading days is a presentation decision and not a general accuracy threshold; it is disclosed and not a silent choice.

Starting point of the period return. The period return starts at the closing price of 7 March 2023, the last price before the event window. From the closing price of 8 March it would be +31.4% for Bitcoin and +2.9% for the S&P 500.

Benchmark for comparison. The comparison is made exclusively with the S&P 500 as a price index excluding dividends, a US equity index. Statements about “the other positions” of a portfolio are therefore only an approximation. The dependence on other equity markets, on bonds, commodities or on the holdings of a specific portfolio may differ. Correlation also measures the linear dependence of daily returns; at other return intervals or in extreme market phases the picture may be different.

Data basis. The daily closing prices of the two markets are formed at different times of day, since Bitcoin trades around the clock and the S&P 500 only during US exchange hours. The closing time of the Bitcoin series is not documented, so the time synchronisation of the two daily series is unresolved. This may change the measured co-movement of daily returns. The Bitcoin series was reconciled against two further Bitcoin series. The values largely agree; for the period return in March 2023 both comparison series give +28.3% instead of +28.6%, for 2022 −64.2% instead of −64.4%, and for the 2022 correlation +0.56 instead of +0.57. The reconciliation shows the consistency of the series with one another, not their origin or accuracy.

Placing this in a portfolio context

The diversification contribution of an investment results from its dependence on the other positions, its weight and its stand-alone volatility, and is not a property that attaches to it permanently. This episode focuses on how dependence changes across market environments. The contribution should therefore be checked continuously and not assumed, and against the actual portfolio rather than a single index. The analysis above describes the past of two markets. It replaces neither the check within one’s own portfolio nor the decision on how much risk a position may contribute; deriving position size from the risk budget is the subject of episode 3 of the series.

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Legal notice

This publication serves solely for general information and professional commentary. It constitutes neither investment advice nor an investment recommendation, financial analysis or an offer to buy or sell financial instruments. Individual investment objectives, financial circumstances or the risk tolerance of individual investors are not taken into account. Information on historical performance and metrics permits no conclusions about future developments. The data used originate from sources that we consider reliable; no guarantee is given for accuracy or completeness. The information reflects the position at the date of publication; there is no obligation to update. Publisher: 21Nexus Capital GmbH, Neuer Wall 54, Hamburg.