Bitcoin volatility since 2012: lower volatility, extreme days persist

The objection and the data

The objection that Bitcoin is too volatile is common and not wrong. It is merely incomplete: a volatility figure describes a single asset, and on its own it is not enough to judge its effect within a portfolio. As a basis, it is worth looking at the data. Realised volatility of Bitcoin against the US dollar has fallen markedly since 2012, yet extreme days relative to the most recent level of volatility have not disappeared. Both parts belong together, because the decline alone would be only half the analysis.

Three years, each four years apart, are compared: 2018 with 84% volatility and 8 three-sigma days, 2022 with 65% and 11 days, and 2026 up to 27 October with 44% and 9 days. What a three-sigma day is, how the figures are derived and where the conclusion reaches its limits is set out below. This page accompanies episode 1 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 of Bitcoin against the US dollar. The series is available for every calendar day without gaps from 1 January 2012; the reference date of the analysis is 27 October 2026. All figures are based on our own calculations from these closing prices; ready-made metrics from third parties are not used.

Volatility is the standard deviation of logarithmic daily returns (sample standard deviation), annualised with the square root of 365.

A three-sigma day is a day on which the absolute daily return is at least three times the standard deviation of the daily log returns over the preceding 30 days. The threshold is therefore relative to the most recent volatility and says nothing about absolute moves. The window ends on the previous day; the current day does not enter the threshold.

All price data are denominated in US dollars. For 2026 the values run to 27 October and are incomplete; the number of three-sigma days for 2026 refers to this period.

Annual figures 2012 to 2026

The table shows all years evaluated, not only the three years compared.

Limits of the conclusion

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

Selection of years. The comparison above uses 2018, 2022 and 2026, i.e. fixed intervals of four years. This is a restriction to more recent history. In the early years volatility was on average markedly higher (2013: 148.9%; 2013 to 2017 pooled: 93.6%), even though individual years such as 2016 were below the 2018 level. The decline is therefore not weaker across the full series. At the same time, the finding rests on years with a considerably smaller and differently structured market. The fixed interval limits the freedom of selection, but does not prove that the result is independent of the selection.

Comparison of contiguous multi-year periods. Three consecutive periods show the same picture: 2013 to 2017 pooled at 93.6%, 2018 to 2022 at 75.5% and 2023 to 27 October 2026 at 45.7%. These boundaries are also chosen, and 2012 lies outside the comparison. The calculation shows that the decline is visible under this aggregation, not that the dependence on selection disappears. Volatility declined across these multi-year periods, but not in every individual year: 2024 is above 2023 and 2025.

Extreme days. Three-sigma days occur in every year evaluated, between 6 and 16 per year. The average is 12.8 days per year in 2013 to 2017, 8.6 in 2018 to 2022 and 8.3 in 2023 to 2025. A trend is thus neither established nor ruled out. Because the threshold is relative to the most recent volatility, the persistence of extreme days also does not imply that absolute moves have remained unchanged. The three-sigma count includes both positive and negative daily returns: in the years compared there was one positive move and seven negative ones (2018), four and seven (2022) and five and four (2026). Intraday moves are not captured. Three-sigma days are therefore neither a count of severe loss days nor a complete measure of downside risk.

Convention. The count of three-sigma days reacts more strongly to convention than volatility does. With the definition used here, 2018, 2022 and 2026 yield eight, eleven and nine days. With the standard deviation computed with divisor n instead of n−1 it would be eight, twelve and eleven; with a window including the current day, four, eight and four. The definition is therefore disclosed here, and the statement reads “have not disappeared” rather than “more frequent”. As a share of observation days, three-sigma days account for 2.2% (2018), 3.0% (2022) and 3.0% (2026, nine of 300 days).

The annualisation factor is not a minor detail: with unchanged calendar-day returns, 2026 volatility using the square root of 252 instead of 365 would be 36.6% instead of 44.1%. The choice of 365 follows from Bitcoin trading on every calendar day and the returns being calculated on a calendar-day basis. As a plausibility check, using returns between US equity trading days (Monday returns span the weekend) and the square root of 252 gives a similar value of 43.2%. For 2012, the three-sigma count only begins on 1 February because the first 30 return days have no look-back history for the threshold; whether they contained exceedances cannot be assessed. The eleven days counted refer to 335 days with a valid threshold estimate; 2012 volatility uses all 365 daily returns.

Placing this in a portfolio context

Individual metrics like these describe an asset on its own. For its effect in a portfolio, two further questions arise: how the asset behaves relative to the other positions, since this dependence changes with the market environment, and how much risk it may contribute to the overall portfolio. Position sizing should be derived from the risk budget, given the chosen risk measure, portfolio assumptions and constraints, not the other way around. The analysis above gives no answer to this; it describes the individual asset only.

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.