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When correlation changes regime

How much the correlation between two assets depends on the window it is measured over: the same two assets can show quite different correlations in different years.

In the demo portfolio
0.15 to 0.44
One calendar year at a time, against the rest of the portfolio

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ρ = Σ (xi − x̄)(yi − ȳ) / √( Σ (xi − x̄)² × Σ (yi − ȳ)² )

Where it misleads

A correlation is a fact about a window, not a property of the two assets: the figure for one period does not say what the next will be. One number over the whole history averages regimes that no single year resembles. And the three to four hours between the closes of a coin and of US shares make the daily correlation read slightly lower than it is.

Compared with

How it is computed here

The daily returns of the two, on the weekday table, are correlated over a window of dates: a calendar year, one of the stress windows the Stress tests tab already uses (chosen by date, not by what the returns did) or a rolling window of 90 sessions. Each figure carries its number of sessions, because a short window is imprecise: an approximate 95% interval comes from Fisher's transformation, tanh(atanh(ρ) ± 1.96 ÷ √(n − 3)).

Worked example

  1. ORB-USD's daily returns against those of the rest of the demo portfolio, on weekdays, one calendar year at a time: 2019 0.25, 2020 0.40, 2021 0.15, 2022 0.44, 2023 0.25, 2024 0.26.
  2. Over the whole history at once it is 0.30.
  3. Same coin, same prices: the number depends on the window it is measured over.

Demo portfolio: seven invented holdings, generated prices, measured by the real engine. Past returns do not predict future ones.

Where it misleads

A correlation is a fact about a window, not a property of the two assets: the figure for one period does not say what the next will be. One number over the whole history averages regimes that no single year resembles. And the three to four hours between the closes of a coin and of US shares make the daily correlation read slightly lower than it is.

Every price on this page is invented. The coin and the index fund are two series generated for this lesson from a fixed seed: they are not any real coin or fund, and none of the figures is market data. The coin is not the Orbit (ORB-USD) that the example portfolio of this site holds: it is a separate invented series, so the figures here are not that portfolio's.

One number, many windows

Correlation says how often two assets move the same way in a day: +1 when always, 0 when there is no relation, −1 when always opposite. It is computed over a window of dates, and the window decides the number.

ρ = Σ (xi − x̄)(yi − ȳ) / √( Σ (xi − x̄)² × Σ (yi − ȳ)² )
  • xi, yi — the daily returns of the two assets on day i, both on the weekday table.
  • x̄, ȳ — their averages over the window.
  • ρ — the correlation, between −1 and +1.

The invented coin and the invented index fund, from 5 January 2015 to 1 October 2026: 2,943 daily returns and ρ = 0.14. No single year looks like that.

Calendar years

Year Sessions ρ
2015 250 0.01
2016 251 −0.11
2017 250 0.06
2018 251 −0.04
2019 251 −0.10
2020 252 0.25
2021 249 0.18
2022 250 0.48
2023 249 0.01
2024 251 0.30
2025 250 0.25
2026, to 1 October 189 0.40

From 2015 to 2019 each year stayed between −0.11 and +0.06; from 2020 on, between 0.01 and 0.48.

The stress windows

The Stress tests tab measures correlation inside windows fixed by date, not by what the returns did. The two that fall inside this history:

Window Dates Sessions ρ Approximate 95% interval
The COVID crash 19 Feb to 23 Mar 2020 24 0.48 0.09 to 0.74
2022 3 Jan to 12 Oct 2022 196 0.51 0.40 to 0.61

In both, the correlation was above the 0.14 of the whole history. That is a fact about these two windows, not a rule. The interval is why 24 sessions say little: it comes from Fisher's transformation, tanh(atanh(ρ) ± 1.96 ÷ √(n − 3)), and a short window gives a wide one.

It moves inside a year too

On a rolling window of 90 sessions the correlation went from −0.24 on 3 November 2016 to +0.59 on 7 June 2022, and was 0.45 on 1 October 2026.

How to read it

  • A correlation is a fact about a window. Near zero says the two moved independently of each other on it; 0.5 says they moved the same way more often than not. Neither says why, and neither says what the next window will be.
  • Fewer sessions, a wider interval. A calendar year has about 250 and an interval of roughly ±0.1; a month has about 21 and one several times wider.
  • The coin's day ends at 00:00 UTC and US shares close at 16:00 New York time, three to four hours earlier, so every figure on this page reads slightly lower than it would if the two closed together.

Compared with

Questions people ask

Does a correlation near zero in one year say what it will be in the next?

No. Between 2019 (−0.10) and 2022 (0.48) the same two assets went from one end of the table to the other. The number describes the window it was measured on.

Why is the whole-history figure 0.14 if no year has it?

It pools every day of every year, so it sits between the quiet years and the high ones and describes none of them.

Why are the stress windows chosen by date?

Because choosing the days by what the returns did biases the result: keeping only the extreme days shrinks the range of the common move inside the sample, and the correlation reads lower than it is. A window fixed by date does not depend on the returns.

Sources

  • Invented series (a coin and an index fund), generated for this lesson from a fixed seed and reproducible in the project's tests; no market data
  • Forbes, K. and Rigobon, R. (2002), No contagion, only interdependence: measuring stock market comovements, Journal of Finance 57(5)

Last reviewed 3 Oct 2026 by Sphinx Risk.

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