By Alex White, FIA, C.Act, Managing Director, Co-Head of ALM at Redington
This happens even when successive data points are independent. To use a height-based analogy: an eight-foot parent’s children are likely be tall too, but the likelihood (based on the mean height of the general population) is the child will still be shorter than eight feet tall.
By contrast, ‘active reversion’ implies an underlying force ‘pulling’ data back to the mean. To illustrate this, imagine someone stumbling forwards in a valley. Once they start lurching to one side, then going further up the same side becomes harder and going back (down) toward the other side becomes easier.
Both ideas can be tested against the data. Let’s take the S&P500 as an example, backfilled with Yale economics professor Robert J. Shiller’s monthly US equity data from 1870 onwards.
Firstly, we can check autocorrelations. This is 3% for excess returns (2% for total returns, 0% for real) – so last year’s return is 3% correlated with this year’s. This means successive annual returns are effectively independent.
If annual returns are independent that suggests active mean reversion isn’t happening; however, it could still happen over a longer period. Crashes tend to be clustered, so one event could lead to two bad years, which could throw off the autocorrelation.
Another test is to compare annualised standard deviations. The idea for this is any active reversion should result in lower volatilities for long-term holding periods.
There are a few ways to tackle this, though the results are similar. We take the whole time series and use rolling annual data and look at the annualised volatilities through time. And we do see a decline.
So, do equities mean revert? Maybe.
We also asked, “what would it look like if there were no reversion?” and simulated 1,000 150-year time series. We took the volatilities of rolling n-year periods, on annual data, to see how this declined through time.
A small part of the decline is from the methodology, as we see in the simulations, but more than that, the results could just be luck. Even with the most extreme of the three-time series - and using a one-tailed test - we still fall some way short of significance. The data has a lot of noise.
There’s even meaningful variation (2.2%) in the annual volatility depending on which month you start from. That is, if you take the 150-year time series from June to June, or from August to August, the volatilities differ by over two percentage points.
But perhaps the clearest example is to add a time series which does show mean reversion, dividend yields. While not exactly like-for-like, the decline in volatility is much harder to argue against there.
Source: Data– Yale/Robert J. Shiller, Bloomberg. Calculations – Redington, a Gallagher Company. Results shown are for excess returns, but similar for total returns (Date: up to June 2025)
So, there’s reason to believe that returns are independent, but not much evidence for active reversion. It might happen, but if it does it’s hard to argue it’s particularly strong. That means markets may be less likely than conventionally expected to bounce back after a fall.
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