Outlier Risk, Part V: Largest Difference From Average Value

In recent updates to this series (see list below) I’ve been looking at various methodologies to identify extreme values in a time series, such as the S&P 500 Index. One motivation for this analysis is that detecting so-called outlier values offers context for deciding if the risk of trend reversion is relatively high. Let’s add another metric to the tool-kit for this task: finding the value that marks the largest difference vs the average value over a trailing period.

As an illustration, we’ll use rolling 1-year returns for the S&P 500. The goal is to find the outlier on a rolling 5-year basis, i.e., the S&P 500 data point that represents the largest difference from the mean over the trailing window. Sometimes this outlier is positive, sometimes negative, depending on the market’s performance in recent history. One application is that when the 1-year return matches or approaches this outlier, it marks a possible turning point and the trend reverses.

Graphing the data since 2000 suggests that this type of outlier analysis offers some value for marking turning points for one-year S&P returns. In several cases, when the one-year performance is close to or reaches the outlier, this point marks an extreme return that begins to reverse.

For a clearer look at recent history let’s zoom in on results since 2018. Note that when the S&P 500 one-year return briefly exceeded 70% in March 2021 it was close to the upside outlier value for the past five years – an event that (with the benefit of hindsight) marked a peak for one-year performance.

The obvious caveat: this measure of outlier analysis isn’t perfect and so there’s always a degree of doubt about whether an apparent outlier event in real time is the genuine article for identifying a peak. Nonetheless, this metric shows promise and can offer context when used with other analytics for monitoring and evaluating trend strength and the potential for reversals. One area for further research: looking at multiple rolling windows for a more robust measure of outlier estimation.

Previous articles in this series:


Learn To Use R For Portfolio Analysis
Quantitative Investment Portfolio Analytics In R:
An Introduction To R For Modeling Portfolio Risk and Return

By James Picerno


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