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Detecting Portfolio Benchmark Divergence with Rolling Correlations

Article Quant Q&A · Author: HammerPower
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Summary

The document addresses how to identify periods when a portfolio and its benchmark diverge despite having high correlation over a full evaluation period. It offers two exploratory approaches: plot the portfolio-minus-benchmark spread and inspect intervals where it changes steeply, or calculate rolling correlations over several window lengths. The example windows range from about two weeks to two months, with a one-year overall period given as context.

Rolling correlation directly measures how closely returns move together over each selected window, and comparing windows can reveal when apparent alignment depends on the horizon. A spread plot is a visual diagnostic, but steepness alone does not establish low correlation because spread movement also depends on scale and relative changes. The responses provide practical suggestions rather than a formal drift test; results will depend on the return frequency, window choice, and whether the portfolio and benchmark series are appropriately aligned.

Key ideas

  • High full-period correlation can conceal shorter intervals of portfolio and benchmark divergence.
  • Rolling correlations across multiple window lengths can locate periods of weaker co-movement.
  • A spread plot can help highlight divergence, but its slope is not by itself a correlation measure.
  • The chosen sampling frequency and window length affect the interpretation of local correlation.

Tags

Portfolio constructionStatisticsRisk management
Full text
# Spot variance drift consequently to style drift


# Spot variance drift consequently to style drift












I am looking for some information on how to spot variance drift for a portfolio in accordance to its benchmarks,

Let's say that we have returns of the portfolio $\textbf{P}=(P_1,...,P_t,...,P_n)$ and its benchmark $\textbf{B}=(B_1,...,B_t,...,,B_n)$ Despite the correlation ($\rho$) of the overall period is satisfying (over $0.90$, from $t=1$ to $t=n$), we would like to find out time periods when it is not the case (locally less than $0.50)$,

The subset found could range from two weeks to several months (usually the full range the period benchmark is one year)

Thanks in advance

## Answer by steinbitur (score 1)

https://quant.stackexchange.com/a/39346

Since the comparison is between two variables P and B I would start using a visual method i.e. make a graph i.e. plot the spread between the variables. Look at the graph and identify in what periods the graph is steep. Where the graph is steep those are the time periods where correlation is low because then the varibles are deviating more then for time periods where the graph is not steep.

## Answer by Magic is in the chain (score 1)

https://quant.stackexchange.com/a/42225

You can plot rolling correlations with varying windows: say 2 weeks, 1 month, 2 months, and so on. For example, say in excel, you calculate the correlation over 2 weeks (10 observations), then just drag the formula to the end of the series. That is one series. Next do the same for 1 month, and so on.

Most softwares should have built in functions for this.

For example, for python, see the discussion here: https://stackoverflow.com/questions/27069003/calculate-rolling-correlation-with-pandas

For SAS , look up Proc Expand.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.