Why Cumulative Return Correlations Can Exceed Daily Correlations

Summary

The document asks why two daily return series can appear weakly correlated day to day but strongly correlated after their returns are cumulated. It also asks whether common correlation thresholds are meaningful without specifying the return definition and measurement horizon. No explanation or answer is included, so the document does not establish why the reported correlations differ.

Its useful research question is that correlation depends on how returns are measured and over what period. Cumulative returns aggregate movements across time, while daily returns capture shorter-term changes; comparing their correlations therefore answers different questions. The example reports a much higher correlation for cumulative returns than for non-cumulative returns, but gives no data, calculation details, or statistical analysis. Readers should treat the figures as an observation to investigate, not evidence of a general rule. The document leaves open which horizons are appropriate and how to define high or low correlation for a particular trading or research objective.

Key ideas

• Correlation comparisons depend on whether returns are measured daily or cumulatively.
• The document reports higher correlation for cumulative returns in its example but does not explain the cause.
• A correlation threshold needs context about the return definition and measurement horizon.
• The example is an observation without supporting data or analysis.

Tags

# Cumulative returns are more correlated than non-cumulative


# Cumulative returns are more correlated than non-cumulative












I was just comparing two daily returns series and noted that the correlation between them is a lot higher if they are cumulated (about .95 for cumulative returns, vs .15 for non-cumulative). I feel that there should be a simple intuitive explanation for why that is. Is it because these returns behave more similarly over longer time horizons? As opposed to day-to-day?

More generally, is it customary to look at the correlation of cumulative, or non-cumulative returns? What time horizons are used? For example, I have heard this rule of thumb that if the correlation is above 0.7, it means that the returns are highly correlated. But I feel that to be meaningful statements like that should also specify the type of the return and the time horizon.

How do you judge correlation between return series? What time horizons and return types do you use? What is highly correlated, or uncorrelated for you?

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