Why Correlation of Returns Usually Matters More Than Price Levels

Summary

The discussion addresses whether to correlate index price levels or returns when studying long-run relationships. One answer favors returns because successive price levels are dependent on earlier observations, which can create misleading correlation. Price differences avoid some level dependence but lack a common scale across assets; returns provide a comparable measure that also aligns with how investment gains are commonly measured. The other answer suggests that apparent price co-movement may instead concern cointegration, a distinct question about whether price series share a persistent long-run relationship.

The example in the question describes one index rising and another falling while claiming their return correlation is positive. That claim does not follow from the listed return sequences: one sequence increases while the other decreases, so their correlation is negative. More broadly, a short example cannot settle which statistic is appropriate for every analysis. Return correlation measures linear co-movement in returns, while price correlation can be dominated by shared trends; neither alone establishes cointegration or explains the economic relationship between indices.

Key ideas

• Correlating price levels can produce misleading results because price observations are serially dependent and often trend.
• Returns offer a common scale for comparing movements across assets and align with performance measurement.
• Price differences remove the price-level scale but are not directly comparable across assets with different values.
• Cointegration tests a long-run relationship between price series and is distinct from return correlation.
• The example’s stated positive return correlation conflicts with the opposing return sequences it lists.

Tags

# Correlation: Use Price or Return? Return doesn't make sense


# Correlation: Use Price or Return? Return doesn't make sense












I am trying to find the correlation between the returns of two indices over a long period of time (10 years+) . Should I be using the index daily price level or the index daily total return? Most places that I have seen have suggested that I should be using the daily returns. I have read numerous issues with regards to using the price level, and few criticisms of using returns.

BUT how can you explain the following using returns over price for correlation. To be simple, let's consider a 3 day period. Index A's returns over the 3 days are +3%, +4%, +5%. Index B's returns over the 3 days are -3%, -2%, -1%. Assuming a start point of 100 for each index, Index A goes from 100 to 103 to 107 to 112 over the 3 days. Index B goes from 100 to 97 to 95 to 94. Clearly these indices are very negatively correlated. They are moving in the exact opposite direction! To that point, the price correlation is -0.937. BUT the return correlation is a +1.0. This makes me think that using price levels is better than returns. Thoughts?

Thanks.

John

## Answer by Svisstack (score 2)

https://quant.stackexchange.com/a/25934

Actually prices dont make sense as they are correlated with previous samples (prices), returns are not. Better will be difference between prices, but then you dont have reference point and comparability between assets, so eventually you need returns. At the end that is what you are interested in I think as profit is usually measured in return.

## Answer by Kiwiakos (score 0)

https://quant.stackexchange.com/a/25936

I suspect that you are mixing correlation and cointegration. What you describe as the co-movement of prices sounds like cointegration.

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