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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

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    $\begingroup$ "Clearly" is a very subjective term. I could read your numbers as "the more positive the returns of index A are, the less negative the returns of index B are", hence positive correlation makes sense. This post answers your quesion: quant.stackexchange.com/questions/489/… $\endgroup$ – LazyCat May 10 '16 at 18:54
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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.

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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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