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?