Realized Correlation

There are mainly 2 types of realized correlation formulas found on OTC markets: 


1. EWRC: Equally Weighted Realized Correlation: Correl 5 where Correl 6


2. WRC: Weighted Realized Correlation:  Correl 7


Several technical reports have investigated how the above WRC formula relates to other proxy formulas that are popular in econometrics, when the underlying assets and weights correspond to an equity index. 

Tierens and Anadu give empirical evidence that in the case of the SP500 index: Correl 8.

In addition, Bossu derives the limit-case proxy formula, subject to some conditions on the weights: Correl 9


This proxy formula is remarkable because we can interpret the numerator as "index variance" and the denominator as "average constituent variance", which is more straightforward than the average of N*(N-1)/2 pairwise correlation coefficients. 

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