If n represents the number of correlations, how is P realized computed?

The realized correlation, P, is computed in a way that captures the relationships among multiple assets or variables by adjusting the summation of the correlations based on the number of pairs involved. In the formula 2 / (n^2 - n) x sum of correlations, the denominator, which is (n^2 - n), represents the number of unique pairs of correlations computed among n variables.

When you have n variables, the total number of unique pairwise correlations can be derived from combinatorial principles and is given by n(n - 1)/2. This count is equal to (n^2 - n)/2, leading to the factor of 2 in the numerator of the formula to balance the equation. Thus, by using this formula, you ensure that the realized correlation appropriately reflects the average of these correlations across all pairs, accounting for the fact that each pairwise correlation is only counted once.

This method allows for a meaningful aggregation of correlations that mitigates the bias that might arise if correlations were simply summed without considering the number of observations contributing to the estimate.