How to deal with correlations not statistically significantly different from zero?
I often find parts of financial correlation matrices not statistically significantly different from zero. Sometimes, these correlations have a tangible effect on results – low correlations lead to high diversification benefit. Also, the sign of correlations can skew the results. Would you consider it appropriate to make these correlations equal to zero to at least get rid of the directionality and, if necessary, fix the negative eigenvalues that might arise due to such corrections?
