# Different group size average comparisons

I have 3800 stocks for which I calculate their return correlations. So I end up with a 3800 by 3800 matrix. Each stocks is related in some way to all the other 3799 stocks. For each stock, I create seven groups out of 3799 stocks based on their relatedness. So say for stock A, group 1 (closest in relatedness - based on a pre-specified knowledge based linkage of like-industries) will have 60 stocks, group 2 will have 300 stocks, and group 3 700 stocks and so on up to seven groups. I then average for each group their correlations with stock A. I want to see if there is a decay in the correlation when we move from group 1 to group 7. But the group size varies... can this be a serious issue?

I then take an average across all groups for each stock and see if the decay holds cross-sectionally? Now the issue is that for each stock, say stock A and stock B the size of each group is different. There may be 60 stocks in group 1 for stock A while there is 40 in group 1 for stock B. How problematic can this be?

• Are you defining "relatedness" by a correlation cut-off (e.g. 0.4 or 0.7) or using clustering algorithms or a pre-specified knowledge based linkage of like-industries? Mar 24, 2014 at 19:02
• Good question! I should have specified this. Relatedness is based on a pre-specified knowledge based linkage of like-industries Mar 24, 2014 at 19:05

• this is the first time I hear about telescoping. Would you have a recommended read on the topic? I am not sure if I understand what you say split out the overlapping stocks in group 1 from group 2 (telescoping) and use a t-test treating individual level correlations. Do you mean to take the t-stats from each individual correlation between BP and the stocks that appear both in group 1 and 2? And then...? Average those t-stats? Mar 24, 2014 at 19:54