I am calculating the skewness of returns of 10,000 randomly selected portfolios with different portfolio sizes(where assets range from 2 to 100 by an increment of 5 . i.e 2,5,10,15,..100). When I increase the portfolio size the kurtosis decreases which is favorable for investors. However, i am puzzled by the fact that when I take the kurtsosis of a 10,000 randomly selected portfolios that consist of N-1 assets (which means if I have 30,000 assets I build randomly 10,000 portfolios where each consists of 29,999 assets) the Kurtosis is much higher than the kurtsosis of portfolios with sizes ranging from 2 to 100. I don't understand how the kurtosis decrease when i increase the diversification but when I diversify to the maximum kurtosis increases and the monotic decrease disappears.

I hope someone could explain this point to me.

Best

J