May 17, 2021

In an equal weighted index, the number of stocks needed to reach e 50% of market capitalization of the index is always one half of the number of stocks in the index. Hence half of the stocks in the index will outperform the index and half of the names will underperform it. Thus, an unskilled manager stock selection is the equivalent of throwing darts at a board with the names of the stocks in the index. The unskilled manager has a 50% chance of outperforming the market at any point in time. In a capitalization weighted index, ranking the stocks by capitalization, the number of stocks needed to reach 50% of the index capitalization is always less than half of the names in the in index. The more skewed the distribution towards the larger cap stocks, the smaller the number of names needed 50% of the index market cap. This leads to an interesting insight: During large cap cycles, the number of stocks outperforming the index will be less than 50%. Hence the dart throwing manager will have a less than 50% chance of outperforming. In turn, during the small cap cycles, more than 50% of the names outperform the cap weighted indices. This suggests that even a dart throwing unskilled manager has a better than 50% chance of outperforming the index. Taken together the size cycles combined with percent of the money managers outperforming their benchmark during the cycles give rise to a cyclicality in the likelihood of an active manager outperforming the market.

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