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The Math Behind Futility

FYI: An overlooked statistical concept shows why it’s so hard to beat a benchmark.
Regards,
Ted
https://www.bloomberg.com/news/articles/2017-04-09/lopsided-stocks-and-the-math-explaining-active-manager-futility

Comments

  • Interesting idea, albeit with a biased presentation.

    The article says "Sure, a couple of funds will ...rise above the benchmark, but for most the result will be far less than the average. "

    The average of the losers will be less than market performance (by definition of "loser"), but not that far less. That's because there are more of them than there are winners.

    Think about dividing funds into outperforming and underperforming buckets. Assuming the funds are of equal dollar size, the larger bucket's average must be closer to market performance than the small bucket's. That's just simple arithmetic.

    For example, suppose there are twelve funds covering the market. Suppose two outperform by $5 (total excess return of $10). Then the other ten funds will underperform (on average) by just $1.

    We can invert the 5 poker chip example in the article. Instead of having funds pick two chips out of a market of five, as the example in the article does, suppose all funds pick two stocks to exclude. Just as 6 out of 10 funds miss the big winner if they pick only two chips, 6 out of 10 funds will miss excluding the big winner if they exclude two chips. So 6 out of 10 funds will be winners (but not big winners).

    All just a little fun with numbers. It gets back to Sharpe's observation that the average dollar must get the average return before subtracting fees.
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