The Math of Stock Picking Works Against Active Managers

The concentration of gains in a minority of index fund holdings—a statistical concept called positive skew—makes it extremely difficult for active managers to beat benchmarks, according to a recent Bloomberg article.

Research conducted in 2015 found that “the distribution of returns in the stock market is bizarrely lopsided,” the article argues. “It’s a pattern of returns that virtually ensures everyone outside of an indexer owns mostly deadbeat stocks.” According to Rob Arnott of Research Affiliates: “The focus is often on the random walk and the coin toss analogy, and the impact of skewness is overlooked.”

In a coin toss, there’s a 50% chance of winning. The article asserts, however, that the collective efforts of active fund managers around the world approaches only 19% (according to Bank of America data).

The concept might be overlooked, the article suggests, because the underlying math is difficult to understand. It explains using the example of a bag of poker chips: “Say you have five poker chips, four worth $10 and one worth $100. The five chips have an average value of $28, but what if you reach into the bag and pull out two chips over and over?” The argument is that most mutual funds work this way, the problem being that the majority of stocks chosen will “fail to snag the $100 chip.” One of the researchers argues that, even in the absence of fund fees and expenses, the odds are that an active manager will underperform the fund’s benchmark.

The result: “Only a few managers will own the biggies, relegating the rest of the industry to mediocrity—or worse.”