Positive Skew and Why Active Management Under-performs Passive Strategies

The story of active management under-performance is retold on a monthly, quarterly, and annual basis.  And it appears that investors are listening, based on the wall of money that has flowed, and is continuing to flow, from active to passive funds.  In this context, I mean “passive” not only to be index tracking funds, but also funds like those offered by Dimensional Fund Advisors, who utilize broadly diversified portfolios to implement their investment strategies.


Much attention has been focused on the cost of trading, and the cost of management, to explain the chronic underperformance of active managers in most major equity asset classes.  But a recent Bloomberg article titled The Math Behind Futility recalls an academic paper written in the late 90s, by Richard Shockley of Indiana University, which offers a mathematical explanation of why costs alone do not explain the totality of underperformance.  The underlying cause is something called skewness, or in this context, the tendency of a minority of stocks within an index to provide outsize returns.  Because active managers tend not to invest in all of the stocks in an index, omitting stocks with positively skewed returns amounts to a “death sentence for anyone who gets paid for beating a benchmark.”


Read more about Shockley’s work and updated research by J.B. Heaton, Nicholas Polson, Jan Hendrik Witte, and Hendrik Bessembinder.



Acne, Jelly Beans, and Butter Production in Bangladesh

Peter Coy writes for Bloomberg about how financial statistics are manipulated to tell stories that investors want to hear, even if they’re not true.   He offers that the “core of the problem is that it’s hard to beat the market, but people keep trying anyway,” then explains how financial firms manufacture investment strategies that are designed to capitalize on statistical anomalies.


Coy gives two examples of how pure statistical analysis, without the benefit of logic and reason, can lead to horribly flawed outcomes. In the first example, an analyst who is trying to find a statistical relationship between the consumption of jelly beans and acne is not able to do so, so he keeps eliminating data based on the color of jelly bean, until he demonstrates a clear correlation between green jelly beans and acne.   In the second example, Coy references a study which found that the best predictor of the S&P 500, out of all the time series in a collection of United Nations data, was butter production in Bangladesh.  Trouble is, while there may be a quantifiable relationship between the data series, there is no causation.   It’s purely coincidence.


There is a term for such over-fitting of statistical data to achieve a desired outcome:  it’s called p-hacking, a reference to the p-value in statistical analysis.  The risk is particularly high with financial time series, because there’s  a powerful market incentive for practitioners to search for and identify previously unknown relationships.


Read the full analysis here.

Update to Why We Use Mutual Funds

We published our “Why We Use Mutual Funds” post about three weeks ago, on March 27, to draw attention to the high, hidden costs of trading ETFs.   In today’s weekend Wall Street Journal, Jason Zweig laments the same point.  Titled “The Expensive Ingredient of Cheap ETFs,” his article explains how trading costs are “one of the worst destroyers of investment returns.”   He oberves, “These costs lurk in the normally tiny space between the market price of an ETF and the per-share value of the stocks, bonds and other assets it holds.”