### Positive Skew is Negative for Active Managers

Let’s play a game. In this game, there are 10 random poker chips in a bag. 9 of these chips will give you a return between -8% and +8% on the money that you bet. The 10^{th} coin will give you a 100% return. The distribution of returns for this game has a positive skew.

If offered to put money down on this proposition you would take it because you would expect a 10% return if you could play the game over and over.

Now let’s add a wrinkle. Your goal isn’t just to make a positive return, you have to beat the bag. The bag puts 10% of their money on each chip and pulls them all. Voila, a 10% return. One last wrinkle, you can only pick one chip at a time.

How many times out of 10 would you beat the bag? Only 1 in 10. 90% of the time you would lose to the bag. It doesn’t matter if we expand the number of chips as long as the bag maintains the same positive skew (we could increase the to 100 chips and you get to pick 10, 100 chips and you pick 1000, etc.)

By now, you’ve probably guessed that the bag is the market, the chips are stocks, and you are, well, you. This is the game we play when trying to beat an index. True, you can be better than the market at figuring out the good chips but given that initial conditions for a random game means you lose 9 out of 10 times, it’s really hard to beat the market. Add fees and the likelihood of beating the market goes down even further.

Positive Skewness has gotten a decent amount of press over the past year because of the championing of JB Heaton who wrote a paper^{1} researching the impacts of positive skew on manager underperformance. Heaton’s paper is similar to research from Dr. Richard Shockley in 1998^{2}. See below for an article written by Bloomberg News on the topic.

*Source: Bloomberg News (“Lopsided Stocks and the Math Explaining Active Manager Futility” by Oliver Renick)*

Given that many of the conversations active managers have today revolve around active versus passive, “positive skew” should be top of mind. This is my push to increase awareness.

Given that active managers can’t change market skew, what should we do? We could measure skill in a different way. Let’s say I want to measure a manager skill. If I take all of the stocks of the markets they’re investing in and then randomly build 100,000 portfolios with the same number of securities as the manager. I can then plot where that manager falls on the distribution and give them a Z-Score for how far away from the norm they are. I could do the same thing for hedge funds by randomly buying and selling securities in the same universe as the investor.

I’m not saying that this excuses active managers from underperforming passive strategies, but it should at least be a more realistic assessment of their skill. My hope is that positive skew becomes just as common an explanation as fees when discussing active manager underperformance. Only by knowing the causes, will we be able to make changes that allow active managers to outperform.

^{1} Nicholas Polson and Jan Hendrik Witte; Hendrik Bessembinder of Arizona State University

^{2}“Why Active Managers Underperform the S&P 500: The Impact of Size and Skewness,” published in the inaugural issue of the Journal of Private Portfolio Management. One of the original authors of the study is Richard Shockley.