Thursday, March 15, 2012

How Fantasy Football Explains the Stock Market

Managing a fantasy football team is surprisingly similar to managing a stock portfolio. In both, you have a fixed budget to spend on a fixed number of stocks / players (say, 15). Your job is to use all of your knowledge in order to predict which stocks / players are going to have the highest returns, be they in the form of dollars or fantasy points.

One fact that I think would surprise people to learn is that most managers of stock portfolios do worse than the market average. Of course, if every manager simply picked 15 stocks from the S&P 500 at random, then about half would do worse than average every year. But in fact, the vast majority of managers — some years, more than 80% — do worse than average.

A year ago, the idea that most professional portfolio managers, people whose full-time job is managing a stock portfolio, could be worse at picking stocks than choosing randomly was inconceivable. However, after another painful year of playing fantasy football, this now makes sense.

To explain, let's consider a hypothetical stock called "Vermaelen Industries". Here is a chart of the price of a share of this stock over the year:


If I were to show this price chart to an investor and tell him that I owned this stock for much of the year, that investor would most likely think I did well. Indeed, Vermaelen Industries had a good year. It went up in price. If I had bought and held it for pretty much any 10 week period, I would have made money.

Of course, Vermaelen Industries is fictitious, but this price chart is not made up. I've translated the points per week delivered by Arsenal centerback, Thomas Vermaelen, into changes in price. When Vermaelen delivered more than an average number of points, his price went up, and when he delivered fewer, his price went down.

Here is a chart of Vermaelen's points per week (ignoring the periods when he was injured):


Show this chart to any fantasy football manager and they will instinctively know the truth: I bought in game week 16 and sold in game week 25. Or in stock market terms, I bought high and sold low.

All fantasy football managers are aware of the fact that players tend to do worse after you buy them and better after you sell them. The fancy name for this phenomenon is mean reversion, but terminology aside, it is an instinctive law of nature to fantasy football managers. Indeed, it's effect is so strong that I feel I can make my favorite team win by selling all of their players and buying players from their rival.

Strangely, this law does not seem instinctive to portfolio managers. Nonetheless, mean reversion is just as real for stocks as it is for football players. And that, I think, is the root cause of why most portfolio managers do worse than the market.

One might think that the tendency to buy high and sell low is a result of irrational thinking. However, I think not. Rather, this behavior is the natural result of rational thinking combined with constant attention.

To explain, suppose that I am choosing, for one of my 15 stocks, between Vermaelen Industries and Kompany Manufacturing. Suppose that I currently own Kompany, but every week, I look at Vermaelen's results and decide if I want to trade.

In order to compare these two stocks, I need to predict the returns of each stock in the future. The simplest way to do that is to look at the average returns of each stock over the year so far. (Other, more sophisticated methods would also give the same result, but let's keep things simple.)

Each week, I will look at Vermaelen's average performance over the year so far and compare that to Kompany's. If Vermaelen's is sufficiently higher, then I will trade. Once I own Vermaelen, I will continue to compare, and if his average performance becomes sufficiently lower than Kompany's, then I will trade back.

With this methodology in mind, it should be less surprising that I bought in week 16 because that was the exact moment at which Vermaelen's average performance so far was at it's highest point. Likewise, it should be less surprising that I sold in week 25 because that was the exact moment when his average performance reached it's lowest point. Indeed, both trades were perfectly rational given current information.

As I've described things, however, I would still have needed some bad luck in order to buy and sell as I did. In particular, to buy in week 16, it must have been the case that week 16 was the first week at which Vermaelen's average performance so far became sufficiently higher than Kompany's. If, on the other hand, it was sufficiently higher at week 15 or 14, then I would have got in on a couple of good weeks and the trade would not look so bad in retrospect.

Reality, however, is not this nice. In particular, I would not have normally had my eye on just Kompany and Vermaelen. More likely is that I owned Kompany and then, at some point, it came to my attention that Vermaelen might be a good buy. Then I crunched the numbers and realized I should trade.

Of course, then we must ask: why did Vermaelen come to my attention? Obviously, he came to my attention in week 16 because he had a couple of fantastic weeks just before then. In general, the most likely time that a player will come to my attention is just after they have peaked. That is the time at which the player's accomplishments are most likely to be talked about (in the media, on twitter, or wherever) and thus come to my attention.

If I watch ESPN Press Pass every Monday, then each week I'm likely to hear about the players who are performing better than usual. Many of these are likely to be players that are peaking. So if this is how I find out about players for potential trades, then I am likely to see considerable mean reversion.

For portfolio managers, there is a simple way to avoid this: don't watch the news every week (i.e. "buy and hold"). However, fantasy football managers have little choice. We have to set our lineups every week, which requires current information about every player. So unfortunately, I can say with some confidence that our suffering will long continue.