March Madness is officially here, and if you’re anything like me, that means you’ve already filled out at least a half dozen brackets, all with different outcomes and champions. Even President Obama is likely to weigh in with his picks later this week, along with 40 million or so potential voters.
The process of filling out an NCAA Tournament bracket is, ultimately, a lot like that of constructing an investment portfolio—trying to find the right balance between the “safe” picks (top seeds, blue-chip stocks) and the “upset” picks (lower seeds, growth stocks); crafting a “unique” bracket that you think can outperform your coworkers (or “the market”); even making picks that will make us feel good when they work out well (picking our alma mater’s team, or values-based investing).
Of course, given the similarities, it’s a shame that we are, on balance, pretty terrible at both tasks—the litany of research regarding the folly of stock-picking is rivaled only by the annual avalanche of “my bracket is already busted” jokes, which will get old in a hurry (annual reminder: nobody cares about your bracket). But just because we’re all destined to be eliminated from our office pools by this weekend, that doesn’t mean we can’t learn a little something about investing in the process. Let’s have a try at it.
The “most likely” outcomes aren’t really the most likely
The biggest mistake that people tend to make when filling out their brackets is picking too much “chalk”, or highly-seeded teams. The mistake is one of confusing the most likely individual outcomes with the most likely aggregate outcome. I’ll show you what I mean.
Let’s consider the case of Kentucky, this year’s as-yet-unbeaten #1 overall seed, and the most overwhelming Tournament favorite in recent memory. As statistician Nate Silver points out, the Wildcats will have at least a 73% chance of winning every game they play in this year’s tournament. Therefore, from an individual game-picking standpoint, it would be completely irrational to ever pick against Kentucky. Everyone should pick Kentucky to win this year’s tournament, case closed. Right?
Even though they’ll be the overwhelming favorite in every individual game they play, Kentucky is still more likely to lose the title than to win it, with title odds of about 40%, versus 60% for “the field” (i.e., anybody else). No, there isn’t any one team in the field who’s more likely than Kentucky to win it all (Villanova, at 11%, comes in a distant second), so if you have to pick one, you’d pick Kentucky. But you’d do so admitting that you’re more likely to be wrong than to be right.
Ultimately, this dynamic boils down to basic statistics—add enough rounds to any game, and the odds of an “unexpected” outcome steadily rise. It’s a sports version of the old “birthday problem”, wherein small odds become large odds quite quickly given enough trials.
As the above chart shows, even if top seeds had a 95% chance of winning every game, they would only need to play 14 games before the probability of “all-favorites-winning” is less than the probability of “at-least-one-upset”. And since teams rarely have that high a single-game win probability (according to Silver, only seven teams in this year’s tournament have that high a win probability in any single game, let alone across multiple games), the real number of games that it takes before we can expect an upset is much lower.
With 63 games in the tournament (okay, fine, 67 if you include the play-in games), there’s basically no way that an “all high seeds” approach, or anything close to it, can win out. Remember, there has only been one year in history where all four #1 seeds advanced to the Final Four, as compared to three years where none of the four did. That’s not a bug, it’s a feature.
In fact, this is why the tournament has adopted the nickname “March Madness”, because officially, anything can happen, and probably will. The reality of the matter is, the craziest and most unlikely outcome that we could ever have in the tournament is for every single favorite to win every single game. That’s why Warren Buffett felt confident enough to offer up $1 billion to anyone who could pick a “perfect bracket”—not just because he knew how mathematically impossible the task would be, but because he knew that America’s predilection toward picking the favorites would cost them dearly and actually make it even more unlikely that they would pick the perfect bracket (spoiler: nobody escaped even the first weekend of the tournament unscathed).
So, what does that mean for investing? Well, constructing a portfolio comprised only of blue-chip stocks is probably a bad idea. Pop quiz: what were the best performing stocks in the S&P 500 last year? Were they the behemoths, the ones with the largest market caps (Apple, ExxonMobil, Microsoft, Google, Johnson & Johnson)? Nope.
While a portfolio consisting only of those 5 names (in equal weights) would have earned a solid total return of 14.8% in 2014 (aided mostly by Apple, which clocked a 40.6% return; 2 of the 5 actually would have lost money), their performance was barely distinguishable from the overall market average.
This table here shows the best-performing S&P 500 stocks last year:
While you’ve probably heard of most of these companies, you certainly wouldn’t build a portfolio around them—and some of them, even I couldn’t tell you what they do without looking it up (when in doubt, guess biotech).
Even the best-informed (and gutsiest) stock picker would have been hard-pressed to allocate a meaningful portion of their portfolio to those names. In large part, that’s because career risk (or, in the case of brackets, risk of humiliation) is a killer—lose money for your clients owning Apple stock, and you’ll be forgiven, but lose it owning Allergan and you may soon be out of a job.
That fear of failure is why football coaches don’t go for it on 4th down nearly as often as they mathematically should—it’s a matter of guessing at which failures will be “acceptable”, and which will not, rather than optimizing one’s chances of winning. It’s also why your bracket probably stinks, and why your portfolio might, too.
You’re overestimating the differences
When we look at a bracket and see that one team is a #1 seed and another is a #8 seed, that’s a very powerful signal to our brains, and it indicates that there’s a large and measurable difference in caliber between the two teams. The reality, of course, is often quite different. The highest ranked #7 seed in this year’s tournament, Michigan State, is ranked as high as 17th in the country by some measures, and played one of this year’s #1 seeds to a virtual tie just last weekend. Large and measurable difference? Not exactly.
Remember that when looking at an NCAA Tournament bracket, we’re dealing with an artificially limited sample set, one that boasts an incredible amount of homogeneity. All of these teams are accomplished (or even champion) teams of one sort or another, or else they wouldn’t be in the tournament field to begin with. The differences between the very best and the not-quite-the-best teams are purely on the margins, and in a one-game sample, random variation means more than those marginal differences.
Every March we’re reminded of this fact when we see familiar names in new places—these can be either players who have transferred from top-tier programs to lesser squads (Kevin Ware, Taylor Barnette, Kyle Wiltjer, Jermaine Lawrence, Paul Jesperson), or coaches who made their star one place before resurfacing somewhere else (Bobby Hurley, Steve Fisher, Larry Brown). So, not only are these teams not all that much different in terms of overall talent, they’re often some of the very same people from one year to the next!
The same dynamic holds true in investing. By definition, if a company has become publicly traded, it is a wildly successful company by any standard measure. We’re not comparing Intel to your local computer repairman’s business, we’re comparing the best and most profitable companies in the world against each other. And just like players and coaches can often switch teams, so too can employees and even senior executives (Meg Whitman, Marissa Mayer). If every stock is a blue-chip, are any stocks truly blue-chips?
And just as individual companies are often more similar than different, so too are different classes of securities (stocks versus bonds, for example). Remember, regardless of what your textbook says, these instruments are typically traded and managed by many of the same industry players and investors. Their behavior with respect to different asset classes will certainly differ, but maybe not as much as we might typically expect.
Sometimes history lies
You hear it all the time in investing: “past performance is not an indicator of future results”. We should definitely apply the same thinking when filling out our brackets. As many of you are no doubt aware, a #1 seed has never lost to a #16 seed since the tournament expanded to 64 teams—they are 120-0. Does this mean they’re invulnerable? Hardly.
Shifting just one line on the seed list to #2, we see that 7 of 120 #2 seeds have lost to their #15 seed opponents, including three in a recent two-year span. Assuming that every #1 seed has a 98% chance of beating a #16 seed in a given game (a high but fair probability), we arrive at a 7.8% chance of a 16-over-1 upset in any given year. That’s probably a lot higher than you might have expected. Frankly, the really unlikely outcome is that we’ve gone this far without seeing a single such upset—assuming that 98% win probability, the odds of an upset-free streak lasting this long are only about 1 in 11 (8.9%). Even if we increase the win probability to 99%, the odds still only increase to 29.9%, meaning we still should have expected at least one upset by now.
Does that mean you should pick a 16 seed this year? No, of course not. But you shouldn’t feel too comfortable automatically picking all of the #1 seeds every year, either.
You also shouldn’t necessarily pick a “dark horse” team just because they pulled an upset last year or the year before (see: VCU, Harvard… and please, take it from me, you definitely shouldn’t pick Harvard this year). For one, the seeding committee will typically respond to those kinds of upsets, and might over-rank those teams in subsequent years. For another, pulling off an unlikely win one year doesn’t make it any more likely that you’ll do the same again; these are independent trials, remember.
Take “the field”
In the world of bracketology, choosing “the field” is unfortunately not an option. Even though we may recognize that Kentucky is more likely to lose the title than to win it, that doesn’t mean there are any better options available to us. We’ve gotta pick somebody. Lucky for us, the same all-or-nothing approach doesn’t hold true in investing.
When we’re operating in the markets, we both can and should choose investments that represent “the field” (they’re called index funds). We’ll still own plenty of the Kentuckys of the world in those funds, but we’ll also get to own some of the lesser-known teams (stocks), for when the unlikely-but-eventually-inevitable “upsets” happen. That way your portfolio won’t end up busted, even if your bracket does. Have fun out there, but check your strategies at the door when it comes to investing—there shouldn’t be any “madness” in anyone’s portfolio.
(P.S.- Go ‘Hoos)