The Baltimore Stockbroker

THE BALTIMORE STOCKBROKER

Here’s a parable. One day, you receive an unsolicited newsletter from a stockbroker in Baltimore, containing a tip that a certain stock is due for a big rise. A week passes, and just as the Baltimore stockbroker predicted, the stock goes up. The next week, you get a new edition of the newsletter, and this time, the tip is about a stock whose price the broker thinks is going to fall. And indeed, the stock craters. Ten weeks go by, each one bringing a new issue of the mysterious newsletter with a new prediction, and each time, the prediction comes true.

On the eleventh week, you get a solicitation to invest money with the Baltimore stockbroker, naturally with a hefty commission to cover the keen view of the market so amply demonstrated by the newsletter’s ten-week run of golden picks.

Sounds like a pretty good deal, right? Surely the Baltimore stockbroker is onto something—it seems incredibly unlikely that a complete duffer, with no special knowledge about the market, would get ten up-or-down predictions in a row correct. In fact, you can compute the odds on the nose: if the duffer has a 50% chance of getting each prediction right, independently of the other predictions, then the chance of his getting the first two predictions right is half of half, or a quarter, his chance of getting the first three right is half of that quarter, or an eighth, and so on. Continuing this computation, his chance of hitting the mark ten times in a row * is

(1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2)= (1/1024).

In other words, the chance that a duffer would do so well is next to nil.

But things look different when you retell the story from the Baltimore stockbroker’s point of view. Here’s what you didn’t see the first time. That first week, you weren’t the only person who got the broker’s newsletter; he sent out 10,240.* But the newsletters weren’t all the same. Half of them were like yours, predicting a rise in the stock. The others predicted exactly the opposite. The 5,120 people who got a dud prediction from the stockbroker never heard from him again. But you, and the 5,119 other people who got your version of the newsletter, get another tip next week. Of those 5,120 newsletters, half say what yours said and half say the opposite. And after that week, there are still 2,560 people who’ve received two correct predictions in a row.

And so on.

After the tenth week, there are going to be ten lucky (?) people who’ve gotten ten straight winning picks from the Baltimore stockbroker—no matter what the stock market does. The broker might be an eagle-eyed observer of the market, or he might pick stocks by slapping chicken guts against the wall and reading the stains—either way, there are ten newsletter recipients out there to whom he looks like a genius. Ten people from whom he can expect to collect substantial fees. Ten people for whom past performance is going to be no guarantee of future results.

I’ve often heard the Baltimore stockbroker parable told as a true story, but I couldn’t locate any evidence that it’s ever really happened. The closest thing I found was a 2008 reality TV show—reality TV being where we go for parables nowadays—in which British magician Derren Brown pulled off a similar stunt, mailing various horse-racing picks to thousands of Britons with the result of eventually convincing a single person that he’d devised a foolproof prediction system. (Brown, who likes dispelling mystical claims more than he does promoting them, exposed the mechanism of the trick at the end of the show, probably doing more for math education in the UK than a dozen sober BBC specials.)

But if you tweak the game, making it less clearly fraudulent but leaving unchanged the potential to mislead, you find the Baltimore stockbroker is alive and well in the financial industry. When a company launches a mutual fund, they often maintain the fund in-house for some time before opening it to the public, a practice called incubation. The life of an incubated fund is not as warm and safe as the name might suggest. Typically, companies incubate lots of funds at once, experimenting with numerous investment strategies and allocations. The funds jostle and compete in the womb. Some show handsome returns, and are quickly made available to the public, with extensive documentation of their earnings so far. But the runts of the litter are mercy-killed, often without any public notice that they ever existed.

Now it might be that the mutual funds that make it out of the incubator do so because they actually represent smarter investments. The companies selling the mutual funds may even believe that. Who doesn’t, when a gamble goes right, think their own smarts and know-how are in some way due the credit? But the data discussed here suggest the opposite: the incubator funds, once the public gets their hands on them, don’t maintain their excellent prenatal performance, instead offering roughly the same returns as the median fund.

What does this mean for you, if you’re fortunate enough to have some money to invest? It means you’re best off resisting the lure of the hot new fund that made 10% over the last twelve months. Better to follow the deeply unsexy advice you’re probably sick of hearing, the “eat your vegetables and take the stairs” of financial planning: instead of hunting for a magic system or an adviser with a golden touch, put your money in a big dull low-fee index fund and forget about it. When you sink your savings into the incubated fund with the eye-popping returns, you’re like the newsletter getter who invests his life savings with the Baltimore stockbroker; you’ve been swayed by the impressive results, but you don’t know how many chances the broker had to get those results.

It’s a lot like playing Scrabble with my eight-year-old son. If he’s unsatisfied with the letters he pulls from the bag, he dumps them back in and draws again, repeating this process until he gets letters he likes. In his view this is perfectly fair; after all, he’s closing his eyes, so he has no way of knowing what letters he’s going to draw! But if you give yourself enough chances, you’ll eventually come across that Z you’re waiting for. And it’s not because you’re lucky; it’s because you’re cheating.

The Baltimore stockbroker con works because, like all good magic tricks, it doesn’t try to fool you outright. That is, it doesn’t try to tell you something false—rather, it tells you something true from which you’re likely to draw incorrect conclusions. It really is improbable that ten stock picks in a row would come out the right way, or that a magician who bet on six horse races would get the winner right every time, or that a mutual fund would beat the market by 10%. The mistake is in being surprised by this encounter with the improbable. The universe is big, and if you’re sufficiently attuned to amazingly improbable occurrences, you’ll find them. Improbable things happen a lot.

It’s massively improbable to get hit by a lightning bolt, or to win the lottery; but these things happen to people all the time, because there are a lot of people in the world, and a lot of them buy lottery tickets, or go golfing in a thunderstorm, or both. Most coincidences lose their snap when viewed from the appropriate distance. On July 9, 2007, the North Carolina Cash 5 lottery numbers came up 4, 21, 23, 34, 39. Two days later, the same five numbers came up again. That seems highly unlikely, and it seems that way because it is. The chance of those two lottery draws matching by pure chance was tiny, less than two in a million. But that’s not the relevant question, if you’re deciding how impressed to be. After all, the Cash 5 game had already been going on for almost a year, offering many opportunities for coincidence; it turns out the chance some three-day period would have seen two identical Cash 5 draws was a much less miraculous one in a thousand. And Cash 5 isn’t the only game in town. There are hundreds of five-number lottery games running all over the country, and have been for years; when you put them all together, it’s not at all surprising that you get a coincidence like two identical draws in three days. That doesn’t make each individual coincidence any less improbable. But here comes the chorus again: improbable things happen a lot.

Aristotle, as usual, was here first: despite lacking any formal notion of probability, he was able to understand that it is probable that improbable things will happen.