Summary: The stock market can be modeled as Omega in Newcomb’s problem. On average, an asset will only outperform if the market predicts that you won’t buy it. So you cannot say “if I had bought that, I would have made a lot of money”, just as in Newcomb’s problem you can’t say “if I had taken both boxes, I would have gotten more money than if I only took one”.

Edited 2018-02-11 to change the title. It originally read “Newcomb’s Problem and Speculative Bubbles”, but this essays argument is about markets, not necessarily bubbles in particular, so the old title was misleading.

Introduction

Newcomb’s problem:

A superintelligence from another galaxy, whom we shall call Omega, comes to Earth and sets about playing a strange little game. In this game, Omega selects a human being, sets down two boxes in front of them, and flies away.

• Box A is transparent and contains a thousand dollars.
• Box B is opaque, and contains either a million dollars, or nothing.

You can take both boxes, or take only box B.

And the twist is that Omega has put a million dollars in box B [if and only if] Omega has predicted that you will take only box B.

Omega has been correct on each of 100 observed occasions so far - everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars. (We assume that box A vanishes in a puff of smoke if you take only box B; no one else can take box A afterward.)

Before you make your choice, Omega has flown off and moved on to its next game. Box B is already empty or already full.

Omega drops two boxes on the ground in front of you and flies off.

Do you take both boxes, or only box B?

The answer is that you should only take box B. All the interesting conclusions of this essay depend on that assumption, so if you think you should take two boxes, you definitely won’t agree with this essay’s conclusions (but you might still find them interesting).

You might not have realized it, but you can actually play a version of Omega’s game right now.

The stock market is Omega, buying the next big company is Newcomb’s problem, and you should (metaphorically) take only one box.

The stock market Newcomb’s problem

Consider a modified (and somewhat sadistic) version of Newcomb’s problem:

Omega sets a single box in front of you and then flies away. It’s opaque, and contains either a million dollars or nothing.

You can choose to either pay $1000 and take the box, or pay nothing and not take the box.

Omega will put a million dollars into the box if and only if it has predicted that you will not take it.

Do you take the box or not?

If you should take only one box in the original Newcomb’s problem, then in this modified version you should not take the box for the same reason. If you take it, you pay $1000 and Omega successfully predicts that you’ll take it, so you get nothing and you’re out $1000.

Buying the next hottest stock works pretty much the same way.

If you don’t take the box (a.k.a. the latest hot stock), it may contain tons of money that you didn’t get. If you do take it, you get nothing. In other words, hot speculative assets will only make lots of money if you don’t buy them.

I just made a pretty outlandish claim. It actually follows straightforwardly from the efficient market hypothesis (EMH), but it will take some work to fully explain.

According to EMH, the current price of an asset already reflects all available information about that asset. A lot of people know everything you know about markets plus more. If you have some knowledge that leads you to believe that an asset’s price is going to go up, other investors already know the same things you do and they already drove the price up.

The market has really strong forces pushing toward making it efficient. The finance industry employs tens (hundreds?) of thousands of people trying really hard to find mispriced assets, who then buy or sell those assets until they’re not mispriced anymore. Anything you learn about the market is going to be old news for them.¹

You can only buy at the height of the bubble

Say you are considering buying the latest big company, Bubbles Inc.

Suppose the company will have a big price run-up. If you can buy in early, you get to participate in the run-up and potentially make a lot of money. If you buy near the peak, you’ll just lose most of your investment.

Pretty much by definition, most people invest near the peak–prices rise when there’s more demand, which means more people trying to buy. If you randomly pick a person who’s buying stock in Bubbles Inc., chances are good they’re buying near the top. And thanks to our friend the efficient market hypothesis, you cannot reliably buy into the stock early on, before it has a big run-up.

Suppose you consider buying into Bubbles Inc. but decide not to, and then the price increases 10x. You might say, oh, I should have bought some, I would have made so much money! But in fact, you could not have bought Bubbles Inc. and still made money.

Counterfactual stock purchases and Newcomb’s problem

When you play the modified Newcomb’s problem described above, you will choose not to take the box and then, after not taking it, see that it contains $1 million. You might be tempted to say, “If only I had taken the box, I would have gotten a million dollars!” That would be true under normal circumstances. But in this game, you only get the money if Omega predicts that you don’t take the box. If you had taken the box, Omega would have predicted you would take the box, and you wouldn’t have gotten the money. There does not exist any counterfactual situation where you take the box and get the million dollars.

Bubbles inc. works the same way. You cannot reliably predict that Bubbles Inc. will have a big run-up (although you might occasionally get it right by sheer chance²). Suppose you were considering buying Bubbles Inc.–you had some reason to expect the price to increase a lot–but then you decided not to, and afterward, the stock made huge returns. If you had acted on that reason, the market would have known you were going to do that (in other words, all the people with more information than you would have acted on the same reason) and the price would have gone up before you ever bought any Bubbles Inc. stock. When you see Omega’s box with $1 million, you should not regret that you didn’t take it; for the same reason, when you see a stock’s price skyrocket, you should not regret that you didn’t buy it.

Mental algorithms

We can understand why the market behaves this way by thinking in terms of mental algorithms. When you do or don’t buy a stock, you run through some cognitive process to make that decision. Thanks to the efficient market hypothesis, you have to assume that lots of other people are running the same or better processes. That means if you decide not to buy a stock, other people’s algorithms might agree with yours and they won’t buy either. But if your mental algorithm does decide to buy, other people will decide the same thing (including really smart people with lots of money, like hedge funds), and they will make their decisions faster than you do. You can’t say “oh, if only I had bought Bubbles Inc. a year ago, I would have made tons of money!”: if your mental algorithm had said to buy it, so would lots of other people’s, and they would have done it before you.

Can you regret making the wrong choice if you chose randomly?

I can think of one situation where you perhaps could have bought Bubbles Inc. before most people. If you chose to buy it purely randomly, then perhaps everyone before you could randomly choose not to buy, and you could end up making a lot of money. If you randomly choose not to buy, perhaps you can genuinely say, “I regret not buying Bubbles Inc., because I know that even if I had, other people still wouldn’t have.”

Perhaps in this situation, you genuinely could have chose differently and taken advantage of Bubbles Inc.’s subsequent rise without the market preemptively taking away your opportunity. But it only works because you’re running a bad algorithm. You definitely shouldn’t buy stocks randomly. On average you will certainly do no better than the market, and on a risk-adjusted perspective you’ll do worse because by choosing stocks at random you’re losing diversification without gaining any expected return. So the only way you can perhaps regret having not bought Bubbles Inc. is if you’re running a bad algorithm.

Real life

Fairly regularly, I hear friends talking about how they considered buying bitcoin five years ago but didn’t. They regret not buying it because they believe they could’ve made lots of money if they had. (As of this writing, bitcoin has returned about 500x over the past five years.)

Except if they had bought bitcoin five years ago, it wouldn’t have gotten a 500x return. If they had had some good reason to buy bitcoin, lots of other people would have had the same reason, and the price would have already risen before they decided to buy any.

That’s not to say nobody took advantage of that 500x return–clearly some people did, because some people held bitcoin in 2012. But very few people did, and nobody could have done so for any reason other than sheer luck³. In 2012, there was no available information reliably demonstrating that the price of bitcoin would increase by a lot–if there were, the smart money would have already driven the price up. If you had had any information that would lead you to buy bitcoin, hedge funds would have had it, too. Much like Omega, the market knows what you’re going to do, and it will stop you from getting any special advantage.

Notes