Crashes, Beauty Queens, and the Hangman’s Noose

[This was originally posted on November 2nd, 2020 in r/thecorporation]

As many of you kind of guessed in my last cryptic post, I didn’t find it likely that we would crash today. While I still have several hours to eat my words, it does not seem likely. I did load up on one UVXY call on Friday expecting it to rise, but paperhanded in the AM at the lowest price of the day of course (now it’s going up).

As I mused on Saturday night while high, we saw a ton of bearish flow last week, which contributed in large part to the hedge unwinding face ripping rally we saw EOD on Friday. This, coupled with other indicators (extreme bearish sentiment, VIX term structure, etc.) was a convincing factor that a crash probably won’t occur.

Let’s take a look why.

— -

In general, we must assume the market is full of rational actors. Now when I say rational, I don’t mean not buying or selling stupid shit (my JMIA leaps would like a word with this), but that every market participant acts in a way that assumes he/she/they want to maximize their profit, whether as a seller or a buyer. This sometimes isn’t true, and has interesting implications with risk measure, but it’s true enough for the sake of argument.

If everyone knows about an event taking place on November 3rd where let’s say it’s certain that the market will drop 10% (as many people are predicting for the election), what would a group of rational actors in the market do here?

1. If they know for certain that the market will drop on 11/3, they can make a profit by buying puts accordingly.
2. However, the market makers writing said puts also know the market will drop on 11/3, and can price the puts according to rationality (factoring in the 10% drop). This follows directly from the Law of Surprise, one of my previous posts. This will lower demand for puts accordingly (since there will be no profit to be made off of a certainty here, keeping people from buying puts.
3. Similarly, if they know that a crash will certainly occur, they can also share their sells and rebuy later, right? Accordingly, if everyone knows that their shares will drop 10%, they will all sell their shares before the event, crashing the market before the event.

In this way, we can reflect about the unpredictability of crashes. Very rarely can a crash be known as a certainty in advance, because the nature of knowing that a crash will occur will cause rational market participants to either:

1. Prevent a crash — This can be illustrated simply. If we know about a crash in advance, historically the market rebounds quickly enough during crashes. As a rational market participant, I could wait out until the crash and buy at the lowest point. This works for the individual, but applied over the entire market, this implicitly prevents the crash, because there will be enough buying power (or more) to match the selling power.
2. Cause the crash to occur at a different time — As I mentioned earlier, if we could all for sure time a crash, you could save yourself by selling before the crash at the last high, and buying later for pure profit (at a discount). This however, isn’t a unique idea — in fact, if you assume the market is rational, every individual in the market would do exactly this. This would cause the crash to occur before the event, as everyone liquidates their holdings (a panic). This would not be predictable.

Historically, crashes rarely occur due to an event known ahead of time. Even in the case that they are caused by a reaction to a specific event that is known, they tend to occur before or after the event in question, as a reaction to panic in participants who are trying to front-run based on public information.

Beauty Queens

This all follows, by the way, from the words of one John Maynard Keynes. In particular, to explain why the market fluctuates intraday even in response to no news (price formation), he devised the concept of a Keynesian beauty contest -

Keynes described the action of rational agents in a market using an analogy based on a fictional newspaper contest, in which entrants are asked to choose the six most attractive faces from a hundred photographs. Those who picked the most popular faces are then eligible for a prize.

A naive strategy would be to choose the face that, in the opinion of the entrant, is the most handsome. A more sophisticated contest entrant, wishing to maximize the chances of winning a prize, would think about what the majority perception of attractiveness is, and then make a selection based on some inference from their knowledge of public perceptions. This can be carried one step further to take into account the fact that other entrants would each have their own opinion of what public perceptions are. Thus the strategy can be extended to the next order and the next and so on, at each level attempting to predict the eventual outcome of the process based on the reasoning of other rational agents.

The end result of this behavior, Keynes argues, is that:

Keynes believed that similar behavior was at work within the stock market. This would have people pricing shares not based on what they think their fundamental value is, but rather on what they think everyone else thinks their value is, or what everybody else would predict the average assessment of value to be.

In general, the stock (and options) market works not based on what we believe the value of the underlying to be, but what we believe others value it at. This ends up causing a ton of strange phenomena, and explains why supposedly rational individuals might actually buy calls on Tesla still.

The Hangman’s Noose

Let’s connect the dots between these two concepts. In general, we can anticipate that the valuation of the market is based on what other people value it at. However, those other people value it by the same metric — they value it based on what other people (other than themselves) value it at.

This causes unexpected results, because you can keep generalizing this over and over (you can assume that those people the other person was valuing it based on are also valuing it based on other people — and that might including you!) Is there an actual solution here?

To that I say — no, there isn’t. The market, in essence, and the prediction of a crash is a generalization of the famous Unexpected Hanging Paradox —

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the “surprise hanging” can’t be on Friday, as if he hasn’t been hanged by Thursday, there is only one day left — and so it won’t be a surprise if he’s hanged on Friday. Since the judge’s sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.

He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn’t been hanged by Wednesday noon, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning, he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.

The next week, the executioner knocks on the prisoner’s door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.

Clearly, crashes do occur. Clearly, there is information out there that can help you predict a crash. In fact, for myself, my NOPE model flashed warning lights on Sep 2nd and Oct 12th. But it’s easy to find these things in retrospect. The only certainty is using information to make a reasonable judgment about risk — in effect, betting on an outcome based on the information you possess. Even people who can so-called predict a crash are just betting on a certain probable outcome, but it is never an actual certainty. The ones who bet wrong — well, that’s survivorship bias at its finest.

Don’t get caught off-guard on your execution day.

- Lily