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Salemicus comments on Open thread, Aug. 10 - Aug. 16, 2015 - Less Wrong Discussion

5 Post author: MrMind 10 August 2015 07:29AM

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Comment author: Salemicus 11 August 2015 07:58:30PM 2 points [-]

Second, when you say they are "a poor investment in terms of expected return", do you actually mean expected return? ... A lottery can perfectly well have a positive expected return even if your chance of getting a positive return is very small.

Yes, I mean expected return. If you hold penny stocks, you can expect to lose money, because the occasional big wins will not make up for the small losses. You are right that we can imagine lotteries with positive expected return, but in the real world lotteries have negative expected return, because the risk-loving are happy to pay for the chance of big winnings.

[If] penny stocks provide negative expected return ... then EMH breaks

Why?

Suppose we have two classes of investors, call them gamblers and normals. Gamblers like risk, and are prepared to pay to take it. In particular, they like asymmetric upside risk ("lottery tickets"). Normals dislike risk, and are prepared to pay to avoid it (insurance, hedging, etc). In particular, they dislike asymmetric downside risk ("catastrophes").

There is an equity instrument, X, which has the following payoff structure:

99% chance: payoff of 0 1% chance: payoff of 1000

Clearly, E(X) is 10. However, gamblers like this form of bet, and are prepared to pay for it. Consequently, they are willing to bid up the price of X to (say) 11.

Y is the instrument formed by shorting X. When X is priced at 11, this has the following payoff structure:

99% chance: payoff of 11 1% chance: payoff of -989

Clearly, E(Y) is 1. In other words, you can make money, in expectation, by shorting X. However, there is a lot of downside risk here, and normals do not want to take it on. They would require E(Y) to be 2 (say) in order to take on a bet of that structure.

So, assuming you have a "normal" attitude to risk, you can lose money here (by buying X), but you can't win it in risk-adjusted terms. This is caused by the market segmentation caused by the different risk profiles. Nothing here is contrary to the EMH, although it is contrary to the CAPM.

Thoughts:

  1. Penny stocks (and high-beta instruments generally, such as deep out-of-the-money options) display this behaviour in real life.
  2. A more realistic model might include some deep-pocketed funds with a neutral attitude to risk who could afford to short X. But in real life, there is market segmentation and a lack of liquidity. Penny stocks are illiquid and hard to short, and so are many other high-beta instruments.
  3. The logical corollary of this model is that safe, boring equities will outperform stocks with lottery-ticket-like qualities. And it therefore follows that safe, boring equities will outperform the market as a whole. And that also seems true in real life.
  4. There are plausible microfoundations for why there might be a "gambler" class of investor. For example, fund managers are risking their clients' capital, not their own, and are typically paid in a ranking relative to their peers. Their incentives may well lead them to buy lottery tickets.
Comment author: Lumifer 11 August 2015 08:34:06PM 1 point [-]

However, there is a lot of downside risk here, and normals do not want to take it on.

By itself, no. But this is diversifiable risk and so if you short enough penny stocks, the risk becomes acceptable. To use a historical example, realizing this (in the context of junk bonds) is what made Michael Milken rich. For a while, at least.

market segmentation caused by the different risk profiles

This certainly exists, though it's more complicated than just unwillingness to touch skewed and heavy-tailed securities.

Penny stocks (and high-beta instruments generally, such as deep out-of-the-money options) display this behaviour in real life.

In real life shorting penny stocks will run into some transaction-costs and availability-to-borrow difficulties, but options are contracts and you can write whatever options you want. So are you saying that selling deep OOM options is a free lunch?

As for the rest, you are effectively arguing that EMH is wrong :-)

Full disclosure: I am not a fan of EMH.

Comment author: Salemicus 11 August 2015 08:47:09PM *  1 point [-]
  1. Who says this risk is diversifiable? Nothing in the toy model I gave you said the risk was diversifiable. Maybe all the X-like instruments are correlated.
  2. No, I'm not saying that selling deep OOM options is a free lunch, because of the risk profile. And these are definitely not diversifiable.
  3. I am not arguing that EMH is wrong. I have given you a toy model, where a suitably defined investor cannot make money but can lose money. The model is entirely consistent with the EMH, because all prices reflect and incorporate all relevant information.
Comment author: Lumifer 11 August 2015 08:53:18PM 0 points [-]

toy model

Oh, I thought we were talking about reality. EMH claims to describe reality, doesn't it?

As to toy models, if I get to define what classes of investors exist and what do they do, I can demonstrate pretty much anything. Of course it's possible to set up a world where "a suitably defined investor cannot make money but can lose money".

And deep OOM options are diversifiable -- there is a great deal of different markets in the world.

Comment author: Salemicus 11 August 2015 09:03:27PM 1 point [-]

Oh, I thought we were talking about reality. EMH claims to describe reality, doesn't it?

Yeah, but you wanted "a scenario where everything is happening pre-tax, there are no transaction costs, we're operating in risk-adjusted terms and, to make things simple, the risk-free rate is zero. Moreover, the markets are orderly and liquid." That doesn't describe reality, so describing events in your scenario necessitates a toy model.

In the real world, it is trivial to show how you can lose money even if the EMH is true: you have to pay tax, transaction costs are non-zero, the ex post risk is not known, etc.

deep OOM options are diversifiable -- there is a great deal of different markets in the world.

There's still a lot of correlation. Selling deep OOM options and then running into unexpected correlation is exactly how LTCM went bust. It's called "picking up pennies in front of a steamroller" for a reason.

Comment author: Lumifer 11 August 2015 09:09:15PM *  0 points [-]

That doesn't describe reality, so describing events in your scenario necessitates a toy model.

Fair point :-) But still, with enough degrees of freedom in the toy model, the task becomes easy and so uninteresting.

It's called "picking up pennies in front of a steamroller" for a reason.

I know. Which means you need proper risk management and capitalization. LTCM died because it was overleveraged and could not meet the margin calls. And LTCM relied on hedges, not on diversification.

Since deep OOM options are traded, there are people who write them. Since they are still writing them, it looks like not a bad business :-)

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