When does a bet fail to reveal your true beliefs? When it hedges a risk in your portfolio.

If this claim does not immediately strike you as obviously true, you may benefit from reading this post by econblogger Noah Smith. Excerpt:


...Alex Tabarrok famously declared that "a bet is a tax on bullshit".

But this idea, attractive as it is, is not quite true. The reason is something that I've decided to call the Fundamental Error of Risk. It's a mistake that most people make (myself often included!), and that an intro finance class spends months correcting. The mistake is looking at the risk and return of single assets instead of total portfolios. Basically, the risk of an asset - which includes a bet! - is based mainly on how that asset relates to other assets in your portfolio.


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23 comments, sorted by Click to highlight new comments since: Today at 2:55 AM

Reminds me of Stephen Hawking betting against the existence of the black holes because, if they do exist, he would be so proud of having participating in their discovery and study he wouldn't care about losing a bet, and if they don't, winning the bet would slightly comfort him of spending so many years of his life studying something that doesn't exist.

That was exactly the example I thought of.

Sounds like "Individual bets don't always reveal the beliefs of every participant because some of them are arbitraging, but the market does."

The market as a whole also hedges against risk, and this affects asset prices. For example if there are two assets with equal expected returns but one is more correlated with the market return than the other, then the less correlated asset should have a higher price because it's more useful for hedging. (See capital asset pricing model for details.) The upshot is that you can't naively derive revealed beliefs without taking this into account. (And maybe introduce additional assets to your prediction market to figure out how correlated the participants believe the various bets are to the market return? There are probably papers about this but I'm too lazy to search for them.)

Intrade sells fed OMC rate binary options. I think if the market was more liquid, it would absolutely get used to hedge interest rate risks, and as people tend to be long bonds and short rates as a result, there might be a bias towards predicting higher rates as people want the protection. But the total holdings and the degree of hedging would be very opaque. Policy prediction markets could have similar problems.

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If a market is being highly influenced by people hedging their bets, then there is significant arbitrage opportunities for others to make money offsetting that. Prediction markets with decent liquidity should be fine, and in fact the presence of a group with hedging interests presents more opportunities for others to do this arbitrage, helping the market.

People who make money offsetting hedging of bets are called "insurance underwriters". Remember, someone is covering those bets.

You appear to be unclear on the meaning of "arbitrage". Simply taking a position that has positive expected return is not arbitrage; it's just plain investing. Arbitrage has positive (or at least nonnegative) 'guaranteed' return. Arbitrage involves taking both sides of a bet, but with a spread. If a lot of people are "overpaying" for one side, that doesn't create arbitrage unless there's someone else "underpaying". In cases where people are hedging on both sides (for instance, corn growers hedge by selling corn futures, pig farmers hedge by buying corn futures), assuming an efficient market the effects of the two hedgers will cancel each other out and the price will converge on an equilibrium price. You would have arbitrage only if you have some special ability to sell to one and buy from the other that market participants in general do not have.

You appear to be unclear on the meaning of "arbitrage". Simply taking a position that has positive expected return is not arbitrage; it's just plain investing. Arbitrage has positive (or at least nonnegative) 'guaranteed' return.

Casino owners are often said to be practicing "statistical arbitrage". What would you call it?

Is there a fundamental difference between 1) a casino's "really high" probability of earning a profit (on bets before expenses), 2) real-world true arbitrage, and 3) positive expected return in the large?

It seems related to the P=BPP problem, in which you can have confidence in a probabilistic solution that's higher than your confidence that your computer works, but which some people deem inferior to a deterministic solution coming from the same hardware.

Is there a fundamental difference between 1) a casino's "really high" probability of earning a profit (on bets before expenses), 2) real-world true arbitrage, and 3) positive expected return in the large?

Arbitrage is a radial category.

This is a very good point.

On a related note: I once landed a job considerably better than I thought I would, and was afraid the company might go bankrupt. I was considering buying some puts on it to hedge my exposure, but realised this was probably a bad idea; I would have to disclose my holdings as part of the job, and they would be unlikely to take kindly to my having a massive short position on them. Is there a better way I could have done this?

Well, first, I think that there are ethical issues in trying to hedge your risk from employment. Your risk exposure is beneficial to the company, and the employment is made with an expectation of it. If I hired a lawyer on contingency, and found out that they managed to hedge out all of the risk of losing the case, I would find this behavior quite unethical, to say the least. An employee should not be indifferent to the bankruptcy of their employer.

The being said, there are informal ways of hedging this risk. The biggest is having a social network of people who support each other through times of unemployment. While families are often in the same line of work, from a risk management point of view it's best to diversify. Besides the other issues, having a spouse that works at the same company as you is quite dangerous if the company runs into financial difficulties. (However, I don't expect to see many personal ads along the lines of "SWM working in bio engineering field seeks SWF in anti-correlated field".) And obviously, buying stock in the company increases your risk and should only been done if your company compensates you for doing so (such as offering free/discounted stock options). If you are offered stock option, the rational, although perhaps not most loyal, course of action is to sell them as soon as you can.

Also most companies have explicit policies against it.

Would you have had to disclose a put option position, or a credit default swap?

I never actually read the details of the disclosure requirements, but it would be strange to demand disclosures of stock but not of options, especially as the later would be more useful to someone seeking to do intersider trading (hence why spreads are, ceteris paribus, wider in options markets), while stocks are more conducive to a long term buy-and-hold strategy.

They vary a lot, so I've never bothered looking into the specific rules around it. I suspect you're right, of course(though CDS bets may be a viable loophole), but I figured it was a question worth asking.

Buy shares in competing companies, maybe?

This is unlikely to be a good strategy, because competitive stocks are usually correlated, and market participants see the bankruptcy of one company as possibly foretelling a weak market for the competitors' products also. Unless it's a very specific and unusual situation.

In fact, some think it is best practice for people whose future earnings are highly correlated with a particular market sector to reduce any stock ownership they have in that sector to reduce their risk. E.g. software developers should have portfolios that underweight software or technology. It has theoretical support, but hardly anyone in the real world does this because of the added complexity as compared with buying index funds and because of outdated thinking around retirement planning.

It's even harder to do when you're young and your portfolio is 100% cash (and human capital).

Is there a reason a company doesn't offer S&P- products - S&P minus a specific industry. If the bank diversified their customer they could just buy straight index funds and then distribute the returns differentially.

Sector ETFs are already pretty inexpensive on an expense ratio basis. Vanguard's sector ETFs for example have expense ratios of 0.14%, which compares with an expense ratio of 0.05% for the cheapest S&P500 ETF. A bank wouldn't be able to do it any cheaper, realistically. Someone could offer ETFs that exclude particular sectors, but it just hasn't been done, and I still don't think it would be cheaper because of economies of scale for the funds that currently have the most capital.

You do have to have a certain amount of capital to successfully diversify using ETFs, obviously, but the bank doesn't really care about you either if you aren't investing at least a few thousand.

A bet reveals that the bettor believes that the bet increases their utility. So it reveals the beliefs of the bettor about the bettor's utility. The relationship between the utility of a bet and the outcome probabilities is more complicated, though.

There seems to be positive correlation between financial investment product purchases and future purchases. Low volume entities fluctuate at a higher rate with less correlation due to a larger percentage of the product being subjected to "insider" or "arranged" trading. Nothing illegal suggested here of course, just day to day trading in the real world. High volume trading instruments, however, can clearly exhibit trending and the trend "lives" are long enough and obvious enough to ride and take profit from indicating that sometimes a bet may reveal intentions.