Bryan Caplan  

Bets, Portfolios, and Belief Revelation

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Adam Ozimek just reminded me that I still need to refute the Tyler Cowen/Noah Smith view that "portfolios reveal beliefs, bets reveal personality traits and public posturing."  Smith's version:
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.
I've attacked this idea before, but here's a better version.  Let's start with two observations.

1.  If portfolios really "reveal beliefs," Tyler and Noah should be able to look at a random person's portfolio and tell us everything he believes.  Yet neither Tyler, Noah, nor anyone else can do this.  They can't even deduce someone's financial beliefs from his portfolio, much less his beliefs about economic policy or the Fermi paradox.  Portfolios say something about beliefs, but every portfolio is consistent with a very wide range of views.

2. Most people's portfolios exhibit extreme inertia.  Even prominent Nobel prize-winning economists admit they follow simple rules of thumb when they invest.  So unless people's beliefs are carved in stone, how could portfolios possibly reveal much about their beliefs?  Tyler is a case in point: He changes his mind a hundred times a day, but he follows a simple financial strategy that hasn't varied in years.

What's going on?  Normal human beings compartmentalize.  When they pick a portfolio, they may take their beliefs about inflation into account to some degree.  When they explicitly bet on inflation, however, they almost certainly take their beliefs about inflation into account to a massive degree. 

How is this possible?  The hyper-rational agent model that Tyler and Noah appeal to is deeply wrong.  Noah gets close to this truth when he writes:
[I]f you take modern portfolio theory seriously - if you don't believe in any sort of mental accounting at all - then you'd have to look at my entire financial portfolio in order to determine what I really believe about inflation.
Given the facts, Noah should have reversed his reasoning: "Since mental accounting is plainly a huge deal, portfolios don't reveal much about beliefs."  If he resists this reversal, I have to ask him, "If even you took months to grasp basic portfolio theory, why on earth do you think that normal human beings conform to it?"

Mental accounting doesn't just mean that portfolios reveal little about beliefs.  Mental accounting also means that bets reveal a lot about beliefs.  Since people compartmentalize, the best way to figure out what someone believes about Question A is to focus on Question A.  And since people are cagey, the best way to focus on Question A is to press them to bet on A.  This isn't rocket science, just common sense.

Tyler and Noah aren't totally wrong.  Orthodox portfolio theory probably works tolerably well for sophisticated investors, clever arbitragers, and Mr. Spock.  As a rule, though, the betting norm is the gold standard of belief revelation.  When a normal person refuses to put his money where his mouth is, he's not being clever as a fox.  He's being shifty as a weasel.

COMMENTS (7 to date)
John Thacker writes:

Loss aversion and other things affect portfolio investing. I think I agree with you that bets are more illuminating.

John Hall writes:

Are you familiar with the technique in portfolio management called reverse optimization? It is the first part of the Black-Litterman process. Basically, the portfolio manager begins with some arbitrary portfolio (the market portfolio in the original approach) and obtains the expected covariance matrix (and a risk aversion coefficient that scales everything). Solving mean-variance backwards (often ignoring constraints) allows the manager to back out the implied expected returns that would be necessary to produce the arbitrary portfolio, given the covariance matrix. If you included some economic variables that are correlated with the financial variables, then the reverse optimization could be used to back out the expected return of the economic variables. What quickly becomes obvious when you take this approach for equities is that the mean is small relative to the standard deviation. One way to interpret that is that there are many beliefs/scenarios that are consistent with your portfolio. However, it is all one distribution.

Kevin Dick writes:

Thank you for this post Bryan. When I read Noah's post, I mentally rolled my eyes at his obvious failure to even acknowledge this possibility... in favor of a conclusion that my priors say would reinforce his ideology. But I just didn't have the energy to engage with him. I appreciate your doing the work.

RPLong writes:

Claim #1 seems far too strong. I am not sure where I stand on this issue, but certainly just because someone makes the claim that portfolios reveal beliefs doesn't mean that person is making the claim that portfolios reveal ALL beliefs.

Dan Carroll writes:

My take on the portfolio vs single bet is what I call the Romney theorem. A $100 bet to Mitt Romney doesn't reveal his beliefs, because he has many other sources of income. A $100 bet to a starving PhD student is a bit more meaningful.

Henry writes:
My take on the portfolio vs single bet is what I call the Romney theorem. A $100 bet to Mitt Romney doesn't reveal his beliefs, because he has many other sources of income. A $100 bet to a starving PhD student is a bit more meaningful.

This reminds me that Romney is to my knowledge the only Presidential candidate who has ever offered a bet (his "ten thousand bucks" to Rick Perry, who decline).

Philo writes:

The portfolio-theory objection to Bryan’s “Put your money where your mouth is” challenge seems sound, in principle. Someone who offers the estimate that the CPI will rise 10% over the next two years may properly refuse to bet on it *if he has already bet so heavily on that outcome that a further bet would unbalance his overall portfolio*. Even if he is pretty confident of high inflation, he will want to do some hedging against the possibility that he is wrong, and a further bet may reduce his hedging below the optimal level. On the other hand, willingness to make a bet on p with a particular person does not prove sincerity, since he may simultaneously be making a similar-sized bet on not-p with someone else.

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