June 14 (Bloomberg) -- Market observers often divide investors into “smart money” and “dumb money.” Our research shows there may be a way to figure out which group you are in.

The first place to look is prices, which reflect the interaction of smart money and dumb money and may contain valuable information about the proportion of either in the market. In other words, the price knows which category we belong to. The trick is to extract that information.

Consider a simple example of a simple market: betting on a horse race. Say there are two horses, A and B. And there are two types of bettors, smart money and dumb money. We place our bet on horse A because we think it is more likely to win. It turns out that 75 percent of the money is on horse B, and 25 percent is on A. These “prices” can help us learn whether we are more likely to be the dumb money or the smart money.

We want to compare the probability that we are the dumb money given the market price to the probability that we are the smart money given the market price. We can write this as P(dumb|market)/P(smart|market). If this ratio is greater than one, then it is more likely that we are the dumb money. Less than one, we are more likely to be the smart money.

Horse Race

Bayes’ Rule tells us how to figure this out. P(dumb|market)/P(smart|market) = [P(market|dumb)/P(market|smart)] x [P(dumb)/P(smart)]. In words, the odds in favor of us being the dumb money given the market price is the relative likelihood of the market price if we are the dumb money multiplied by the prior odds that we are the dumb money. Notice how we are using the market price -- in this case, the amount bet on each horse -- to help us figure out where we belong. We do this by asking if these prices are more likely to occur if we are dumb or if we are smart.

Suppose we believe that there is much more dumb money than smart money at the track today. If we are dumb money, we’d expect to be betting in the direction of the relatively larger group. Yet we’re in the minority. That’s pretty unlikely to be the case if we’re the dumb money, given our beliefs about the proportion of each type of bettor at the track.

By contrast, if we are smart money, we’d expect to be betting with the minority. And that’s exactly what we see. So [P(market|dumb)/P(market|smart)] <1, which pushes us in the direction of thinking we are the smart money.

Now, turn to the prior odds. Let’s say we are pretty confident that we are smart money. That means [P(dumb)/P(smart)] <1. Overall, combining the two, we think it is more likely that we are the smart money than the dumb money. The market prices helped us figure it out.

We wish we could say that it is this easy to determine in circumstances other than this hypothetical race between two horses. It isn’t.

We need to have pretty accurate beliefs about how much dumb money is in the market. If there is actually much more smart money at the track than dumb money, then these prices are much more likely if we are the dumb money.

Also, it may be hard for us to even consider the possibility that we are the dumb money. Often, the identifying characteristic of members of the dumb group is thinking too strongly that they are the smart money. Are we making that mistake here? If so, it may prevent us from learning that we are the dumb money.

Costanza Rule

There is an episode of the television comedy “Seinfeld” in which George Costanza complains: “My life is the opposite of everything I want it to be. Every instinct I have, in every aspect of life, be it something to wear, something to eat ... It’s all been wrong.” Jerry Seinfeld persuades George that the answer to his predicament is to do the opposite of everything he’d normally do. By doing so, George enjoys great success.

Can dumb money also learn that it is dumb and by doing the opposite enjoy the benefits of being smart? The awareness that we are part of the dumb money can lead us to change the direction of our bets: We might go long instead of going short, bet on no default instead of a default, sell Facebook Inc.’s shares instead of buying them.

Unfortunately, deciding to do the opposite of what one normally does is difficult. After all, George only pulled it off for a single episode.

(James B. Heaton is a partner at the law firm Bartlit Beck Herman Palenchar and Scott LLP in Chicago. Nicholas G. Polson is professor of econometrics and statistics at the University of Chicago Booth School of Business and a contributor to Business Class. The opinions expressed are their own.)

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To contact the writers of this article: James Heaton at jbheaton3@gmail.com; Nicholas Polson at ngp@chicagobooth.edu

To contact the editor responsible for this article: Max Berley at mberley@bloomberg.net