On The Ubiquitous Missing Information in Markets: What Neuroeconomics Has to Say

‘Ambiguity’ is the Hallmark of Trading and Investing

The situation of taking a position when the odds are uncertain because of missing information is referred to by economists as “ambiguous”. F Knight in his book Risk, Uncertainty, and Profit was the first to emphasize ambiguity in 1921. Ambiguity (otherwise known as knightian uncertainty) is the hallmark of finance and should be acknowledged as such. To quote Nassim Taleb, the “rules of the game” are unknown in the financial arena.

What does this actually mean? Just that in many if not most trading and investment situations, the odds are not objectively known, and players may have little information and hence also little confidence regarding the true odds.

Offhand, such lack of confidence might seem counter intuitive: after all, observing relative frequencies should allow one to infer the underlying probabilities, don’t you think? Indeed, take a particular asset as being an urn from which you can draw a red or black ball where the red pays more but it isn’t known what the proportion of red to black is. After sampling the urn several times, one feels much more confident about its odds.

This is all nice in principle, but real world finance is far trickier and there are several reasons for our inability to confidently judge the probabilities in practice. True, we can observe the performance of a particular stock every period (be the relevant horizon one hour, one day, one month), and infer something about the stock’s odds.

But, these odds themselves change. Recent leading-edge econometrics literature has revealed unexpected jumps to affect stocks and bonds at an extremely high frequency.

In addition, a certain kind of probability is inherently subjective and cannot be inferred from observing relative frequencies: what about the chance of a landslide for Barack Obama on November 4th? Here the lack of information is irreducible and has to do with conflicting evidence.

Further, behavioral studies have shown that people feel they are missing information when betting against another person who is better informed. And even when there is no better informed opponent, people act as if there is.

To What Extent Does This Matter?

For all these reasons, taking a position is not a decision about known odds but a decision with ambiguous information.

Why does this matter? Because choice depends on how much relevant information is missing or how ignorant people feel compared to others, as Chip Heath and Amos Tversky first pointed to in a beautiful paper (1991).

Mr. Spock Does Not Care about Ambiguity…

At first glance we may assume the reverse, that is that traders and investors won’t act differently in the face of risk and ambiguity. Indeed, standard economics invites us to do so, because expected utility theory totally ignores the importance of confidence in judged probabilities. Its bosom stance is that the probabilities of outcomes should influence choice, whereas confidence about the probabilities is irrelevant. The proof is very clean and ushers in a misleading view of decision-making under uncertainty.

Here is the logic of expected utility theory. (Readers who don’t like Mr. Spock can skip this bit without any damage — homo economicus being characterized by Mr. Spock is due to Richard Thaler.)

Suppose two assets, a risky one, which will deliver 100 dollars or 0 with equal probability, and an ambiguous one, which will deliver 100 dollars if Mr. Obama wins the election, and 0 otherwise.

Do you prefer to invest in the risky asset or the ambiguous one? Now consider a symmetric ambiguous asset which will deliver 100 dollars if Mr. Obama loses and 0 otherwise. Again, ask yourself whether you prefer to invest in the risky asset or this ambiguous one.

Choice consistency leads to choose the ambiguous asset in the second case if you have preferred the risky asset in the first case. Why? Because for expected utility theory, choosing the risky asset in the first instance reveals your probability that Mr. Obama will win the election to be smaller than 1/2. Therefore, you should prefer the ambiguous asset in the second case, since for you the probability that Mr. Obama will lose is higher than 1/2.

… But Human Beings Do

By ignoring the influence of confidence in choice, expected utility theory is missing a key point. Most of us will invest in the risky asset in both instances. This is Ellsberg paradox, first revealed by Ellsberg in his paper “Risk, Ambiguity, and the Savage Axioms” (the “Quarterly Journal of Economics”, 1961).

Actually, the premise that confidence about the probabilities is irrelevant is wrong on both the behavioral and the neural level. Under ambiguity, the brain is alerted to the fact that critical information is missing and that the ensuing uninformed choice therefore is more potentially dangerous.

A milestone study by Ming Hsu and colleagues, published in “Science” in 2005, has revealed the level of ambiguity (when choosing between a risky bet and an ambiguous one) to be positively correlated with activation in the brain areas known as the amygdala and the orbitofrontal cortex, and to be negatively correlated with activation in the caudate nucleus within the striatum, well known to be implicated in reward prediction.

An Evaluation System in the Brain that is Sensitive to the Levels of Uncertainty

Further, in their study, activity in the caudate built more slowly than activity in the amygdala and the orbitofrontal cortex. This is strong evidence for the existence of two connected systems. Upstream, a vigilance system sensitive to the level of uncertainty in the context (the OFC / amygdala complex), signals uncertainty to the anticipatory reward system downstream (the striatum). In other terms, the OFC and the amygdala evaluate uncertainty and modulate the expected reward signal in the striatum. Interestingly, in the same study, the authors further demonstrated that OFC-damaged subjects do not distinguish between the risky bet and the ambiguous bet, thereby acting in a way that is consistent with expected utility!

Inhibition of Impulsiveness when Facing Ambiguity

Further study by Scott Huettel and colleagues at Duke University, has confirmed that specialized neural mechanisms are involved under ambiguity and that they are well dissociated from those implicated in risky situations. Interestingly, this study — published in “Neuron” in 2006 — links the inferior frontal sulcus, within the lateral prefrontal cortex, to decision-making under ambiguity. This is interesting to more than one extent. First, this region — and others around — has been shown by Etienne Koechlin and colleagues, in a study published in “Science” in 2003, to be crucial for contextual control, when one needs to resolve the multiplicity of possible scenarios to set one’s own rule for behavior.

Remember Taleb: in finance the rules of the game are typically unknown, so we have to construct them…

Further, in the same study, Huettel and colleagues have found that the ambiguity effect in the inferior frontal sulcus is less pronounced in those subjects with a higher degree of cognitive impulsiveness — as measured by the BIS impulsivity scale. Although this is purely correlational, it is tempting to conjecture that the inferior frontal sulcus plays a role in inhibiting impulsiveness here, presumably by sending an alerting signal — pointing to a lack of confidence — to the striatum downstream.

So What?

Acknowledging the prevalence of ambiguity aversion in finance has already had far-reaching implications. For instance, ambiguity aversion might explain the well-known home-bias in investing, as well as the equity premium puzzle – this route to explain the equity premium puzzle has been explored by Larry Epstein.

We would argue that outside academia as well, traders and investors should pay special attention to the underpinnings of their behavior when deciding under knightian uncertainty.

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