JUST before the hovering finger clicks the mouse to trade, there is one thing that online investors of the future might want to check: their “Rationalizer”. The device, a prototype of which was unveiled this week, is an emotion-sensing system designed to help investors keep a cool head when buying and selling. [...]

The Rationalizer, which is still under development, consists of a bracelet that measures something called a galvanic skin response. This is a change in the electrical resistance of the skin which can be caused by various stimuli, like anger or elation. It cannot determine if the emotional arousal is negative or positive, only that it is happening.

ABN’s interest reportedly stemmed from a study by Andrew Lo and Dimitri Repin, “Psychophysiology of real-Time Financial Risk Processing” (Journal of Cognitive Neuroscience, 14(3), pp, 323 – 339,  2002), showing that day-traders who exhibit more intense emotional reactions also have significantly worse trading results.

One may question the efficiency of using this new device, trading performance wise. My guess is that this kind of practice is based on a somewhat misguided view on emotions. This view emphasizes the negative effect of emotions on behavior, the idea being that emotions vitiate rational decision-making. Here “emotions” stands for “passions.” Automatic emotional responses mediated by structures such as the anterior insula or the amygdala – see Joseph LeDoux’s beautiful book “Emotion, Memory, and the Brain” (1994) for the functions of the amygdala in fear conditioning – would trump higher-level responses mediated by the prefrontal cortex. Very Platonic stance, sometimes referred to as “dual process theory.”

This is not to say that emotions never prompt us into the wrong direction, they surely do, often “short-circuiting” logical reasoning and long term planning that are essential to efficient trading (Cf Andrew Lo and collaagues, “Fear and greed in financial markets : A clinical study of day-traders” American Economic Review, 95(2), pp. 352-359, 2005). The dual process theory is thus heuristic in that it highlights such phenomenon. However, it may lead to a hyperemphasis on emotions as sources of mistakes. Such hyperemphasis is wrong-headed. Because in many domains, nonconscious emotional biases drive behavior before conscious knowledge does; without such emotional inputs, overt knowledge is in effect insufficient to ensure rational behavior.

Antoine Bechara, Antonio Damasio and colleagues highlighted this role of emotions in implementing rational decisions (“Deciding advantageously before knowing the advantageous strategy“, Science, 275, pp.293 – 1295, 1997). Further, John Allman, an eminent neurobiologist from Caltech, has been pinning down the role of the Von Economo Neurons (VENs) of the anterior cingulate cortex in providing humans with a system for quick and intuitive behavior in the face of uncertain ever-changing conditions. This work stresses that in complex situations involving fast intuitive assessments, such as day-trading, fast intuitions are melded with slower, deliberative judgments (e.g. “Intuition and autism: a possible role for Von Economo neurons“, Trends in Cognitive Sciences, Volume 9, Issue 8, pp. 367-373, 2005), whereby emotions are best viewed as informational inputs serving deliberative processes. Consistent with this view, recent studies on decision making under uncertainty has revealed the amygdala and the anterior insula to provide uncertainty signals. See, e.g., the paper by Wofram Schultz and colleagues “Explicit neural signals reflecting reward uncertainty” in Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 363(1511), pp. 3801-11 (2008); or the one by Tania Singer and colleagues “A common role of insula in feelings, empathy and uncertainty” in Trends in Cognitive Neurosocience, 13: pp. 334-340 (2009). A famous paper by J Coates and J Herbert, “Endogenous steroids and financial risk taking on a London trading floor” (PNAS, 105(16) pp. 6167–6172, 2008), helps pinning down the nature of these uncertainty signals: these may be relayed to the neural structures involved in decision making through neuropharmacological signals. For instance cortisol, which has receptors in the insula and the amygdala, would signal market risk in the brain.

All this suggests that emotions are key information providers when deciding under uncertainty. They make us tuned to our environment. Actually, in some contexts of fast and intuitive decision-making in the face of unstable (high vol) conditions, one expects that the stronger the emotional uncertainty signals of the day-trader, the higher the performance. To be more specific, I would not be surprised that for a trader “in the zone” at a particular point in time, the light pattern of  “EmoBow” (the object displaying a moving light pattern to illustrate the user’s mood) reach a deep red. Shall one conclude that the trader is too aroused emotionally at that moment, and hence should take a deep breath? Or merely that he has achieved a state of focus that intense, that all the relevant stimuli in his environment are integrated as emotional inputs? In the second scenario, stopping the decision process is like stopping a high-speed driver in the middle of the race.

The annual Society for Neuroeconomics meeting, held in Evanston this year, reviews a cornucopia of pre-publication research papers centered on the topic of decision making under risk and ambiguity. With everything from electrodes being implanted into patients who were having brain surgery for intractable epilepsy to the actual formulas of computational neuroscience (which a hedge fund or two lists as their primary strategy) to the one-trial learning of a Monterrey Bay slug, there is an almost incomprehensible amount of information presented over the course of three days.

A couple of extrapolated highlights especially for speculators though -

#1) Inter-temporal discounting refers generally to the phenomenon of taking the money and running – i.e. “why can’t I just wait until my target“? There were numerous studies presented both in session and on poster boards… too many for this short de-brief. Stay tuned -

2) Too many choices reduces the likelihood of a choice at all.  Colin Camerer (pronounced cam-er-er) presented this last and given his stature as a game theorist and neuroeconomist… it was worth the change flight fee!  Too many things on your charts anyone?

3) Courtesy of Nichole Lighthall of USC – under stress, men will react by “more trials” (i.e. over-trading?) whereas women will react by being more careful. Sound familiar?

4) Cal-tech is again coming to aid of the Theory of Mind idea in perceiving and executing in complex games. (In other words, the Social Markets Hypothesis). This IS going to be big – and the original paper does appear on its way belated way to The Journal of Finance per Dr. Peter Bossaerts.

5) And just to make your day – The University of Iowa discussed in some detail why if you engage in “self-control” (i.e. sticking to a trading plan), it is experimentally proven that you will subsequently have less ability to engage in “self-control”. … This could be a disheartening fact for many short term discretionary or even model based traders… but look at it this way, at least it isn’t just you!

So… just a few highlights… and points to look forward to as Trader Psyches and our new parent The Re-Think Group discusses The Psychology of Risk over the next few months!

Oops – one more – our “French PhD Chick” Elise is defending her dissertation on October 9th in Switzerland. Wish her luck and we (sort of) look forward to changing her name to Dr. Payzan Le Nestour. We also hope to bring her to the US as an advisory researcher!

In his milestone paper “Portfolio Selection” published in the Journal of Finance in 1952, Harry Markowitz, the pioneer of “modern finance,” recommends to use the Expected return-Variance (E-V) rule, both as a working hypothesis to explain investment behavior and as a guide to “investment” – as distinguished from speculative behavior. This rule implies that an actor who considers yield to be good, risk to be bad, and speculation to be banned, should diversify in such a way that his portfolio lies in the “efficient frontier.” The idea is very simple. When building your portfolio, combine the securities in such a way that for a given expected return (E) of your portfolio, its variance (V) is minimum. This defines all the efficient combinations (E,V). Then, according to your degree of risk aversion, pick one such combination – a risk averse person will prefer a low E – low V portfolio, whereas a risk lover will choose a high E-high V combination. The beauty of this rule lies in its apparent readiness. Given a probability distribution of yields of the various securities, computing the set of efficient (E,V) combinations is straightforward. But this is misleading, because it dodges the main issue: Where do the expected returns and variances estimates come from? In other terms, how do we set our probability beliefs?

At the end of the paper, Markowitz himself recognizes that he has been silent about the origin of these beliefs throughout:

“To use the E-V rule in the selection of securities, we must have procedures for finding reasonable expected returns and variances [...] I will not pursue the subject here, for this is “another story.” It is a story of which I have read only the first page of the first chapter. In this paper we have considered the second stage in the process of selecting a portfolio. This stage starts with the relevant beliefs about the securities involved. We have not considered the first stage: the formation of the relevant beliefs on the basis of information.”

Dodging the question of belief formation is murderous

It seems that fifty years from this paper, we are still stuck in “the first page of the first chapter.” Quite ironically, after Markowitz’s paper, such E-V rule has become ubiquitous in real-world finance, despite this inherent indeterminacy. Why does such belief indeterminacy matter? After all, is it so complicated to use a mix of statistical analysis and practical judgment, so that we derive sensible probability beliefs? In the first instance, one can use observed yields and volatilities from the past, to get statistical estimates of the true yields and variances. The problem is elsewhere. By emphasizing belief formation related to the expected returns and variances, we are missing the key point. Belief formation about world uncertainty is the issue, which is totally buried by Markowitz here. Markowitz implicitly assumes we live in a Gaussian world of “mild uncertainty,” where price changes are characterized by stability around the average. In such a world, Markowitz’s “E” and “V” are relevant objects. But what if randomness is not mild at all in our world? What if there is not such a thing as “value,” and returns have infinite variance? In such a world, sensible people do not average but rather arbitrage between times and places. If so, by putting forward “E” and “V,” maybe Markowitz leads us to wrongly interpret the world we live in.

Returns uncertainty, viewed from the empirical side

And there is good evidence that it is the case. If returns were Gaussian, we would have 68% of small price changes within one standard deviation of the mean, 95% within two standard deviations of the mean; and outliers (large changes) would be extremely rare: according to the Gaussian model, index swings of more than 7% should come once every 300,000 years… Rather, empirically, we observe too many large and too many small changes in the prices (this is what we call “fat tails”). Moreover, we observe irregular trends of large changes followed by clusters of small changes. That is, trouble runs in streaks (a wild day might be followed by a wilder day). This means that “persistence” is far larger than expected, would the world be Gaussian. As such – at least for investing horizons from two hours to six months, the Gaussian hypothesis is the wrong interpretation.

Uncertainty in the finance world: Where do we stand?

What is the correct model of uncertainty in finance then? There is no definite answer to that paramount question. Actually, two distinct routes are possible.

Nonstationarity

The first one assumes nonstationarity. For instance, the widespread use of GARCH models is to capture the foregoing phenomenon of persistence, while staying within the Gaussian boundaries. The idea is to introduce changes in volatility – that is, instead of considering one single Gaussian distribution for the returns, consider multiple ones, each characterized by its own level of volatility. When real world volatility soars (resp settles), make the Gaussian curve grow (resp shrink). This indeed enables to fit the data. Poissonian uncertainty has also been suggested as a model to replace the Gaussian (Brownian) model. Gaussian risk involves a high probability of a small change, while Poissonian risk involves a small probability of a large change (jump).

The multifractal model

The second route is the one taken by Beno?t Mandelbrot, the father of fractal geometry. It avoids to assume nonstationarity. Rather, he proposes real world randomness to be best described as “slow.” The Gaussian model entails a randomness that is too mild. Conversely, “wild randomness” is characterized by an extreme degree of unpredictability: tails are huge, “everything can happen,” whereby there is no way to forecast the returns (both expectation and variance of price changes are infinite).

Slow randomness is in between: there is no stability around the average, and tails are fatter than in the Gaussian world. Mandelbrot’s model of real world uncertainty is remarkably elegant – and I’m not (only) saying that because Mandelbrot is French. Not only his framework generates the fat tails and persistence phenomena observed in real data, it also suggests using quantitative tools to rigorously measure (1) how fat the tails are, and (2) the degree of persistence in the returns.

Alpha and H

Two parameters summarize these two dimensions, alpha for the size of the returns, and H for their sequences (dependence). The first parameter comes from modeling the tails with a Power Law. For x large (we are at the tails), It sets the ratio of probability of a return larger than n x over the probability of a return larger than x to be n^{-alpha}. Intuitively, the smaller alpha, the fatter the tails (i.e, the larger the instability: the realization of an outlier moves the average).

With a Gaussian distribution, alpha equals 2; under wild randomness, it is 1. Alpha in between points to a world of slow randomness, the one we presumably live in many instances. The second parameter is very intuitive too. It says something about the sequences of the price changes (runs) rather than their size. The question is how much the past shapes. In a Gaussian world, over a given period (say, 10 years), the range between the highest return and the lowest one is sqrt(5) times the empirical standard deviation of the returns from one year to the next. However, when randomness is characterized by persistence, the high-to-low range widens not by a square-root law but as a H power, with H larger than 1/2. This means long term dependence, and captures the fact that turbulence clusters.

Blueprint: Assessing real uncertainty is like constructing “dikes”

No model is universal. Plainly, interpreting properly the nature of the randomness we face in our investment decisions is context-specific. So, how do we choose between the models? We don’t have to be blind about uncertainty. Once we no longer take for granted the Gaussian assumption, all we have to do is appraising properly the world we invest in. That is, we can track — and perhaps forecast – how turbulent the market is becoming, using fractal geometry and the alpha and H measures.

In “The Prince,” N Machiavelli compares “Fortune” to a violent river, and suggests ours constructing dikes to protect ourselves. What does it means for finance to construct such dikes?

Just that we need to assess alpha and H.

And in practice?

If alpha is smaller than 2, then we should definitely think again about the E-V rule. (Same thing if H is different from 1/2.) If so, we should ignore “E” and “V” and merely focus on both alpha and H, with which to evaluate true risk.

Sadly, things are not that simple, because measuring? alpha and H is in practice very difficult.
In 1991 Andrew Lo reported that Mandelbrot’s tests for H can confound long-term memory with the effects of short-term memory. And the measures of H are not robust: there is no consensus as for the S&P 500 index for example: the estimates for H vary from 0.53 to 0.74. Furthermore, the degree of dependence varies a lot from one type of financial asset to another (gold prices, oil markets, foreign exchanges, might have long memory, whereas cotton, British government bonds, do not). So, overall, it is unrealistic to hail alpha and H as new yardsticks for finance.

We’d better acknowledge our ignorance: Doubt is good

To be honest, it is impossible to claim with certainty that one model is the correct one at a specific moment in time. Accounting for model uncertainty is the hallmark of modern econometrics and (truly) modern finance. Is it a retreat into – at least lucid – blindness? I don’t think so.

The only relevant question is referred to by Nassim Taleb as “tinkering:” How to make sound investment choices in a world we don’t understand? Modern finance tackles this problem, by putting forward rules of behavior under “ambiguity.” By “ambiguity,” we academics precisely refer to these situations of missing information about “the rules” of financial investment, the one we model as a big game of betting under unknown odds (more on this here).

F.Nietzsche wrote in his “Ecce Homo:”

“No doubt, certainty is what drives one insane.”

I think “modern finance” drove us insane because it has forgotten to doubt.

‘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.