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Thursday 15 October 2009

Ambiguity Aversion: Investing Under Conditions of Uncertainty

Uncertainty Is Not Risk

A huge amount of effort in financial circles is spent trying to measure and manage risk. Basically risk that can’t be quantified isn’t really risk, because unless you can put a number on it, it doesn’t really exist. Perhaps we should apply the same idea to budget deficits.

Way back in 1921 the economist Frank Knight dismissed such ideas as deluded. As far as he was concerned any system involving humans was far too unpredictable to be hedged and hemmed by numbers. What Knight identified was the difference between measurable risk and unmeasurable uncertainty. However it took a man with a bunch of balls and couple of jars to shown exactly how deeply ingrained into the human psyche the fundamental nature of uncertainty is.

Extrapolate If You Dare

By all accounts Knight was deeply cynical about human nature, to the point where he dismissed the attempts of most economists to develop forecasting techniques on the basis of historic data as futile. Extrapolating from the past to the future was always bound to end in failure, he believed, because some things – especially those involving people – are inherently unpredictable. Specifically Knight distinguished between risk – which you can measure – and uncertainty – which you can’t.

For the most part investors ignore uncertainty. Which isn’t surprising, because so does most of the investment industry. Generally people operate on the basis that there’s a measurable risk in investment but that if you’re reasonably careful in how you invest you can mitigate against this. Tomorrow’s conditions will be the same as yesterday’s so we can operate on the basis that what worked yesterday will also work tomorrow.

When this all changes, however, and uncertainty rears its wild head we find ourselves lost. The historical signposts are suddenly spirited away in the middle of night and we, in the jargon, find ourselves investing under conditions of uncertainty. Our reaction to this is rather interesting and goes a long way towards explaining stockmarket plunges. It turns out that most of us are hugely adverse to the ambiguity such situations throw up and our preferred option is to run away as quickly as possible.

Urns ‘R Us

The classic experiment demonstrating this was reported by Daniel Ellsberg in 1961. The experiment is simple but the explanation is convoluted. So bear with this.

Ellsberg offered his participants a choice of two urns each of which contained 100 balls. Urn A contained 50 red and 50 black balls. Urn B contained an unknown mixture of red and black balls. Each person was asked to make two decisions – firstly to choose which colour ball they wanted to pick and secondly to choose which urn they wanted to pick it from. Be clear: both decisions were under the control of the subjects.

A significant majority of the participants chose Urn A, the one with an equal number of red and black balls. Yet this creates a paradox, which is the sort of thing that gets psychologists very excited and requires the tranquillisers to be administered by the men in white coats – to the men in white coats.

Ellsberg’s Ambiguity Paradox

Let’s say you chose red and then chose Urn A. You know that you have a 50% chance of getting a red ball. Logically this means you think that if you chose Urn B then you would have less than a 50% chance of getting a red ball. However, this means that if you chose Urn B you think you would have a greater than 50% chance of getting a black ball. Which means that you should have chosen black and Urn B, not red and Urn A. At which point the paradox asserts itself.

Our brains strain against seeing this as a paradox – the majority of people will choose Urn A and insist that it’s less risky to do so. But it isn’t: the probability of selecting a red ball from Urn B is exactly the same as the probability of selecting a red ball from Urn A. The risk is the same, what’s different is the uncertainty.

It turns out that humans are extremely disinclined to operate in conditions of uncertainty unless absolutely necessary. We much prefer a defined risk to an undefined one. Generally this is referred to as ambiguity aversion.

Less Uncertainty, Same Result

Rather than simply accept the findings and throw away their nice models economists have proposed a number of hypotheses to rescue the classical approaches to risk. One is that people naturally expect deceit on the part of the experimenters, so they assume that Urn B is rigged against them. Another is that people simply can’t work out the probabilities of Urn B because there’s too much data and opt for the ‘safe’ choice.

In Size Doesn’t Really Matter Pulford and Coleman set out to investigate these ideas. Remarkably their experiment shows that ambiguity aversion applies even when each urn contains only two balls. This suggests quite strongly that the only factor involved in this is human hatred of the uncertainty involved in the choice.

Dynamic Urns, Dread Markets

Nice and theoretical though this is one might reasonably wonder what it has to do with the real world business of investing or, indeed, life. The answer is, roughly speaking, everything. Our hatred of uncertainty can drive us into all sorts of outwardly irrational behaviour when the hidden ambiguity inherent in many decision making processes is suddenly made clear.

Unlike Ellsberg’s urns the real world of stock investment is a dynamic process in which the balls we draw from the jars are constantly replaced. In normal conditions if we withdraw a red ball a new red ball replaces it. In time we come to expect a certain proportion of red and black balls – winners and losers. We’re instinctively modelling risk but we’re doing so under assumed conditions of certainty. Red ball out, red ball in. We sample the past and forecast the future.

When the randomness that is uncertainty strikes our instincts serve us badly. Suddenly our red ball is replaced randomly by something else. Our initial reaction to this is to assume that it’s a mistake and to continue to operate as though our internal models are still working. However, as it becomes clear that our assumptions of certainty have broken down then ambiguity aversion kicks in: we hate uncertainty and we run from it. Cue stockmarket wobble and then collapse.

Ambiguity and Overconfidence

Even experienced investors may fail to recognise the onset of uncertainty. The stockmarket collapses of the 1970’s as the world reeled under multiple crises certainly seem to have been such a situation. The sudden recognition of problems that had previously not been evident – oil supply worries, corrupt world leaders, flared trousers and glam rock – led to a whole host of reactions including, ironically enough, the first attempts to build risk management models to protect against such future events. The irony, of course, is that these models have themselves ended up contributing to the problems because they don’t – because they can’t – capture the nature of uncertainty.

Interestingly the studies of ambiguity aversion show a clear and consistent balance between those who choose the certain urn A and the uncertain urn B. Roughly 20% to 30% of people embrace the uncertain option: there are people who instinctively see opportunity in uncertainty and rush to take advantage of it. Studies of entrepreneurs, for instance, show that they tend to be much less worried about operating in conditions of uncertainty than the rest of us. Of course, it may be that they’re just significantly more over-confident and deluded than everyone else, but the research is silent on this.

Certainty Is An Illusion

The idea that the future is unknowable goes against the last four hundred years of human progress, much of it built on the idea that we can predict and therefore control what is yet to happen. Nonetheless if it were otherwise our lives would be much less rich in terms of experience. Knowing with certainty what tomorrow will bring would be rather dull, don’t you think?

As for investors, well, we need to learn that uncertainty and ambiguity dog our every step. For it is when we are at our most certain that we are at most risk. Find that in a risk management model.

Related Articles: Alpha and Beta - Beware Gift Bearing Greeks, Correlation is not Causality (and is often Spurious), Risky Bankers Need Swiss Cheese Not VaR


  1. as it becomes clear that our assumptions of certainty have broken down then ambiguity aversion kicks in: we hate uncertainty and we run from it. Cue stockmarket wobble and then collapse.

    Another fine exploration of another important topic.

    I view the words above as a good description of the cause of stock crashes. But my take is that the problem is not that some things cannot be known. The problem is that there are some things we prefer not to know.The certainties that we enjoy during insane bull markets are false certainties. For example, the idea that there is some mystical world somewhere where stocks offer a strong long-term value proposition regardless of price is a fairy tale. Millions today are certain this is so. That doesn't make it so.

    If investor behavior really could not be quantified, there would not have been so many people who saw the crash coming and said so publicly in very clear terms. Robert Shiller knew. Cliff Asness knew. Andrew Smithers knew. Rob Arnott knew. John Walter Russell knew. Jeremy Grantham knew. Rob Bennett knew. It's only those who believed in Passive Investing who were surprised.

    The problem, of course, is that most of us came to believe in Passive Investing during the time when prices were insane. What people miss is that that is so by definition. We cannot get to the sorts of prices that applied from 1996 through 2008 unless the vast majority of investors come to believe things about investing that are patently absurd. We wouldn't agree to pay irrational prices for stocks unless we were working from a model that was rooted in irrationality (the idea that the price you pay for something doesn't matter is in a fundamental sense irrational).

    You can tell when investor emotion is out of control. You cannot tell by asking the investors involved, however, or by consulting the investing model that became popular during the time when prices went out of control. You need an objective standard, something that is not affected by the prevailing emotions of the day.

    I believe that the objective something that tells the tale is P/E10. P/E10 doesn't tell us what stocks are selling for at a given time (that number is influenced by the emotions of the time). P/E10 tells us what stocks should be selling for, given the earnings that are being generated by the underlying companies. That number is not affected by emotion. Thus, that number reveals the amount of emotional content present in the price at which stocks are selling. That's what you need to know to know how risky stocks are at any given time.


  2. Choosing the 50-50 urn is no more, or less, rational than choosing the other one.

  3. P/E10 as the basis for prediction of financial entity performance has been convincingly refuted here:
    by showing that any arbitrary time period data series (e.g. recent 10 years) is subject to coincidental fit to any given theory.