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Wednesday 24 March 2010

Investor Decisions - Experience is Not Enough

Economic Paradoxes

At the heart of Prospect Theory, the seminal approach behind behavioural finance, lies a puzzling paradox. Although the theory argues that people overweight the chances of unlikely events occurring – so, of instance, we worry much more than we ought to that our children will be kidnapped – the evidence from the field suggests exactly the opposite.

So, it seems we have a dilemma at the centre of the behavioural universe. Either way traditional economics gets it wrong but so, it seems, does the newfangled psychological kind. Given that we start the analysis with only three choices – that people correctly weight rare events, underweight them or overweight them – then it’s a bit disappointing that the two main branches of economics manage to slightly miss the correct answer.

That’s “slightly” in the sense of “completely and utterly”, of course.

Overweighting Rare Events

Prospect Theory is actually not such a radical departure from traditional economics as you’d think from the hype and hyperbole. Under the covers it’s an extension of the Bernoullian multiplication at the heart of expected utility models. The key idea is that each possible outcome of a model is multiplied by a decision weight and many breakdowns in the traditional concept of utility based models have been explained by showing that the results are consistent with people overweighting their expectation of rare events occurring.

Underlying this is a perfectly straightforward commonsense explanation – that the possibility of unlikely but extreme events has a salience that resonates with us. So, the possibility that our children might get stolen leads us into creating a society in which they’re exposed to as little risk as possible; we take out excessive amounts of insurance to cover the miniscule likelihood that our flight may crash and we create huge anti-terrorism bureaucracies to defend ourselves against people whose weapon of choice is a rock.

The Allais Paradox

Of course, commonsense isn’t something that science based researchers put much faith in and the predictions of Prospect Theory have been put to the test many times. The classical paper by Tbersky and Kahneman, Prospect Theory: An Analysis of Decision Under Risk, came up with the following anomaly:
Problem 4. Choose between:
L: 3 with certainty
H: 4 with probability 0.8; 0 otherwise

Problem 5: Choose between:
L: 3 with probability 0.25; 0 otherwise
H: 4 with probability 0.2; 0 otherwise
In essence these are the same question (in fact Problem 5 is just Problem 4 divided by four). However, in the first problem 80% of people preferred L, while in the second just 35% made the same choice: this apparently irrational result is known as the Allais Paradox and can’t be explained by standard expected utility theory.

Prospect Theory, on the other hand, can explain it by arguing that people overweight outcomes with small probabilities and vice versa. However, in the first problem the certainty attached to L causes us to overweight that result instead – as we’ve seen so often the allure of certainty is powerful in situations otherwise replete with ambiguity.

Overestimating the Probability of Underestimating

So, as we can see, people are biased towards overweighting the probability of unlikely events occurring. Only, if we think a bit about this, this itself seems unlikely. After all, one of the recurring themes of psychologically induced investing mistakes is that people consistently underestimate the probability of a market crash occurring, despite the historical evidence that they happen with discouraging frequency. In fact, it would seem more reasonable for people to underestimate the likelihood of rare events yet researchers have carried on for years apparently not finding anything particularly odd in the findings of Prospect Theory.

When we find this kind of discrepancy one of the first things that we should suspect is not that the research is directly flawed but that there’s something about the research conditions that’s triggering an odd reaction: the sort of stuff we discussed in Be a Sceptical Economist. After all, we don’t normally get presented with clear odds on the probability of being drowned by a tidal wave while sunning ourselves on the beach. However, if we were involved in such an event and survived it’s pretty easy to imagine that we might start to overweight the possibility of it happening again. So it’s at least a possibility that presentation of the options makes the rare event salient and available in our brains and it’s this unusual combination of circumstances that’s causing the results.

Overturning the Allais Paradox

This possibility was explored by Greg Barron and Ido Erev who investigated a different experimental set up. They speculated that in real-life people aren’t presented by fixed odds of things happening but have to make their own minds up based on feedback based on what are, in reality, very small samples of the whole of life’s experiences: a situation in which most people won’t experience extreme events. What, they wondered, would people do in such situations?

They re-ran the Allais Paradox problem but instead of telling their participants what the odds were they left them to find out for themselves through interacting with a computer. Although Kahnemann and Tversky’s results showed that only 20% of people preferred the H option in Problem 4 – an four in five chance of $4 instead of a guarantee of $3 – in Barron and Erev’s feedback experiment no less than 63% selected this option. In the light of repeated experience people underweighted the rare event, rather than overweighting it.

Violating Behavioural Finance

The research investigated a range of predictions from behavioural finance and found that only loss aversion was robust under the experimental design. The outcome of the Allais Paradox was reversed, people took less risks when losing than when winning and they consistently underweighted small probability events. Basically these findings appear to complete bugger-up behavioural finance.

However, although this seems like a straightforward violation of Prospect Theory in fact it isn’t. The limitation of the original approach is that it’s restricted to so-called “one-shot situations” where a single decision is being made. The new results are coming out of feedback from multiple, small decisions:
"At a first glance, the current study could be criticized on the grounds that it focuses on an extremely artificial and unimportant set of decision tasks. According to this criticism, decision makers never face the same important decision problem twice. Obviously, however, this criticism ignores the observation that many common activities involve small feedback-based decisions. And, as noted in the introduction, these small decisions can be consequential even when the expected payoffs of the different alternatives are small and similar. The expected cost of stopping at a ‘dark’ orange traffic light, for example, is only few seconds."
So maybe it’s context that’s causing these different results. However, as Barron and Erev also discuss, there’s a second, related reason. When Weber, Shafir and Blais looked at how animals make decisions they found results roughly in accordance with Barron and Erev. Which suggests either that mainly people are no better at decision making than small rodents with a cheese fetish or that we’re making decisions based on the same information – feedback from the real-world gained in multiple interactions.

Being Human

Now, of course, one obvious difference between people and animals is that we’re capable of symbolic thought. After all, if presented with Prospect Theory’s original descriptive tests the only reasonable prediction we could make about the the animals' responses is that they would either eat the tests or run off and make a nest with them. Only humans would try and figure out what the symbols meant.

So, one partially alternative theory, which we’ll shortly revisit in more detail, to the complete reworking of behavioural finance is that the conception of rationality that lies behind these models is somehow wrong: humans can make decisions either based on experience of life's relatively small sample set or on the basis of symbolic analysis of the available data. On the stockmarket, then, we can either act like mindless cheese-eating surrender rodents in response to short-term feedback or we can perform thoughtful analysis of historical data – aka read and think – and plan our decisions carefully.

Related Articles: O Investor Why Art Thou Rational?, Gambling, From Iowa to Soochow, Stocks Aren't Snakes


  1. On the stockmarket, then, we can either act like mindless cheese-eating surrender rodents in response to short-term feedback or we can perform thoughtful analysis of historical data – aka read and think – and plan our decisions carefully.

    My sense is that most of us today do some of both.

    My hope is that over time we are moving gradually from the mindless rodents mode to the thoughtful humans mode. I don't think we are there yet, but I see evidence of progress having been made in recent decades.

    Part of the reason why we are not there today is that in the old days most of us didn't have money to invest. It is the growth in productivity of our economy that created this "problem" where we need to figure out how to finance retirements (in the old days we just worked until we died). So we are still in the early stages of figuring out this investing business. Hang on, Sloopy!


  2. There doesn't seem to be anything particularly behavioral about the Kahneman-Tversky "anomaly." I mean, problem 4 is the choice between a risk-free 3 and a risky 3.2, whereas problem 5 is the choice between 0.75 and 0.8 with both being risky. So long as the price of risk is positive, these choices might be the ones made by Home economicus. The essential question is therefore being begged, because the price of risk is implicitly assumed to be irrational. But this is an empirical question, not a deductive one, and the interesting experiment would be one that tries to untangle the rational and irrational components of the price of risk.

    As you point out, the iterative situation is quite different: given a choice of a million payments of 3 with certainty or a million independent payments of 3.2 with probability 0.8, Homo economicus would surely plump for the latter. Unfortunately, this iterative effect constitutes a confounding factor in the "probability learning" version of the experiment. So, while interesting, it is hardly conclusive.

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