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All In: How the limits of human rationality affect the perception of risk

Everyone’s life is made of choices, most of which are characterised by a certain degree of risk and uncertainty: the decision to vaccinate your child, to buy an insurance policy or to accept a gamble in order to win a sum of money. How do we approach risk? Are our choices based on rational thinking or do we consider all information that is available to us?

The Israeli psychologist and Nobel Prize in Economics Daniel Kahneman, together with his compatriot and colleague Amos Tversky, revolutionised our knowledge of human rationality. The two researchers showed through simple mathematical models that human behaviour in uncertain situations is quite different from that of the homo oeconomicus widely acclaimed in Economic Theory.

Making decisions…

“Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows:

– If Program A is adopted, 200 people will be saved.
– If Program B is adopted, there is 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved.
Which of the two programs would you favour?”
If you prefer to adopt Program A, you have just answered the same way as 72% of the people interviewed by Kahneman and Tversky (1984). Now imagine you have to choose between two new outcomes:
– If Program C is adopted 400 people will die.
– If Program D is adopted there is 1/3 probability that nobody will die, and 2/3 probability that 600 people will die.
Now, which program would you prefer?
If you preferred to adopt program B, you would have again answered as 78% of the people interviewed.
These results show that the vast majority of the participants did not realize the mathematical equivalence between programs A and C. Indeed, both programs ensure that 200 people will survive and 400 people will die. So, why do people give different answers when faced with the same problem?

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Loss aversion

As we saw previously, the majority of people prefer to adopt program A and save 200 people for sure. This behavior, named “loss aversion”, was identified by the physician and mathematician Daniel Bernoulli in 1738. Loss aversion means that people choose to avoid risk when facing uncertain outcomes and thus prefer predictable and certain scenarios (probably this behavior has evolutionary roots and it has allowed human beings to survive through centuries). Even though the expected value of the certain outcome is lower, people are willing to pay a premium to avoid uncertainty. We present another example to explain better how loss aversion works:
“You have the opportunity to receive £80 with 100% probability; or
You have 4/5 probability to win £100 and 1/5 probability to win £10.”
Almost everyone prefers the first option, despite the expected value of the second gamble being greater (80% * £100 + 20% * £10 = £82) than the first one. In this way, Bernoulli showed that our choices are not based on economic value (expected value), but on the psychological utility of the outcome.


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From Loss Aversion to Prospect Theory

Although Loss Aversion describes why people prefer to adopt Program A (saving 200 people for sure) rather than Program B, it fails to explain why people prefer Program D to Program C.
Prospect Theory has been able to fill this theoretical gap. In 2002 the psychologist Daniel Kahneman, regarded as the father of Behavioural Economics, won a Nobel Prize after his work on Prospect Theory, which he would have shared with Amos Tversky had he not died years before.
According to this theory, it is often possible to frame a problem in more than one way. The axioms of rational thinking unequivocally state that a simple change in the phrasing of a problem cannot influence the preferences of rational decision makers, the so-called “Econs” dear to Financial Theory. However, in reality, the perception of common people (the “Humans”) is flawed and changes in the framing of a question often affect the actual desirability of an option. As we previously saw, Kahneman and Tversky systematically found inconsistent preferences when rephrasing the presentation of two mathematically equivalent alternatives to a problem. They called this bias in human decision-making the “Framing effect”.

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Four cognitive features that affect our choices

The authors found out some cognitive features that play a key role in the assessment of financial results, and are also involved in perception, judgement and emotional processes.  

1) People perceive outcomes as gains or losses from a neutral reference outcome. To better understand this point, let’s go back to our example. The potential Asian disease’s victims are 600, although when we read the options, the starting point becomes secondary. If the respondents had kept attention to the starting point, they would have understood easily that Program A and Program B were equivalent.  

2) The response to losses is more extreme than the response to gains. The displeasure associated with losing £1,000 is generally greater than the pleasure associated with winning the same amount.
3) Turning on a faint light has a big impact in a dark room, whilst the same difference is not perceived in a bright room. In the same way, the difference in subjective value between gains of £10 and £20 is greater than the subjective difference between gains of £110 and £120.

4) Conversely, people making choices in the loss domain tend to exhibit risk-seeking behaviour. This explains why people are keener to accept the risky option when they have to choose between the certain death of 400 people and 1/3 probability to save everyone.

The first three features are illustrated in the so-called “Prospect Theory Flag”. The S-shape shows a decreasing response for both gains and losses. However, the two curves are not symmetric and indeed the losses’ curve is steeper than the gains’ one. The objective economic value of losses and gains is reported on the X-axis while the Y-axis represents the associated positive (+) or negative (-) psychological value.

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The Equity Premium Puzzle

A phenomenon that sparked the interest of researchers for Behavioural Economics is known as the Equity Premium Puzzle. This paradox consists of the exceptionally high yield investors require for holding stocks rather than other financial instruments perceived as safer. One of the theories that best explains such phenomenon is named “Myopic Loss Aversion” (Benartzi et al. 1995) and primarily builds on the concept of loss aversion in a short period of time.

Prospect Theory as a possible explanation

The paradox rapidly disappears if we suppose investors are highly risk-averse and have an investment horizon of less than 12 months, considered to be short in Financial Theory. This combination describes the excessive fear of realising multiple losses, however small, rather than focussing on potential gains in the longer term. The aversion to the uncertainty around an investment generates remorse for either making or not a decision that turns out to be wrong, such as not selling a stock which value then plummeted. This behaviour is consistent with the shape of the utility function shown before, where the higher steepness of the curve in the loss domain represents the higher psychological weight attributed to a £500 loss rather than a gain of the same magnitude.


Risk-seeking behaviour

The Italian researcher Fabio Tramontana (2016) theorises that Prospect Theory can explain the psychological processes unknowingly affecting and driving our choices. One of the most serious implications is that people are prone to take risks when dealing with significant losses. This can explain, for example, why it is so difficult to give up on a poker match when you are on a losing streak. If the player is losing a sum of money, he faces the choice to go on with the game or to give up. If he accepts to stop he will realise the loss for sure while if he chooses to go on he has an opportunity to regain what he lost or lose even more money (Tramontana, 2016).

Furthermore, Prospect Theory could explain the recent political triumphs of populist candidates. These behaved in unpredictable ways and were in many aspects gambles for the average voter. In a world of unhappy people it is increasingly likely that voters unconsciously frame elections as a choice between a certain loss (the candidate representing the “establishment”) and an opportunity to change for the better. If he loses this bet results are probably going to be worse than they already are but if he wins, although this is less likely than the negative scenario, he will be able to invert what he perceives to be the disastrous policies of his country.

According to Kahneman, politics and institutions have the responsibility to help “Humans”, who are very different from “Econs”, to make sensible choices. A possible strategy could be the “Re-framing” of the options available to people in order to affect their sense-making process of a decision. Alternatively, a greater emphasis on logical and mathematical education during school years could train the more accurate “slow thinking” process and blunt the strength of its bias-prone “fast” counterpart.


Francesca Amenduni


Alessio Pastore

Graduated with an MSc in Finance from Durham University Business School and he currently works as a Fixed Income Algorithmic Trader for Credit Agricole. His interests lie in the interaction between the Quantitative and Behavioural aspects of Finance and the impact of psychology on investment decisions.

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