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The Actuary The magazine of the Institute & Faculty of Actuaries
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Human behaviour

It’s a problem that has been faced by all actuarial students. You’ve been studying for hours, your concentration is going and you wonder whether you should persevere or take a break and come back later, refreshed and recharged. Wouldn’t it be great if you could learn about your subject while watching TV? Well, you can, but only if you’re studying the chapter on behavioural finance in ST5 and watching Deal or No Deal.

In case you don’t know, in each episode the contestant is given one of 22 boxes, each with a monetary value between 1p and £250,000. The contestant chooses one of the other 21 boxes, whose contents are revealed, giving more information on the value of the contestant’s box. The process is then repeated until only one box remains and the contestant wins the amount of money contained therein. Periodically, the contestant is required to either accept a cash offer made by the Banker for the contents of their box (Deal) or continue opening boxes (No Deal).

Using a simple expected utility theory model, and assuming the contestant is risk-neutral with a utility that increases linearly with wealth, we can say that, if the expected value of the unopened boxes is no greater than the Banker’s offer, the contestant should Deal, otherwise they should opt for No Deal. However, the contestants often do not act in this way and some of the reasons why they don’t are explained by behavioural finance.

If a contestant were to play a large number of games, then the above strategy would result in the maximum gain for the contestant. From this, we deduce that this is the ‘correct’ way to play the game. However, in practice, the contestant only gets one game and has no opportunity for future gains to compensate for any loss suffered in the first game. So contestants are likely to accept offers below the expected value of the boxes, in order to avoid the ’loss’ suffered if their box is revealed to be worth less than the Banker’s offer. The fact that people are more likely to accept a gamble if they are allowed to repeat it is related to the behavioural finance concept of myopic loss aversion.

Although the contestants may be expected to avoid taking large risks on a single gamble, they are not risk-averse in all such situations. Often, when a contestant has had a bad round, knocking out several high-value boxes, the Banker seems to sympathise with the contestant. The offer will be lower than that offered in the previous round but may be higher than the expected value of the remaining boxes. However, such offers are usually rejected as contestants become determined to minimise the ‘losses’ they have made, and refuse to accept an offer lower than one they had previously rejected. This demonstrates a key finding from prospect theory, which is that people tend to become risk-seeking when facing losses but more risk-averse when facing gains.

The converse to this effect is that some contestants who do well also tend to show risk-seeking behaviour, as they feel they can’t lose. This reveals another important point in prospect theory — the decisions that people take depend upon their current and past levels of wealth, not just the payoffs from the decision they currently face.

Another aspect of behavioural finance demonstrated is that people tend to make mistakes when estimating probabilities. The probability that the contestant’s box contains the £250,000 or the 1p is clearly equal to 1 divided by the number of boxes still in play (assuming the amounts have not been revealed already), but many contestants seem to believe that a particular box (the one they had originally planned to choose) is significantly more likely to hold £250,000 than 1p, demonstrating that the ‘valence’ of an outcome has a large influence on probability estimates of its occurrence.

There are other effects of behavioural finance displayed by many contestants, but I’ll let you look for them yourself. That way you’ll be studying actively, not passively.

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Rob Giddings is a trainee actuary at the Government Actuary’s Department.