Why are some of us more reluctant to take risk than others? Why are older people more averse to risk than younger ones? A new theory helps explain why - and much more.
For years, economists have been unhappy with the conventional textbook theory of risk aversion. This says that we have diminishing marginal utility of wealth: each extra pound brings us less satisfaction than the previous one. Because of this, we discount potential winnings and so refuse to take some bets even if they have positive expected pay-offs.
Sadly, however, as Matthew Rabin and Richard Thaler pointed out back in 2001, this theory is "not plausible". They show that it implies that a man who'd reject a 50-50 chance of losing £10 or winning £11 would also reject a 50-50 chance of losing £100 or winning an infinite amount of money: this is because if we discount one extra pound, we'll discount subsequent ones even more. But this is daft.
In a recent paper, however, economists at Columbia University have come up with a more sensible theory.
To see it, ask yourself: how much would I pay for a 50-50 chance of winning nothing or £100? The expected gain here is obviously £50, but risk averse people would pay less than this. How much less?
The answer depends on how we interpret (or code) the £100 and the stake. We imagine how we'd feel about that extra £100, and how we'd feel if we lost the stake money.
This coding, however, is imprecise, or noisy. We can't say for sure exactly how we'd feel about winning £100 or losing our stake. And the natural response to uncertainty is to do nothing unless the odds are in our favour. The noisier is the coding, the more risk-averse we'll be.
This might seem simple - although the Columbia economists wrap it up in fancy maths, as is required by academic convention. But it explains a lot.
First, it's consistent with a finding by Shane Frederick that people with greater cognitive abilities tend to be more tolerant of risks with positive expected pay-offs. If cleverer people find it easier to translate prospective monetary pay-offs into feelings (as is plausible) then they'll feel less uncertainty about gambles and so will take more.
It also explains a recent finding by Chris Brooks and colleagues. They show that older people are more risk averse than younger ones, even controlling for things that should affect attitudes to risk such as being retired or (arguably) having shorter time horizons. This might be because older folk are wise enough to know their limits. US researchers have shown that people's ability to take financial decisions declines after the age of 53, on average. If older people know this they should be more cautious about their ability to translate gains and losses into mental wellbeing and therefore be more cautious.
Thirdly, it explains ambiguity aversion - the tendency to avoid gambles with unknown pay-offs even more than we avoid ones with known pay-offs. Being unable to attach probabilities to pay-offs introduces another layer of noise into the coding process, thus making us more cautious.
Another thing it explains is the certainty effect: our willingness to pay more to reduce a risk from (say) 10 per cent to zero than to reduce it from 30 per cent to 20 per cent. Our attitudes to risk are a bit like our attitudes to shapes. If a picture is hanging slightly off-vertical, it unsettles us; we're sensitive to small deviations from the horizontal or vertical. But we're not so sensitive to deviations from 45 degrees. Psychologists call this the oblique effect. A similar thing is true of risk: we code the difference between a zero and a 5 per cent probability as more significant than that between, say, 50 and 55 per cent.
Yet another thing this approach explains is the tendency to back outsiders even at unfavourable odds - the habit that leads to the favourite-long-shot bias in sport betting and to the excessive buying of speculative shares; Aim stocks, which are more speculative than most, have underperformed the All-Share for most of the past 20 years.
When we think about pay-offs it's natural to ask: what could I do with that money? For small sums the answer is often 'not much', whereas for big amounts it is. This can generate a non-linearity between pay-offs, at least when it is combined with mental accounting. For me, for example, a £2,000 win is better than 20 times a £100 win; it would get me an expensive guitar whereas £100 wouldn't make much difference. Non-linear coding can make objectively inferior outside bets more attractive than shorter-odds ones.
Finally, all this is consistent with an obvious fact, that all of us have different attitudes to risk, even controlling for wealth, education and so on. And we have different attitudes to risk in different domains: people who enjoy risky sports don't necessarily take lots of financial risk, and vice versa. Traditional theory has long been puzzled by the fact that people both buy insurance and gamble. The new theory solves this puzzle. It's simply because we code gains and losses differently in different contexts: our house being burgled is not just different in degrees from losing a tenner on the gee-gees, but is different in kind.
None of this is to say that the idea of diminishing marginal utility is wholly useless. It is the case that the fourth pint of beer doesn't taste as good as the first. But you can't build a general theory of choice upon what happens at last orders in the Lord Nelson.
In thinking about risk, we should perhaps ditch conventional economic theory and instead ask: how would I feel about particular gains and losses? How do we translate monetary changes into feelings? This translation differs not just across domains and from person to person but also from time to time. This might help explain why asset prices are so volatile - which is something else that conventional economics struggles to explain.