Risk aversion, semantics, and usefulness

Is the concept of risk aversion useful? Can we measure it? Richard Thaler and Andrew Gelman opine.

First, we should establish that stock market commentators use the words “risk aversion” very differently than academics. Commentators mean “aversion to risky assets”, simply meaning that the perceived relative benefit of  risky and risk-free assets has changed for traders in the market. In that context “risk aversion” is not about trading off risk and return, it’s about expectations of risk and return. This is inconveniently inconsistent with academic usage, but not the first or only case where a word is generally used differently from academics.

Academics use “risk aversion” to measure how an individual trades off risk and return. Thus when expectations of stocks change, this doesn’t change risk aversion – it just changes the amount of risky assets a person holds relative to risk-free assets given a static way of trading them off.

However, a great deal of the evidence from behavioral finance has shown that mathematically measured risk aversion parameters aren’t stable or consistent. Given that questions required to estimate the mathematical parameters [gamma, lambda, rho] involve probability and compensatory payoffs, I think it’s easier to say people have a hard time with these questions than that they don’t have different levels of risk aversion. In other words, it’s hard to measure risk aversion well.

However, when we measure risk aversion in a more intuitive way, we get far higher levels of reliability. Our psychometric measurements over two years, during some of the most turbulent periods in markets showed an incredibly high level of reliability (r=0.78, if you want the numbers). There is far less noise in psychometric measurements than mathematical estimates due to numeracy, market context, time horizon and financial knowledge.

Which isn’t to say risk tolerance doesn’t change – but I’d say it gradually drifts, rather than abruptly changes, like most personality factors in our life. As Andrew notes, the fact that the expected demographics (age, sex, education, marital and family status) all point in the correct directions imply that there is something in there.

Finally, I think its getting a bit carried away with comparisons to heliocentric universes. What’s the use of a utility function? Well, I’d agree that very rarely will observational data perfectly reflect a utility function. However, the utility of a utility function (much like the value of money) is not necessarily in it’s descriptive accuracy, but in it’s prescriptive value. Inasmuch as we can use a utility function to assist people in making rational risk management decisions, utility functions are very useful. They don’t make the genuine mistakes that people often make, for one. And we have to respect that people’s level of risk aversion does seem to vary systematically, and take that into account. Exactly how you do that takes a lot of thought and care, but it’s still useful.

I think even heliocentric models had predictive power – Copernicus just had a better, more concise model to replace it. I’d love to know what model beats a utility function for usefulness in general applicability.

Leave a Reply

Your email address will not be published. Required fields are marked *