Saturday, March 01, 2008

Why Risk Aversion Isn’t

Many fields use technical terms that sound self-explanatory and aren’t. The result is that many people believe they know what those terms mean—and don’t. I am confident that there are millions of people who believe that they understand what the Theory of Relativity says, even if not the mathematical details. The theory says that everything is relative. Surely that is clear enough.

Clear—but almost entirely unrelated to what the Theory of Relativity actually says.

Economics has similar problems with terms such as efficiency and competition. One particularly serious case is risk aversion. It is serious because outsiders are not the only ones who think they understand it and don’t.

Risk aversion sounds as though it means aversion to risk; one would expect a risk averse person to avoid dangerous hobbies, a risk preferring person to be drawn to them. It is not true. There is nothing in the definition of risk aversion that implies that a risk averse person is less likely to take up hang gliding or mountain climbing than a risk preferrer.

The definition of risk aversion, as any good textbook that covers the subject will explain, is that a risk averse person, faced with the choice between an uncertain set of monetary payments and a certain payment with the same expected value, will prefer the latter. As that definition suggests, it is a statement not about his taste for risk but about his taste for money.

To see why we would expect people to be risk averse, imagine that you are faced with two possible jobs. One pays you $60,000/year. The other has equal odds of paying you $20,000/year or $100,000 year.

We expect most people to prefer the former job, all else being equal. To see why, imagine that you are shifting continuously from it to the other. You are giving up dollars in the future where you lose the bet—where the salary is $20,000—in order to get dollars in the future where you win the bet. That means that you are giving up (probabilistic) dollars used to buy things you would get as your income increased from $20,000 to $60,000 in order to get (probabilistic) dollars to buy things you would get as it increased from $60,000 to $100,000. As your income increases, you buy the more important things first, so we would expect the gain from getting a dollar at the high end to be less than the loss from losing one at the low end. As this (entirely conventional) exposition shows, risk aversion is simply declining marginal utility of income.

The fact that your marginal utility of income decreases as your income increases tells us nothing at all about how the marginal utility of other things changes as the amount you have of them changes, hence the fact that you are risk averse does not tell us what your attitude will to risk that involves non-monetary payoffs.

Your doctor calls you into his office to give you some very bad news. You have been diagnosed with a disease that, if untreated, will kill you in fifteen years. There is an operation which will let you live thirty years—but half the time it instead kills the patient. You have a choice of a certainty of fifteen years or a fifty/fifty gamble between thirty and zero.

As it happens, the one thing in life you most want to do is to produce and bring up children. Thirty years is long enough to do that; fifteen is not. You grit your teeth and sign up for the operation. You are risk preferring in years of life, because years of life have increasing marginal utility to you. You may be, probably are, risk averse in dollars because dollars have decreasing marginal utility to you.

Risk preference, as economists use the term, is not about risk.

13 Comments:

At 1:10 AM, March 02, 2008. Jonathan said.

As a non-economist, my conclusion would be that economists have chosen the wrong term for the concept they want to think about. Maybe they should call it monetary-risk aversion, or something.

The obvious definition of risk aversion is aversion to risk (hang-gliding, etc.). If economists prefer a different, less obvious definition, they have the freedom to use it amongst themselves; but are they entitled to insist that their own definition is the right one and everyone else is wrong? I doubt it.

Your discussion of the subject is interesting, regardless of this issue.

At 8:51 AM, March 02, 2008. Joe said.

But what job has equal odds of paying you $20,000/year or $100,000 year? A more realistic scenario is between being a salesperson earning a $60,000 straight salary vs. $40,000 salary plus 15% commission on sales. If, like most people, you are not confident in your selling (persuasive) abilities, you’ll take the straight salary deal. OTOH, an already successful salesman will take the commission offer. The same applies to people going into business for themselves. As I see it, it’s an aversion to the risk of failure.

At 10:48 AM, March 02, 2008. dWj said.

It seems to me this hinges partly on what one means by risk. I view a situation in which one has a 50/50 chance of winning $10 (versus losing nothing) as a risky situation; in conversation, I have learned that others do not (as there is zero chance of ending up behind; my argument that a 50/50 chance of winning $10 is valuable, and is lost when it is resolved unfavorably, seems to win few converts, but leaves me uncomfortable with the intellectual coherence of other people’s views of risk).

Come to think of it, I remember another conversation in which a coworker seemed to think it strange that one would want to hedge one’s assets, and not merely one’s liabilities. I was surprised that someone with a reasonable grasp on negative numbers would draw the distinction.

At 3:57 PM, March 02, 2008. Alan said.

There’s a practical application of this stuff to finance, and I think (though I may be wrong) that many of the experts get it wrong, at least partly. Standard advice is to have a stock-heavy portfolio when you’re young and gradually shift to fixed-income investments as you age, the argument being that when you’re old, you don’t have enough future years left to make up for a bad few years in the stock market now. My thought is that (1) as you age, you get richer, so your risk aversion should be lower; (2) once your kids finish school, a big drop in income doesn’t do the damage it would do if they were still getting educated, so one major reason for risk aversion goes away. So, if anything, I’d expect to see people’s portfolios shifting toward equities as they age, especially if they have children. Anybody know if there are studies on this?

At 5:27 PM, March 02, 2008. Anonymous said.

Producing children is not the most important thing in my life.

In creating men, nature took a gamble. We have been a very successful species, but we are also self-aware, and entirely capable of having other goals — perhaps some goals directly contradictory to the goals of our genes.

My genes are not the only things I carry that reproduce. I produce and spread ideas as well. One might imagine that a personality fond of copying itself onto other people could be highly successful, and it might be successful at the expense of the genes of the people it manages to infect.

In case you were wondering, I lean towards nurture in the nature/nurture debate. I was never taught producing children is the most important thing in life, so that’s probably why I think it isn’t.

At 8:45 PM, March 02, 2008. Charmer La Sec said.

David,

This concept reminds me of performance pay systems. The idea being that you can attract better people by giving them the opportunity to earn more money, but having an base salary lower than the median income as a means of leverage.

My company is studying this idea because we think it will bring in solid employees.

In your example, we would want the person who would choose the 20k salary, with the possibility of earing 100k.

Do you have any thoughts on such pay programs?

At 10:05 PM, March 02, 2008. reticent man said.

Your distinction makes no sense to me. It seems like the phrase risk-aversion means exactly what everyone would think it would mean, just that when economists use it, it’s qualified as risk-averse with respect to money.

But I have no problem using the term risk-averse with respect to other things, and people will readily understand what I mean. I don’t think it makes sense to restrict the term to only money just because economists use it that way. If the context requires it, you can and should always qualify what you’re talking about. So the only real confusion would be caused by people not understanding the context of the use of the term, which could be blamed as much on the writer/speaker as the reader/listener.

I’ve used the term to explain to people who have no economics training how I’m risk-neutral and maybe even risk-preferring for time, and small to medium amounts of money, while being risk-averse for large amounts of money. And people understand.

At 10:17 PM, March 02, 2008. RL said.

David,

I admit to being one that, based on your explanation, has confused risk aversion in the past. But you confuse me still. If, per your explanation, risk aversion is simply marginal utility applied to money, what’s the point of the concept? We don’t need special terms for marginal utility applied to other goods and services.

At 10:27 PM, March 02, 2008. David Friedman said.

rl asks:

If, per your explanation, risk aversion is simply marginal utility applied to money, what’s the point of the concept?

Not marginal utility but declining marginal utility. The concept is useful because it points to a consequence of declining MUI that is of real world importance—explains people buying insurance, for example.

At 9:27 AM, March 03, 2008. Michael said.

Echoing agreement with the post and some commenters.

valueinvestingresource.blogspot.com/2008/01/risk-uncertainty-and-profit-frank-h.html

At 8:44 AM, March 04, 2008. Jason said.

Granted, one can’t separate risk aversion in neo-classical economics from concavity of the utility function. But so what?

That is to say, do these models fail to capture something from the real world (namely, people with convex utility functions, who we would consider risk averse)? You have a nice article on why we might not see risk preferrers in the real world, but this isn’t to say there aren’t people who prefer risk.

There is nothing inconsistent in economic theory by positing a model where an agent is risk averse over one argument in his utility function, but risk preferring over another. The mathematical equivalence between decreasing marginal utility and risk aversion seems a natural counter part to the real world definition of risk aversion and is one of the places where I feel economic models do a great job of formalizing our thoughts.

Jason

At 6:30 PM, March 04, 2008. Anonymous said.

Alan,

(1) Note that you are illustrating David’s point by using risk aversion to mean aversion to risk. In the technical sense of risk aversion, the balance of stocks vs bonds says nothing about whether a person is risk averse. (However, if somebody held a non-diversifed portfolio of stocks, that would make them a risk-preferer. That’s because a non-diversified portfolio has the same expected return as a diversified one, but greater risk).

(2) On the question of whether a person’s taste for financial risk should increase or decrease over time. the best argument in support of the conventional wisdom of decreasing investment risk over time is that as you age, your earning power (human capital) decreases. However, if your labor income is replaced by Social Security and/or pension, then your appetite for risk may actually increase (since SS is a more reliable income stream than employment income for most people).

At 5:36 PM, March 11, 2008. Sten Thaning said.

Over here, there is a game show called Deal or no Deal? (I guess it exists in the US as well?) which, if I understand the rules correctly, illustrate your point.

The contestants can choose between a guaranteed sum of something like $50,000, or equal odds of getting $20,000 or $100,000. The point is that the offered sum is always slightly lower than the expected return if the contestant continues to gamble. Logically, it seems like it is always preferable to continue the game. However, in reality most contestants stop before the end and accept the offer. (I think. I haven’t actually watched the show.)

If the risk aversion theory is valid, the contestants should stop when the marginal utility has declined to the point that taking the money is preferable. It could be interesting to study at which sums this usually happens.