Risk aversion is not irrational


Jason Collins


February 9, 2012

Several times over the last few years, I have come across someone willing to claim that risk aversion is a bias or that standard economics cannot explain it (such as this claim by David Sloan Wilson - although he mistakenly named it the Allais paradox).

Yesterday, I saw the other half of the equation. I was looking for reviews of Richard McKenzie’s Predictably Rational?: In Search of Defenses for Rational Behavior in Economics,when I came upon an article by McKenzie containing a snapshot of the argument from his book. He writes:

[C]onsider one of the main experiments that behavioralists Kahneman and Amos Tversky use as evidence for the limitations of perfect rationality as a behavioral premise. They offer their subjects two options: Option A is a “sure thing,” carrying a payoff of, say, $800. Option B is a gamble with an expected payoff of $850: The subjects have an 85-percent chance of receiving $1,000 and a 15-percent chance of getting nothing. The behavioralists report that a “large majority” of subjects choose Option A, in spite of its having an expected value $50 lower than Option B. According to behavioralists, this majority choice demonstrates a form of “bounded rationality.” In other words, the subjects’ rational decision making is impaired by mental constraints on information processing and calculating capacity, not the least of which is risk aversion (with risk aversion evident in people heavily favoring Option A).

McKenzie then provides a “rational” explanation for the phenomena:

 I have repeated this exact choice experiment with my fully employed and executive (business-seasoned) MBA students for several years at the start of their first class—before we discuss rationality, decision making, or any microeconomic concepts and lines of analysis. Just as Kahneman and Tversky report, a “large majority”—between 70 and 85 percent—of my MBA students choose Option A, the sure thing. But would conventional economic thinking fail to predict such an outcome? Not really. As Dwight Lee explained four decades ago (and economists in earlier epochs have presumed), expected value is not all that matters for rational decision making. What the behavioralists miss is that variance in outcomes is also consequential in assessing options. Option A has no variance; Option B has a substantial variance, with the outcome ranging from zero to $1,000. Hence, for many choosers, Option A can be more valuable than Option B. Indeed, if expected value were all that mattered, people would never buy insurance. Is the purchase of insurance irrational?

In economics, the trade-off between expected value and variance is often discussed through the concepts of expected utility and risk aversion. As utility is assumed to diminish with higher rewards, the expected utility of a gamble is less than the utility of the expected outcome with certainty. People balance risk and reward.

But while McKenzie is correct to claim that the experimental result may not be irrationality, I am not aware of anyone active in the field who claims that it is irrational. In regard to McKenzie’s example, Kahneman and Tversky did not claim that the preference for a sure outcome of lower expected value is irrational. It is the universality of the risk-reward trade-off that they challenged. Kahneman and Tversky noted that if framed as a potential loss (an 85 per cent chance of a $1,000 loss versus a sure $800 loss), the experimental subjects became risk seeking. They prefer the gamble. The subjects prefer both higher variance and a higher expected loss. A simple model of expected utility does not show this result, nor does an intuitive explanation of a variance-value trade-off.

Kahneman discusses the history, implications and flaws of expected utility theory in more detail in his fantastic book, Thinking, Fast and Slow. (He also points out the flaws with the alternative approach of prospect theory). His discussion of expected utility is one of the best there is, and shows that he does not consider the existence of a trade-off between variance and expected outcome to be irrational in itself. It is the lack of consistency in how people make this trade-off that is the interesting result.

Despite the article, I will still read McKenzie’s book. The chapter list looks good, including some consideration of the evolutionary foundations of behaviour. and it has the odd good review. The title also plays to my dislike of calling behavioural biases and heuristics “irrational”. I will assume for the moment that the article is not representative of the book.

Postscript: After writing this post, I found this on Less Wrong.