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Thoughts About Risk Aversion

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Risk aversion is a straightforward name for the psychological fact that humans are often willing to pay a premium for certainly, or at least for limiting the zone of uncertainty.


Suppose you, dear reader, appear on a television game show. The master of ceremonies says to you,
"I can give you a nice crisp $100 bill right now!"


You say, "oh, goodie."


"Or!" he continues with a dramatic flourish, "I can flip a coin. If the coin comes up tails, you'll get nothing. If the coin comes up heads, you'll get $200."


Let us suppose there is no element of what finance types call "counter-party risk" here. Your counter-party is the emcee. We'll assume he is entirely trustworthy and that there is nothing tricky about the coin flip itself.


The expected value of the coin flip, in simple arithmetical terms, is ($200 + 0) ÷ 2 = $100. The value of the payoff if you reject the coin flip is, again, $100. So you should on one quite abstract level be indifferent which course the emcee takes. You might even want to flip a coin to decide whether to tell him to flip the coin.


Except that you won't. Unless you are an extraordinary specimen you, dear reader, will be risk averse. One of the choices involves just taking what has been offered you, the other involves the risk that you'll end up with nothing. You'll opt for the former.


Let me stop there. If any of my readers is NOT risk averse in the sense I've just described, let me hear from you in the comments.
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  1. HenryJune 1, 2014 at 8:22 AM

    One's decision whether to take the $100 or risk it for $200 may depend upon a factor that you have not considered: how badly one needs the $100. If I am starving and the $100 will enable me to eat, I'll take it. If I would use the $100 to purchase a luxury item, then I might as well risk it in the hope of being able to buy a $200 luxury item.

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  2. ChristopherJune 2, 2014 at 3:17 PM

    Henry,

    Good point. Even to a poor person, though, this point seems at first blush to cut both ways. It means that losing the chance to lock in the first $100 would be that much more devastating, but it also means getting the $200 would be a more tempting boon.

    If we think of the utility of money as a curve we can resolve this (the way you suggest). To someone who has nothing, $100 is extremely important. The likelihood of a second chunk of money of the same nominal value will also be important, but maybe a smidge less so.

    Bill Gates, meanwhile, is at or near the top of a concave curve. Another $100 will mean literally nothing -- the line is horizontal. Conceivably the curve has headed down, so another $100 is just a burden to Gates, a little extra weight he'd be expected to carry about in his wallet until he got it home and could safely use it to tip the butler or something. "Whew! what a relief to have that off of me! I wish I had bet on the next coin flip and lost!"

    A similar point is often made through a slightly more complicated thought experiment known as the St Petersburg paradox, because of its origins in a pre-Napoleonic era in Russian history when St Pete was a gambling mecca.

    I'll link you to a discussion of that.

    http://www.econport.org/content/handbook/decisions-uncertainty/basic/paradox.html

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