Smarter than the Average Bearish Investor?

"Even when it ... hurts you on average to take the gamble, the smart people ... actually like it more":

Would You Take the Bird in the Hand, or a 75% Chance at the Two in the Bush?, By Virginia Postrel, Economic Scene, NY Times: Would you rather have $1,000 for sure or a 90 percent chance of $5,000? A guaranteed $1,000 or a 75 percent chance of $4,000? In economic theory, questions like these have no right or wrong answers. Even if a gamble is mathematically more valuable ... someone may still prefer a sure thing. People have different tastes for risk, just as they have different tastes for ice cream... The same is true for waiting: Would you rather have ... $3,400 this month or $3,800 next month? Different people will answer differently. Economists generally accept those differences without further explanation... Shane Frederick, a management science professor at the Sloan School of Management at the Massachusetts Institute of Technology, ... discovered striking systematic patterns in how people answer questions about risk and patience, including those above. This short problem-solving test, he found, predicts a lot:

1) A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

2) If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?

The test measures not just the ability to solve math problems but the willingness to reflect on and check your answers. (Scores have a 0.44 correlation with math SAT scores, where 1.00 would be exact.) The questions all have intuitive answers — wrong ones. Professor Frederick gave his "cognitive reflection test" to ... students... Participants also answered a survey about how they would choose between various financial payoffs, as well as time-oriented questions like how much they would pay to get a book delivered overnight.

Getting the math problems right predicts nothing about most tastes, including whether someone prefers apples or oranges, Coke or Pepsi, rap music or ballet. But high scorers — those who get all the questions right — do prefer taking risks. "Even when it actually hurts you on average to take the gamble, the smart people, the high-scoring people, actually like it more," ... They are also more patient, particularly when the difference, and the implied interest rate, is large. Choosing $3,400 this month over $3,800 next month implies an annual discount rate of 280 percent. Yet only 35 percent of low scorers ... said they would wait, while 60 percent of high scorers preferred the later, bigger payoff. ...

The connection between cognition and risk preferences challenges some of the "prospect theory" developed [by] Daniel Kahneman and Amos Tversky. They observed that people would accept larger risks to avoid losses than to achieve gains, even when the two choices were mathematically equivalent. The same person might take a sure $100 instead of a 50 percent chance of $300, yet prefer a 50 percent chance of losing $300 rather than a sure $100 loss. This result, which has implications for investment and insurance, is one of the major findings of behavioral economics. Although prospect theory "is spectacularly true" for the low-scoring group, Professor Frederick writes, high scorers treat potential gains and potential losses about the same. ...

The correct answers, by the way, are 5 cents, 5 minutes, and 47 days.

Comments

[reason]

Well,
I got all the answers right, and would have picked all the "high risk" choices, but then I personally think I am risk averse. I am certainly very cautious in my real world investments.

But the hypothetical exercises are too small to be a really significant risk for me, and the rewards were too obviously high. In the real world, I see the risks far too clearly (particularly at the moment).

[Emmanuel]

I think that Postrel goes too far in saying that the paper puts into doubt parts of Kahneman-Tversky. Prospect theory suggests that people are risk-averse in the domain of gains ("don't risk it; you've got it made"), while they are risk-seeking in the domain of losses ("what have I got to lose").

Suggesting that IQ affects the performance of problem-solving tasks is obvious. Of course more intelligent people are less likely to make aberrant decisions. But, what would the results be if intelligence were treated as a control variable, and frames were used? I'd think that the results would be closer to Kahneman-Tversky's.

BTW: Look at table 1. I am shocked--just shocked--that only 26% of students at Princeton got all three questions right. I'm no rocket scientist, but these are quant questions of less than intermediate difficulty. The parents of these kids should ask Princeton for a refund of the $50,000 or so they pay yearly for their children's education.

[Robert]

Princeton surely must assume that the solving odf these algebraic twisters were assimilated at age 13 or so during Introduction to Algebra.

The other Princeton, Educational Testing Service, are the ones that should be quaking in their proverbial boots since 26% probably means that the SAT either fails as a filter or can be effectively crammed for and then forgotten with the first taste of one's collegiate beer.

[paul]

Emmanuel: it's currently a bit more than $40K per year for the checks made out to Princeton. Maybe $50K a year by the time this year's freshmen are seniors, but Yale has only gone up by $3K-$4K in the last 3 years (inclusive of the current academic year). Anyway, I suspect that the problem lies more with pre-college prep -- high schools, junior highs and middle schools and elementary schools -- than with Princeton itself.

[cm]

Nice quizzes. But regarding the $3400 now vs. $3800 later, one must be careful in how the problem is posed. It implies a 280% interest rate only when receiving the money is a sure thing, i.e. there is no hidden risk premium. In many practical situations there is substantial risk involved, and it may actually make sense to take the smaller amount and run.

[bailey]

cm, RISK? What risk? We're living in the new America, there is no risk "smart" investors can't "hedge". At least that's what JPM (check out their derivative holdings some time) & MANY of our most prominent bond managers (Fed will bail us out) think. Is it wrong to bet that helicopter Ben will come to the rescue?

[Bruce Wilder]

The three questions, really, are more a test of arrogance, than of intelligence, since they are, as the article notes, a test of "the willingness to reflect on and check your answers." In that light, it is not surprising that such a low percentage of students at an elite university would get suckered at least once, by the apparent "intuitive" answer dangled in front of them in each case.

I wonder how many people noticed that, if the lily pads covered a square meter on the first day, the lake would have to be bigger than Lake Superior. Talk about your ecological disaster!

[anne]

Of course, the Federal Reserve, as any developed nation central bank, will always aid bond investors, not by flying in money but by the reverse. The point of a central bank is to limit inflation, not to create it unless there is dangerously little inflation or deflation. So, any bond holder can have full confidence in the Fed but that is not of concern in buying bonds. Bonds are bought when relative value dictates, beyond Fed "insurance."

[cm]

Bruce: The pond example further conflicts with "common sense" in that keeping up highly exponential growth (and 2**n definitely qualifies as such) in two dimensions, e.g. on the surface of a sphere, for an extended period is physically close to impossible. (Something that I'm not sure most economic actors understand -- no offense anybody please.)

So failure to judge the task in an imagined "real" domain as opposed to the "abstract" domain is actually not necessarily a full-blown failure of reflection, as reality doesn't work that way. But I may be splitting hairs here ...

[jim brady]

cm
highly exponential growth (and 2**n definitely qualifies as such) in two dimensions, e.g. on the surface of a sphere ...

Now where have I heard of something like that before? Ah yes I remember now a bubble! The problem is of course the surface keeps getting THINNER and eventually POP!

[anne]

There is too much to know, to know what this professor or that tells us we need to know. What is salient about my students is that they know superbly what is of interest to them, and they can and do readily learn what they must.