Real Or Risk-Neutral Wolf?

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Includes: DIA, QQQ, SPY
by: John Cochrane

Today's Torsten Slok chart. In Wednesday's chart, we saw that the market forward curve keeps forecasting a recovery that never comes. Here, we see the same pattern, over a much longer time period, in the survey of professional forecasters. They're always forecasting that interest rates will rise.

I think there are deep lessons from this chart. And not the simple "economists are always wrong," or even "economic forecasts are biased." The chart offers a nice warning about how we interpret surveys.

Expectations matter a lot to modern macroeconomics. But you can't directly see expectations. So many researchers have turned to surveys to measure what people say they "expect." And they find all sorts of weird things. People "expect" stock returns to be implausibly high in booms, and low in busts. Professional forecasters "expect" interest rates always to go up.

The trouble here, I think, is that we have forgotten what "expect" means to the average person.

To the average person, "expect" means about what the upper 95% quantile means for a statistician. "Expect" is what happens if most things go right. "Risk" is all downside, the chance of something going wrong. The idea that "risk" means you might earn a lot more money than you "expected" will leave some glazed eyes.

Statisticians developed the concept of "conditional mean." They adopted the colloquial tern "expect" to denote it. Economic survey researchers then use responses of "what do you expect?" to infer subjective conditional means. But the average person never took a statistics class, and those that did haven't changed their use of colloquial language.

Understanding how real people use the word makes sense of a lot of surveys. I once delved into venture capital and discovered that analysts were using 40% rate of return hurdles. This makes no sense, right? Except if you understand that "cash flow expectations" means "how much we'll make if everything goes right" -- about the 95% quantile, not the conditional mean -- then a 40% discount rate might be a reasonable rough and ready way to adjust for that.

Moreover, the average person doesn't distinguish well -- and if he or she does, the survey never asks -- whether "expect" refers to the true or the risk-neutral distribution.

The risk-neutral distribution -- probability multiplied by pain (marginal utility) -- is a wonderful concept. For many decisions, the risk-neutral probability is a good sufficient statistic: Pay attention to probable events or painful events. When someone wishes you a safe flight, they're not ignorant of the vanishing probability of a plane crash. They are multiplying low probability times the high marginal utility (pain) of the event. A rise in interest rates, to a long-term bond investor, is a painful event.

The market forecast in forward rates is exactly the risk-neutral mean. And today's chart suggests that survey forecasters' response to "what do you expect" isn't straying far from the risk-neutral mean either. (Or, it's not straying that far from forward rates!)

In sum, next time you see a paper that uses surveys to measure "expectations," ask if the survey respondents knew the difference between "mean," "median" and "risk-neutral vs. true probability?" (Of course not.) Then you can ask why the author assumes one rather than the other.

More constructively, when using surveys, it's important to make use of the data in ways such that the precise meaning of the word doesn't matter. It would also be interesting to develop some survey methodology that recognized the colloquial meanings of "expect" have little to do with the statistical concept.