Monday, 29 October 2012

Quantitative finance and Medical charlatanism

PSY headquarters moved to Cancun, Mexico this week, giving me some time to post a blog article on one of my favourite subjects: the abuse of "science" in quantitative finance (see for example the article on OpRisk last month).

This was triggered by an op-ed piece on "There is life in this ‘investable’ rally". Here Goldman's chief global equity strategist, one Peter Oppenheimer, does what one would expect a good equity sales guy to do: he pumps equities. The part which triggered my hulk reflex ("you wouldn't like me when I'm angry") was this paragraph:
In July the equity risk premium was as high as 9 per cent. Over the past two months it has fallen to 8 per cent on our estimates. This is still very high by historical standards: the long run average is close to 4 per cent. It is not surprising that the ERP remains unusually high, given the current macro dislocations, but our estimate of the appropriate level of the ERP is around 6.75 per cent.
This kind of thing really irritates me. In the previous sentence the guy even gives a definition of the equity risk premium:
the additional rate of return investors require for investing in equities over and above what they can get on a relatively risk-free asset like bonds.
Great. Not exactly F = ma, but a definition nevertheless. So let me get this straight, these guys know what equities are going to return, so they can compare that with the yield on bonds, and thus deduce what the ERP is and was? OK, so I'm being pedantic, the definition is obviously short-hand, clearly there is some acknowledgement of uncertainty in the definition, they clearly only know what the expected return on equities is.

Sorry, still not OK, how do they know this value? I mean, is there some sort of "god model" (Mammon one presumes) which gives a mean and standard deviation of the distribution of future returns? Clearly from a stable distribution since no time horizon is given.

Alright, alright, cry pedant once more. Clearly they've taken an average of historic equity returns and compared that to historic bond returns.

Sorry, still not happy. That doesn't tell you what premium investors required, a-priori, compared to bonds. And we still haven't addressed the time horizon issue.

In order to actually estimate the equity risk premium one would have to take a sample of investors, ask them what return on equities they expected to achieve over the next year, say, and compare that to the one-year bond yield. Then one would risk what economists call the fallacy of composition by taking an average. Of course, one would have to do this on a regular basis over a long time period in order to generate the numbers casually thrown around in the quote above.

But one suspects that what they have actually done is to pull some numbers out of the air, call them assumptions, and calculate the net present value. Of course, we don't know, because he doesn't say. He just presents some numbers.

At least those numbers are rounded, unlike, for example, the similar figures in this article on Zerohedge (not clear from the context if they are from Goldman again or from Zerohedge themselves).

Snake oil for you sir?

Ben Goldacre and Simon Singh are a couple of journalists / authors who have written extensively on pseudo-science and the abuse of science in the medical industry. They address various forms of charlatanism in their writing, and a very brief summary of one particular aspect is the following:

Modern medicine doesn't offer effective treatments for some ailments, perhaps because some problems or conditions are intrinsically difficult by their natures. Things like chronic back pain, autism, some allergies, etc. When faced with a patient who is suffering from chronic back pain, a responsible physician will confess helplessness and recommend ways to live with the condition.

However, for various reasons (instant gratification society, misrepresentation of modern medicine as being all powerful, etc) some people won't accept that answer and will carry on looking for a solution. And they will find and army of charlatans willing to sell them one. Chiropracters, reiki crystal peddlers, faith healers, etc. All claiming to have the answer the doctors don't, for a small fee.

And sometimes these alternative "cures" work. Perhaps just by coincidence, perhaps the issue would have cleared up on it's own anyway, perhaps due to the placebo effect. But it happens often enough to keep alive the fiction that there is a cure which modern medicine doesn't know, or won't acknowledge.

For a much more detailed analysis, I highly recommend Goldacre's book Bad Science, which has a lot of stuff on cognitive biases which you may recognise if you've ever read up on behavioural finance.

Digress much?

Now to unify the two threads of thought above: our man from the FT op-ed article has no way of knowing what value the equity risk premium currently is, or ever was. In fact it's questionable whether there is such a thing as he defines it. When asked whether one should invest in equities right now, a responsible investments adviser should reply that it all looks very uncertain, but we believe that equities are a good bet for reasons a, b and c. But keep in mind x, y and z.

Replacing the qualitative arguments a, b and c with numerical values calculated from some undisclosed model with undisclosed assumptions is simply an attempt to imply some superior knowledge. Rather like the chiropracter giving himself an official sounding title and hanging impressive looking certificates on his wall.

And the reason that investors trust those claiming this superior knowledge is similar to the reason the patient with the chronic back pain trusts the faith healer. Both want to believe that someone has some insight the rest of the world lacks, that someone can play Yoda to our Luke. That somehow the world is a less uncertain place, that at least someone has control.

Sorry people, but it's scary out there. The guy with the numbers with many decimal places probably knows less than you think.

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