Quantum economics – real or fake?
Since I started working in quantum economics, a persistent problem was finding suitable venues for publication. Journals in economics or finance wanted nothing to do with it (the exception was Wilmott magazine), so most papers were published in physics journals like Physica A, which meant that no one working in economics ever heard about them. The field clearly needed its own journal! A few years later, with help from many people and Sage Publications, Quantum Economics and Finance was launched.
While my motivation for co-founding the journal was because I wanted the field to succeed, I'll also admit that there was a selfish interest in that I thought it would give me somewhere to publish my own work - which for some reason often fails to find a home. However it turns out that my papers are so weird, that they are rejected even by my own journal.
The first paper to run into trouble was A Quantum Oscillator Model of Stock Markets". One of the main findings is that volatility over a period T is described by the equation
where x is log price change over the same period, adjusted for average drift. The equation was a prediction from the quantum model, and it turned out to hold surprisingly well for a range of asset types including stock market index price data (see figure below for the S&P 500). The formula is useful because it leads to a minimalistic two-parameter model for the implied volatility surface.
RMS annualized volatility plotted against normalized price change for the S&P 500. The solid lines, from darkest to lightest shades of grey, are for periods of 1, 2, 4 and 8 weeks. Dashed line is the quantum model. Figure from A Quantum Oscillator Model of Stock Markets.What makes the above equation a falsifiable prediction rather than a curve-fitting exercise is that (a) I had no idea it was valid until I tested it and (b) it does not involve any extra parameters, other than a base volatility. Yet when I submitted the paper for review - again, in my own journal! - neither reviewer showed interest in the equation, or its success in modelling empirical price data.
One reviewer in particular wasn't having it. As they wrote: the modeling methodology is not appealing. A mass parameter, a fake Plank [sic] constant, and a frequency are introduced to finally describe a quadratic behavior ... It is hard to believe that a classical model cannot reproduce the same. Am I right?"
The reviewer here was talking about parameters from different parts of the paper which had no effect on the equation, whose sole parameter is the base volatility. (The financial version of the Planck constant simply scales between energy and transaction rate so can be set to 1.) Perhaps they would have found an equation with zero parameters more appealing, less fake?
The paper went to a tie-breaker, who backed publication. Phew!
Next up, Blinded by Science: The Empirical Case for Quantum Models in Finance". The theme of this follow-up paper was that people working in economics and finance systematically ignore - or simply do not see - empirical evidence that doesn't fit their classical assumptions, such as the no-arbitrage principle.
Reviewer 1 nailed the do not see" thesis right off the bat by stating: I do not see the point of the paper." It turned out there was a lot more they didn't see.
The paper brought out the same equation and pointed out that it was a new finding. The reviewer shot that down by saying that many models ... have considered non-constant volatility." They were therefore very confused" by the claim that this was a new result.
On then to Reviewer 2 who wrote that: This stylized fact is well known ... So there is nothing new here ... No, nothing leads to this equation which is a purely arbitrary choice of the author, and nothing guarantees that in practice volatility follows [it] (and it is of course not the case)."
So to summarise, the equation is not a prediction, it's a stylized fact and a purely arbitrary choice which is nothing new and of course not the case and everyone knows it except they don't because it's wrong anyway.
The reviewer then swivels their laser-like focus to the somewhat peripheral topic of music theory, because I had remarked as an aside that the energy eigenvalues of the oscillator have frequency ratios of 1, 3, 5 so the tone produced is a major chord. The reviewer set me straight: it is true that a major chord is composed a the tonic (1), major third (3) and dominant (5), but this has nothing to do with frequencies, only with the position of the notes in the diatonic scale - and actually there are 2 tones between 1 and 3 and 1.5 tone between 3 and 5, therefore the frequency ratios are absolutely not 1, 3 and 5."
It seemed telling that even for this, a reviewer would rather trust their hazy understanding of theory rather than look at something real, like an actual guitar. A major C chord has notes C, G and E. So if you play these notes, it gives a major C chord:
NoteFrequencyRatio to C1
C132.703
G297.9992.996636
E3164.815.039599
The other critiques of the paper were no more coherent. One bizarrely insisted that I had mistaken volatility for its square, the variance, perhaps because they could not see" a square-root sign in front of it.
Apparently there is a new form of therapy called rejection therapy" where people are counselled to deliberately seek out situations where they are rejected, as a way to build robustness and lose their fear of failure. (Actually, it's not that new - when the Greek philosopher Diogenes was once seen begging in front of a statue, he explained that it was so I can get used to being rejected.") Quantum economics has certainly proved fruitful as a way to have my work rejected in new and surprising ways, with untold therapeutic benefits.
On a more serious note, though, I think this shows the difficulty in getting new ideas accepted in science, especially if they are in conflict with mainstream results. I have prior form in this area, since I did my D.Phil. on model error in weather forecasting and found it almost impossible to publish papers which pointed out the limitations of weather models. As I wrote in my 2007 book Apollo's Arrow, a typical pattern was illustrated by one research head who claimed the research both showed nothing new, and flies in the face of most of the available experimental evidence'."
I have no idea who the anonymous reviewers for Quantum Economics and Finance were, and because the paper was rejected I didn't get the chance to respond to them (until now!). But the thing I found strangest about these reviews was that at no point did the reviewers engage with the empirical evidence. It was another example of how experts do not see" data which contradict longstanding assumptions based on classical theory. They just stated (as one put it) that there is nothing new here" and it is of course not the case." But if the equation for volatility is well-known, provide the references. And if it doesn't work, show the evidence, instead of dismissing it out of hand.
The paper's rejection was especially ironic given that it described a number of cases where classical results were widely accepted even when they blatantly contradicted empirical data (see for example here). Where were the skeptical reviews for those papers?
As I may have mentioned, I am in the fortunate position of having co-founded a journal where I can submit this work, and at least get a hearing. Most researchers, especially people who are new to a field, will of course not have that advantage. Which might explain why the field of economics has been stuck in a time warp for such a long time.
As for critics who call the quantum model fake", the country legend Dolly Parton once said I may look fake but I'm real where it counts." In fact Parton put this to the test when she entered unannounced a Dolly Parton look-alike contest at a bar - and lost. To a man. Parton herself came last.
Sometimes to tell if a thing is real or fake, looking isn't enough; you have to listen to the sound it produces.
Which in the case of the quantum model, is a major chord.
Update: The article Blinded by science: The empirical case for quantum models in finance" has since been published in real-world economics review.