For years now, financial academia has tried to model the markets and the risks associated with those markets. Nobel prizes have been awarded (Black, Merton and Scholes) and praise has been heaved upon those who have opened up our eyes to the underlying truth of the markets. Modern portfolio and risk management is accepted as a given and goes unquestioned at all the major institutions. There is one small problem, it is all based on a fundamentally flawed assumption, namely that the markets move in a random walk and therefore should behave statistically.
I have not read the books of Nassim Taleb, like The Black Swan, because every time I have read the reviews I have been blown away by how obvious the “black swan theory” was. I never appreciated the real reason why Taleb used this metaphor and I also never understood why he used it to express such an plainly obvious fact of nature, which was that there was always a risk of an outlier event occurring that would destroy the best laid plans. Given my lack of financial training (I’m a scientist) I had no idea that modern portfolio and risk management theory relied so heavily on Gaussian distributions. I have had the “random walk” arguments with several people, but I just didn’t know how much of our financial system was based upon it or how little it accounted for outlier events.
As a scientist with a background in calculating the geometries and electronic structures of molecules, I can certainly understand the allure of Gaussian distributions and a reluctance to abandon them. Ever since the development of quantum mechanics in the early 20th century, humans have been able to exactly calculate the electronic structure of a hydrogen atom (1 proton and 1 electron). We can also get the calculation of H2+ just about right without any serious work. The problem arises when we want to calculate the structure of larger molecules like benzene or DNA. What we usually do is to take combinations of the atomic wavefunctions, mix them together, and iterate until we find a lowest energy configuration given the rules of quantum mechanics. Back in the 1930’s, John C. Slater introduced the Slater type orbital (STO) which was the most accurate representation of the atomic orbitals that would be used as a basis set to build the larger molecular orbitals. There was one problem with the STO, namely, it was an extremely difficult and expensive mathematical problem once the molecule became three atoms or larger. This issue was the “two-electron integral problem” and remained one of the greatest problems in quantum chemistry for many years. (Side note: My graduate level quantum mechanics course was taught by a former student of John Slater, which was pretty cool.)
Slater type orbital
Gaussian Type Function
The solution to the problem was not to find a way to quickly calculated the complicated STO two-electron integrals, but was to approximate the STO’s with a set of Gaussian type orbitals (GTO). These approximations were introduced by S.F. Boys in 1950 and completely revolutionized the way we calculate the properties of molecules. Gaussians have some very nice properties that make them very easy to work with. The biggest advantage being the ability to use a single Gaussian function to represent the product of two separated Gaussians on different centers, thus reducing the number of integrals to be calculated. There are some drawbacks to using Gaussians, but most of these can be compensated for using various techniques. The bottom line is that we still use the GTO approximation today and probably will for the foreseeable future. The infrastructure has been built and there is simply is no viable alternatives to GTO’s.
STO vs GTO
Now back to the markets. Any time I have argued with an academic about using Gaussians in trying to model the market, I have always said that I believe the only reason why they use Gaussians is because they are easy to deal with, at least mathematically. I also try to argue that it is impossible to use any other distribution because it is impossible to model the main driver of market movements (human psychology). After several of these arguments, I now understand that Taleb’s black swan was not meant to convince me. He was talking to the financial academics who cling to Gaussian distributions and will never let them go because without them, they are useless and powerless. Hopefully one of the side effects of this current crisis is that this obviously flawed discipline will finally be discredited by the entire financial world and we can concentrate on building systems and regulations that realistically take risk into account.
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