--------- #1324 - How Politicians Use Math
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- When it comes to math politicians and economists and financial managers do not have a good understanding of reality. They tend to use math to get the numbers they want. Physicists use math and revel at getting numbers they do not want. This was not expected? Why?
- The financial math models currently used on Wall Street grossly oversimplify things. So much so they loose touch with reality. A lot has to do with their use of math as a ‘normal distribution”. This model assumes the events are “ random” in nature. When events are outside a normal distribution they are ignored as outliers, not relevant to what they expect to see. They prefer to view systems in total equilibrium, while the train is going off the cliff. Here are some examples:
- The 2008 financial crisis, Lehman Brothers, and AIG financial firms go bankrupt ( although one was bailed out with our taxes). These firms were using financial models that assessed risk using the Gaussian Curve for a random distribution of the data. This is the same “ Bell Shaped Curve” your teachers used in grade school to grade papers. This always assumed you had a “normal” distribution of students.
- When these models are presented to the mathematically illiterate it results in a false sense of security. Not only will future results not match reality the unexpected result is “ inevitable” . Managers prefer numbers that “ feel good”, so there was no attempts to ask “ why?”
- The Gaussian distribution of truly random events clusters around an average ant tapers off in a predictable way. Above and below the average are “standard deviations” that can be calculated:
------------------- 1 sigma standard deviations around the average include 68% of the distribution of events. An event inside this distribution has a 68% chance of happening.
------------------ 2 sigma standard deviations around the average include 95% of the distribution.
---------------- 3 sigma standard deviations include 99.7% of the distribution. There is only 0.3% risk of the events not occurring inside this distribution around the average. OK, if it is outside 3 sigma it has almost no chance of happening. This is the model that was making elite managers feel good.
- The Gaussian model says that if an event is 100 standard deviations out it has a probability of 1 chance in 10^350 of occurring. That is a 1 followed by 350 zeros. That event is impossible right? If the math had included all the “outliers” in the data we find that the distribution more accurately follows the “Power Law” distribution , not the Gaussian distribution. The Power Law distribution has much longer tails. Looking at this same data we would say the event had a 1 in 100,000,000 chance of happening, not one in 10^350. If enough of these events occur the chances of seeing this event becomes much more likely. That is the way reality works. Rare events will happen, be prepared.
- When this Power Law distribution was used to predict downturns in the market on the Shanghai Stock Exchange the math predicted the market collapse in 2008 and 2009 within a few days of it actually happening.
- Power Law math is much messier so it tends to be ignored. Reality is even more complex than this model so it becomes even more difficult. The challenge becomes to figure out the “most important” ingredients to put in the model and deal with those alone. Simple is better but it has to be right. What causes a Power Law to apply to the model? Here is an illustration of how financial leverage creates greater uncertainties.
- Say you spot an under priced stock. You buy it. Normally a buy would push the price up a bit. Say, you were leveraging on borrowed money to amplify your returns. You borrowed more money to make more purchases. This tends to push the price even higher. Say the bank cuts you off as too high a risk This might force you to sell some of the stock. You might have to sell some other assets prematurely. As prices slide down others might begin selling as well. The amplification cause the tails of the distribution curve to broaden and extend outward with higher and higher risk. The result is a high probability of a crash.
- This same Power Law analysis can be done with CEO pay, with the number of bird sightings to estimate the population of a certain species, with very large firms affecting the market place, with out-of-control growth, with herding behavior of investors, all of these calculate incorrect results with based on the Gaussian models. Power Law models are an improvement but even that complexity is not enough. Thoughtful analysis of what is behind the numbers is needed. Are the important ingredients part of the model? Are outliers part of reality that need to be included? Math is a tool. You need to know how to use it. All models are an approximation of reality. Expect the unexpected to happen.
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