A Theorem for All Markets
Investor’s and researcher’s Holy Grail is a theorem that explains how markets work. One that can serve as the basis of a realistic and predictable model. The prediction part being the most sought after.
To create this theorem, a person needs a few proven facts. Then he or she can use deductive reasoning to arrive at a logically valid series of steps. From here, a theorem could be declared. So let us begin with a little research on the proven facts of market behavior.
Benoit Mandelbrot, the inventor of fractal geometry, admits that markets like the natural world defy easy explanations. He explains in his 2004 book, (Mis)behavior of Markets: A Fractal View of Financial Turbulence, that markets revert to the mean. The problem is that their path to the mean is very chaotic.
Much of Mandelbrot’s research on markets was derived from more than 100 years of cotton prices. From this, he explains, “Far from being well-behaved and normal as the standard theory then predicted, cotton prices jumped wildly around.” Thus changing the majorities view on market theory.
Edward Thorp, math professor and inventor of quantitative investing, is an interesting person with allot to say on the topic of markets. Besides being a hedge fund manager, he was also a professional gambler. Much of which is discussed in the book, A Man for All Markets. Which is summarized as gambling and investing share a number of key traits. In both, one needs to measure the probabilities of outcomes and then vary the size of their bets based on the calculation.
As a fund manager, Thorp delivered a 20% annual returns for over 30 years trading options. One thing of particular importance is this statement from an interview in 2017, “If we observe various bubbles and disasters we have faced over the last century, most of them have occurred because there was too much leverage.” Thus, bubbles are hard to predict. However, predicting when a bubble will burst is nearly impossible.
Furthermore, Thorp achieved success by following a quantitatively based strategy. In short, he hedged stock warrants due to discovering frequent mistakes with their pricing. The standard practice of options traders today.
Next we have Warren Buffet who is potentially the most successful investor of all time. In his 2018 letter to shareholders, he writes, “The years ahead will occasionally deliver major market declines — even panics — that will affect virtually all stocks. No one can tell you when these traumas will occur.” Later concluding that stocks can be wildly unpredictable over shorter time periods, but predictable over long periods. In effect agreeing with Mandelbrot.
After gathering the synopsis of three market experts, we have the following truths:
- Short term market behavior is very chaotic and impossible to predict.
- Long term (years or decades) market behavior is much more predictable.
- Bubbles occur when leverage is great.
- Declines and panics in the markets will occur.
As a result of these items, the pricing of options can be wrong and opportunities for arbitrage are possible. From here, we can create our theorem. If only it was this simple.
This theorem could be based on several different strategies. One is to simply hold an index fund. Another is to measure leverage or debt within a market in hopes of discovering a bubble about to begin or end. In addition to many more. Regardless of our strategy, the theorem has to be proven outside of testing using a formal verification.
In software development, we prove algorithms in the same manor. This was the inspiration for the present article. Meaning we prove the algorithm is correct without having to test for every conceivable state. Thus ensuring it will give the proper output based upon specific inputs.
The easiest way to visualize this is with driving instructions. Such items are proven based upon existing truths. An instruction such as “turn left on Main Street and you will arrive at your destination,” can be verified by looking at a map. This is the level of correctness we need for our theorem.
The problem is that we are dealing with levels of correctness or probabilities. We can balance risk with potential reward using multiple proven methods — but none are absolute. The question becomes, can we prove that given a market state of X with an investment of Z, a return of Y will be obtained?
I think it is almost possible given a long term market outlook. Maybe possible with certain arbitrage opportunities. Not very likely with short term markets. However, if we can measure the correlation between market leverage and bubbles forming, then prove causation, we could use that to develop a proven prediction.
Conclusion
Thank you for reading. I am interested to know what you think about the potential of building a theorem to predict markets. Furthermore, if this article caused you to think of a person or network, please share it with them. I would really appreciate it. To learn more about building nearly defect free financial software, visit https://toddmoses.com.
