Mandelbrot Leads to a Better Model?
A recent article in Bloomberg by Mark Buchanan, a theoretical physicist, addresses some of the ideas we discussed in our most recent quarterly letter. Specifically, he further explores the idea of the “unexpected” happening far more often than Wall Street realizes and the use of “fat tails” to best account for what actually happens in markets. Using these and other similar concepts, we believe someone will build a mathematical model that does a superior job of predicting the vagaries of stock price movements (particularly versus today’s prevalent Value at Risk models). But, of course, we also recognize that models are never fully adequate or sufficient, which only highlights the necessity to always remember George Box’s maxim that, “All models are false; some are useful.” Some excerpts from the story:
It seems that we’re complete suckers for the illusion of certainty and the seeming unlikelihood of the unthinkable, even though financial and economic history is one long string of crises. This time always seems different, until it turns out not to be.
Nothing in mainstream “neoclassical” finance theory explains these persistent crises. Almost without exception, economists since Adam Smith have viewed economic systems as being in balance or equilibrium, and as having a natural tendency to return there after any disturbance. In this view, crises can be understood only as anomalies, the consequences of unusual outside shocks.
All this makes for tidy and comforting theory, with simple mathematics, but it fails utterly to account for the most basic market dynamics. Most notably, large and violent events — like the stock market crash of 1987 or the flash crash of last May — happen far more frequently than equilibrium theories suggest. In fact, the pronounced frequency of market upheavals is precisely what’s most constant in economics.
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This particular pattern — scientists describe it as a “fat tail” in the probability distribution — suggests that really big movements are much more common than we might suppose. Thinking of markets in terms of the usual statistics that apply to things like people’s heights or weights or test scores leads to gross underestimation of the risks of rare catastrophes. A credible economic theory of markets — something we do not yet have — would explain why the distribution of market returns shows such a preponderance of large events. It would account for why the mathematical form of this distribution is so uniform in markets the world over. And, importantly, it would explain why markets share the same pattern with many other natural systems.
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Simple ideas of equilibrium and balance may flatter our Platonic prejudices, but they don’t fit the real world. Nothing in the mathematics and physical science of the past 30 years stands out so much as the increasing importance of the irregular, the chaotic and the disordered in every part of the natural world. In many cases, this disorder isn’t simply random, but rather contains important regularities. Finding the expected disorder in the marketplace, and understanding its origins, could give economics a much stronger scientific foundation.
* Value at Risk is defined as a technique used to estimate the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities.