I recently read “The Misbehaviour of Markets” by Benoit B. Mandelbrot and wanted to summarize some thoughts on randomness in markets.
The 1980s and 90s saw many different financial crises, which forced many investors to rethink the concept of risks in financial markets.
1982: Latin America Debt Crisis (Mexican Default)
1987: Black Monday (DOW drops 20%)
1997: Asian Economic Crisis
1998: Russian Default (LTCM)
2000: Dot-com Bubble bursts
The popular practises to measure risks would have let you to believe that any single one of those events is improbable enough to be nearly impossible (and could therefore be ignored from risk calculations), let alone all those improbable events happening in a fairly short time period. But the seemingly impossible happens all the time in financial markets.
These flawed risk models that lead individual investors and institution to underestimate the tail risks of markets rely on these (wrong) assumptions:
- Prices are statistically independent
- Prices are normally distributed
However, these Assumptions that till today are used in economic modelling completely break down in real financial markets:
1_ Prices are not independent. Today does influence tomorrow. Changes in (perceived) fundamentals in Assets can create different reactions from holders. A short term focused investor might sell his stock at the first sign of bad news at the horizon, while an investor with a longer term horizon might only sell his stock after Months or Years of the “bad News” playing out and impacting the company's revenue. (or maybe investor 2 is just less skilled). The point being that different market participants have different time horizons when reacting to fundamental changes, so today's news will impact the market's future decisions.
After the impact of fundamental changes to the Asset's price where it starts to trend in either direction, the psychological effect of Reflexivity starts to kick in where the rising (or falling) Asset Prices make the fundamentals appear less or more appealing to investors, which leads to a feedback loop.
The Reflexivity of rising prices however is not only a psychological effect (/bias) which distorts the investors' perception of companies fundamentals after rising or falling prices. But rising stock prices can also alter the underlying fundamentals of a company itself. A Company might for example gets more cash on hand by selling their now more valuable stock which can be reinvested to strengthen future cashflows, or a companies credit rating can be upgraded which allows cheaper access to credit.
Interestingly, the concept of dependency can also be observed in other aspects of psychology (other than markets) like Sports, where a Basketball player is statistically more likely to hit a third shot if he had hit the previous two shots.
2_Prices are not normally distributed. Economists assume a Gaussian bell shape for the distribution of price changes. This is also false. Price swings are way more extreme than a bell curve model, but rather have very fat tails in the extreme price changes. This hints at the existence of multiple fundamentally different types of randomness:
- Gaussian bell curves of “normally” distributed results. The outcomes of randomness are resulting from being restricted by Biology, Physics or other natural Sciences. For Example: Human Height distribution or global Temperature distribution.
- Wild Randomness (Cauchy): variations are much more harsh and extreme and can't be fit into a bell curve shape. For Example: Unpredictable variation in a coastline or Daily Price changes (Volatility) in Financial Markets.
Analogy: Blind Folded Archer
A blindfolded Archer shoots at a target, and we measure the distance by which he misses (or hits) his target. Most of the time he shoots within close proximity of his target, but once in a while he misses by a huge margin and the arrow travels miles (even close to infinite if the archer is strong enough). A bell curve distribution doesn’t fit this case of blindfolded archery. His biggest misses are thousands of times larger than his average shot. His shots never settle down to a nice, predictable average mean. The variance of outcome is too large, and his scores have infinite expectancy, hence also infinite variance.
The two ways of looking at randomness (of Gauss and Cauchy) can also be found in other fields, and is more a way of looking at the world more broadly than just randomness.
Gauss views big changes as a result of small changes, which can be quantified and estimated, while Cauchy views big events as unpredictably large.
In history, modernists agree on a gauss view and view the world as shaped by millions of different trends and millions of different individuals which ultimately converge to the history of our world while traditionalists view the world as shaped by a few individuals which have had unpredictably large influence on the future of history (Caesar, Newton, Einstein, Hitler)
Market turbulence tends to cluster. Reflexivity at its best: falling asset prices create financial instability, which causes asset prices to fall more, which causes even more financial instability. It's like an avalanche, once started it becomes harder and harder to stop the further it advances.
These periods of clustering of Market turbulence are disproportionally important for the overall returns of an asset. In the 1980 40% of the positive returns oft the SPX500 came during 10 trading days (0.5% of total trading days).
Simply assuming these fat tails away paints a very distorted picture which doesn’t reflect the reality. Big Price changes are not caused by many small moves but rather few huge events, which don’t fit into any bell curve shapes.
This graph illustrates these points:
Volatility clusters and the Standard Deviations display results more similar to the shoot of the blindfolded archer, with extremes, which are many multiples larger and impact the averages disproportionally.
Big price changes are far more common than the standard financial models allow, and almost all blow-ups and financial crisis are results of underestimating these tail risks and using wrong Gaussian mental models to think of these risks.
Thanks for reading!
