As any investor will know, there are no defined set of rules in financial markets; investment management is a far cry from a hard science where normal distributions and other statistical methods work well. While it’s common knowledge that many concepts in modern finance have massive shortcomings (e.g. Markowitz’s modern portfolio theory and the efficient frontier, Sharpe’s capital asset pricing model, the Black-Scholes option pricing formula), a lot of these Nobel prize winning ideas are still in heavy use by investment practitioners.
Yet, applying statistical methods based on historical data to try and quantify a precise level of risk in financial markets is doomed to fail. The birth of probability is centered around the quantification of risk, which is inherent in different gambling pursuits where there are a defined set of rules and static outcomes. The book by Benoit Mandelbrot and Richard Hudson, The (Mis)behaviour of Markets, aims to provide a new methodology for the way market participants should be viewing risk in financial markets.
They begin by displaying why traditional statistical methods are inept at accurately quantifying risk (e.g. the odds of the stock market crash on October 19, 1987 happening were one in ten to the power of 50, a number so small it basically has no meaning). Mandelbrot and Hudson provide evidence as to why prices in financial markets follow power laws (not a normal distribution) and are fractal in nature (meaning they scale). The authors also introduce a concept of the “H coefficient”, which aims to quantify the influence that past prices have on current prices; essentially illustrating how impactful the concept of momentum is for different asset class.
The book does an excellent job of illustrating why traditional methods do a poor job at quantifying risk in financial markets, but the book lacks a concise and coherent path forward. For financial market practitioners, one of the biggest takeaways would be to combine the theory of scaling and price dependence to create theoretical data sets that more closely resemble potential future price action, as opposed to only relying on historical data for backtests and risk quantification. For non-professional readers the book is a good reminder that risk quantification in financial markets is not an exact science, and many methods that rely on historical data will ultimately underestimate future risks given their inability to accurately model “fat-tail” or “black swan” events.