A book review on Amazon provides a prickly rebuke to Mandelbrot and Hudson’s new theories on finanical risk:

Because the two main assumptions of modern finance are flawed, all related models are flawed as they understate risk. If such models understate risk, they actually overprice stocks and underprice options, and also understate the capital financial institutions should hold to withstand market risk.

If the author had stopped there, I would have given him a 5 rating. However, such a rebuttal of finance theory would make no more than a great essay. Instead, he attempts to build an entirely different edifice of modern finance over 300 pages. And, his theoretical foundation lacks any robustness. That’s why I call it a castle of cards.

Mandelbrot builds his edifice of modern finance on two new parameters that would replace the mean return and volatility of return or standard deviation (mean and standard deviation being the parameters defining a normal distribution). His first parameter is Alpha, derived from Pareto’s Law, is an exponent that measures how wildly prices vary. It defines how fat the tails of the price change curve are. The second one, the H Coefficient, borrowed from a hydrologist named Hurst, is an exponent that measures the dependence of price changes upon past changes.

Well, what is wrong with these two measures? He confesses at the end of the book that no two individuals calculate the same Alpha and H Coefficient when using the exact same historical data! Apparently, there is no one established way to calculate these two parameters. The divergence between the various methodologies can be huge. Using one method, you could derive Alpha and H coefficients that suggest a stock is not risky, using another method you would reach the opposite conclusion. So, after reading nearly 300 pages of intense theories you get that their own foundations are at this stage nonexistent. If Alpha and H are mathematically not replicable and well defined, you can’t apply his multifractal geometry model in any meaningful way.

I haven’t read the book yet, so I’ll wait before commenting, but I thought the reviewer provided some excellent points on the inherent flaws in risk calculations, worth noting here.