Bests & Worsts Reviews from Amazon

The author renders a brilliant critique of modern finance theory. He criticizes all its components, including CAPM, the Efficient Market Hypothesis, and the Black Scholes model as being flawed. All these theories rely on two main assumptions. The first one is that market prices are normally distributed. The author, using price charts, demonstrates that market prices do not follow a normal distribution; but instead a Cauchy distribution. Such a distribution is associated with fatter tails. This means that catastrophic drop in market prices happen more frequently than a normal distribution suggests. The second assumption of modern finance is that market prices are independent of each other. Yesterday's prices have no influence on today's. The author makes a case that even if prices are not correlated, their volatility is correlated over time. Thus, big price swings tend to cluster. If a stock moved by 10% yesterday, it is likely it will move by an above average amount today even if we don't know the direction of that change. He calls this correlation of volatility (instead of price) long-term dependence. 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. It will be up to someone else to build upon Mandelbrot's work and render it applicable to investment management by firming up the algorithms to calculate Alpha and the H Coefficient. Only then, will fractal geometry maybe turn out into a feasible challenge to the foundation of Modern Finance. But, at this stage contrary to what Mandelbrot pretends, it is not. If you are interested in investment and finance theory, I strongly recommend other books such as: Robert Shiller's "Irrational Exuberance" and "Market Volatility." Also, Nicholas Taleb's "Fooled by Randomness" is very good. Also, Roger Lowenstein's "When Genius Failed: The Rise and Fall of Long Term Capital Management." This last book is a fascinating account of why a hedge fund failed because it relied excessively on the normal distribution, and used time series that were way too short when building its pricing models.