Wild price swings, business failures, windfall trading profits – these are key phenomena. In all their drama and power, they should matter most to bankers, regulators and investors. – Benoit Mandelbrot
Your mutual fund’s annual report, for example, may contain a measure of risk (usually something called beta). It would indeed be useful to know just how risky your fund is, but this number won’t tell you. Nor will any of the other quantities spewed out by the pseudoscience of finance: standard deviation, the Sharpe ratio, variance, correlation, alpha, value at risk, even the Black-Scholes option-pricing model. The problem with all these measures is that they are built upon the statistical device known as the bell curve. This means they disregard big market moves: They focus on the grass and miss out on the (gigantic) trees. Rare and unpredictably large deviations like the collapse of Enron’s stock price in 2001 or the spectacular rise of Cisco’s in the 1990s have a dramatic impact on long-term returns –but “risk” and “variance” disregard them. – Benoit Mandelbrot & Nassim Taleb
When people talk about Sigmas in terms of disaster probabilities in markets, they’re crazy. They think probabilities in markets are Gaussian distributions because it’s easy to compute and teach, but if you think Gaussian distributions apply to markets, then you must believe in the tooth fairy. – Charlie Munger
Benoit Mandelbrot distinguished between ‘Joseph’ effects and ‘Noah’ effects. Joseph effects – seven fat years here, seven lean years there – occurred when markets were evolving gradually and continuously. Noah effects were cataclysms – the Flood, or the week of September 11 2001, when the New York Stock Exchange closed for five days and dropped 7.5 per cent on re-opening. Because Joseph effects rule the market most of the time, they are what models measure. But Noah effects make and unmake investors. – Financial Times
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