Mandelbrot: Old Formulas Will Not Work in Volatile Markets

Sunday, June 05, 2005

Don't shy away from this post because it states "fractal geometry" in the next sentence (I didn't even when it was our wedding anniversary this weekend), the rest is understandable.
The world's foremost capacity on fractal geometry, Yale professor Emeritus Benoit Mandelbrot, attacks established financial science on all fronts. In his new book "The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin and Reward" he contradicts today's axiom that market prices change continuously according to the bell shaped curve of normal distribution. While most financial theories are based on this assumption, Mandelbrot takes the stance that exactly the discontinuous price jumps on the far ends of the bell shaped curve have the most impact on portfolio performance, but are blacked out in most finance formulas.
Mandelbrot supports his attack on conventional wisdom with the fact that in the 1980's 40 percent of the S&P's profits were gained in 10 days or 0.5 percent of time. Therefore market timing plays a much bigger role in performance enhancement than Nobel laurate Harry Markowitz' Capital Asset Pricing Model may suggest, he writes. Accordingly the formulas of Nobel prize winner William Sharpe (Sharpe ratio) and the Black-Scholes model for option pricing put too much emphasis on the normal distribution of the standard deviation of market prices. Giving examples ranging from the crash of 1987 to several other big-swing days since then Mandelbrot derives the fact that these hefty price changes are not explainable under the assumption of normally distributed price movements.
Following the professor's arguments, these foundations of modern market theory might create a risk in itself because they rely on flawed assumptions that contradict actual history.
Correcting these models Mandelbrot arrives at a much greater possibility of ruin. Current accepted risk-models imply a 1:10 000 000 000 000 000 000 (that is one to 10 billion billions) chance of ruin. No, says Mandelbrot who details that the actual risk of ruin lies in the range of 1:10 to 1:30 when one includes the (not so) irregular big price movements. He concludes therefore that portfolios have to be structured far more diversified than they are now, spreading over a far bigger range of asset classes.
According to Mandelbrot theories that excluding extreme price shifts which are due to a massive change in market participant's expectations enhance the risk of markets as it is wrongly assumed that all risks are perceived correctly. But this might be proven wrong on melt-down days and put more pressure on markets as participants would have to get used to an event that are not taken care of in their risk assessment models. That moment may not be too far away when one monitors the discontinuous price changes in major market indices that almost every day disprove the theory of continuously fluctuating prices between the close and the sequential opening.


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