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Multi-fractal Identification of “Sick” Markets: The LIBOR Scandal Case

Journal 36: Global Finance and Regulation

Price behaviors are not smooth – they follow booms and busts in healthy markets. Benoit Mandelbrot (1924–2010) was the founder of fractal analysis in economics. He argued that the “main feature of price records is roughness and that the proper language of the theory of roughness in nature and culture is fractal geometry” [Mandelbrot (2005), 1]. In 1963, Mandelbrot already identified an erratic but regular pattern in cotton price. Particular price changes cannot be forecasted but there are scale invariances. Through an hourly, daily, or monthly scale of time, the shapes of price curves remain the same [Mandelbrot (1963)]. The cause may be that even if there are many bits of information in the market at any given time, the price changes for individual transactions may depend solely on what the traders regard as the most important piece of information. In addition, the individual bits of information may follow a specific distribution with properties leading the price changes to move asymptotically in a specific way [Fama (1963)].

Sharing the concerns of a growing population of experts [Shojai et al. (2010)], the fractal perspective highlights the inaccuracy and the dangers of modern portfolio theory (MPT).