Enhanced model accurately captures extremes in stock market performance
Enhanced model accurately captures extremes in stock market performance lead image
A new statistical model overturns the persisting assertion that stock market inefficiency is not testable. In fact, after using their model to compare the performance of three global stock markets, two Italian economics researchers conclude that market efficiency as viewed over long time spans stems from “compensating inefficiencies”—extreme upward and downward price spikes.
In Chaos: An Interdisciplinary Journal of Nonlinear Science, Sergio Bianchi and Massimiliano Frezza, both of the University of Cassino, introduce a new twist to the emerging multifractional Brownian motion model of market behavior. They incorporate the measure of Holder pointwise regularity, enabling analysis of how widely sequential data points in a dynamic system vary within a specified time period.
By adding a Holder exponent, the researchers found they could quantify information efficiency and account for fluctuations that result from arbitrage or other market-influencing actions. It also eliminated what might be called the ½ constraint of other fractal stock market models. This cap sets the ceiling and floor for deviations from a smooth curve, such as the familiar one showing the long-term rise in market prices. Spikes above and below are not considered.
By accommodating extremes on short time scales—roughly 21-30 trading days—the enhanced model is more reflective of differing investor behaviors. It enables fine-grained analyses that capture periods of extreme market turbulence, such as the 2007-2009 global financial crisis.
In their article, the authors describe how well the model corresponds to the closing price of the Dow Jones Industrial Average (DJIA) since 1928. The authors also compared the performance of the DJIA, Germany’s DAX, and Japan’s Nikkei since 1992, finding the DAX to be the most efficient of the three.
Source: “Fractal stock markets: International evidence of dynamical (in)efficiency,” by Sergio Bianchi and Massimiliano Frezza, Chaos: An Interdisciplinary Journal of Nonlinear Science (2017). The article can be accessed at https://doi.org/10.1063/1.4987150 .
