Multifractal properties of price fluctuations of stocks and commodities

– We analyze daily prices of 29 commodities and 2449 stocks, each over a period of ≈ 15 years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities can be attributed mainly to the broad probability distribution of price fluctuations and secondarily to their temporal organization. Furthermore, we propose that, for commodities, stronger higher-order correlations in price fluctuations result in broader multifractal spectra. The study of economic markets has recently become an area of active research for physicists [1], in part because of the large amount of data that can be accessed for statistical analysis. Markets are complex systems for which the variables characterizing the state of the system —e.g., the price of the goods, the number of trades, and the number of agents, are easily quantified. These variables serve as fundamental examples of scale-invariant behavior —the scaling laws are valid for time scales from seconds to decades. Much interest has concentrated on stocks, where a number of empirical findings have been established, such as [2] i) the distribution of price changes is approximately symmetric and decays with power law tails with an exponent α + 1 ≈ 4 for the probability density function; ii) the price changes are exponentially (short-range) correlated while the absolute values of price changes (“volatility”) are power law (long-range) correlated. Unlike stock and foreign exchange markets, commodity markets have received little attention. Recently, it was found [3] that commodity markets have qualitative features similar to those of the stock market. This similarity is intriguing because the commodity market has special features such as: i) most commodities require storage; ii) most commodities require transportation to bring them to the market from where they are produced; and iii) it is plausible that commodities may exhibit a slower response to change in demand because the price depends on the supply of the actual object.