Chart: Distributions of the daily returns and their best fit Power Law alpha exponent for EURUSD, S&P500 and natural gas
The increasing number of financial markets participants start to understand that applying models based on normal distribution can be disastrous to their investment performance.
Pareto distribution based on the Power Law may be a better alternative.
Still, various financial assets may follow Pareto distributions with different parameters, especially different alpha exponents.
Above you can see a chart of probability densities of daily returns for three assets: EURUSD, S&P500 index and natural gas, together with the alpha exponents fitted to them.
The alpha exponent describes the concentration and fatness of the tails of the distribution, which can be seen here: WolframAlpha - (1/x)^2.5062, (1/x)^2.078, (1/x)^1.6326, from 0 to 50
[ R code ]