Since the pioneering studies of Mandelbrot, a great deal of interest has arisen for the parameters of fractal finance theory. With this in mind, the present study attempts to examine the risk composition of S&P 500 index industries through panel data analysis. In the modelling of industries’ stock return risk, we use internal and external variables which are related to the companies’ financial ratios and stock market movements. In the first section (sigma-risk) of the study, we model the stock return risk through standard deviation, while in the second section (alpha-risk), the alpha parameter of stable distributions has been used for the same purpose. Panel data analysis results demonstrate that in the sigma-risk model for the healthcare industry, there is a significant internal variable (roa) that negatively affects the industry risk. However, for the alpha-risk model, some significant variables are obtained for the service industry. Another important finding is the changing level of market risk under the two models. While in the sigma-risk model, the magnitude of the market (external) risk variable is high, under the alpha-risk model, we have seen that market risk is relatively low despite the fact that it still has the highest effect on industry risk. JEL Classification: C33, G10, G30, G32