This research views the concept of risk in the stock market trading by examining the volatility of closing market prices through the ruggedness of information as represented by its fractal dimension. Using the historical data of the closing stock prices of McDonald’s, Bank of America, and AT&T, the researchers applied fractal statistics and equated the riskiness of the stocks to their fractal behavior (i.e. fractal spectrum). An analysis of the fractal spectrum revealed a distinct behavior exhibited by the different stocks. This behavior was further explored by dividing the fractal spectrum into discrete scales that correspond to a shift in the behavior, and performing an intercompany comparison to ascertain the riskiness of the stock.