Abstract Financial instability estimates the changes of the cost of a monetary instrument. It is a proportion of properties of the Stock prices stability. Fractal investigations are used to assess the money related instability. Forecasting of stock prices acts as an important challenge based on the Random Walk theory. This paper deals with comparison of two years 2013 -2014 and 2017(Jun to Nov) of stock prices. Explain the instability by the method of Box-Counting technique to find the Fractal dimensions of the Geometric Brownian Motion based on the Random Walk defective value. This creates the possibility that Fractal measurement is related with the monetary unpredictability. Its an essential instrument for both money related investigators and Financial specialists.