This paper analyzes two main frameworks that challenge the “mainstream” finance theory and the random walk hypothesis. The first framework is based on investor irrationality and is called Behavioural Finance. The second framework views the financial market as a chaotic system and is called Fractal Theory of a financial market. Behavioural Finance attacks the assumption of investor rationality, thus challenging the conventional finance theories on the micro level. Fractal Theory challenges the EMH and the “macroeconomics” of finance. This paper presents a step towards unifying the frameworks of Behavioural Finance and Fractal Theory. After a review of the relevant literature, a model of the financial market is suggested that rests on the predictions of both Behavioural Finance and Fractal Theory. As a next step, a mathematical algorithm is described that allows to test the financial market for consistency with the presented model. The mathematical algorithm is applied to 10 years of daily S&P500 price quotes, and consistent statistical evidence shows that the predicted fractal pattern reveals itself in the S&P500 prices. The new model outperforms the random walk in out-of-sample forecasting.