Scientific working paper explains the influence of four selected cognitive biases regarding the investment behaviour of German private shareholders. In detail, it contains a theoretical treatment, as well as an empirical impact study of these four biases. Starting with the definition of cognitive biases in chapter 2, the term German private shareholders will be defined afterwards. Then the relevance of psychology in the stock exchange and the consumer behaviour from the behavioural finance perspective is analysed. The theories regarding the capital market prices developed by Fama, Hansen and Shiller give different perspectives towards the need of psychology in the stock exchange. Taking account of the different approaches, a model is developed to illustrate investment behaviour of private shareholders which is influenced not only by cognitive biases and social-psychological effects but also by rational behaviour. The subsequent experiment was executed on a diversified compositionof six private shareholders and investigated the following four biases: anchoring effect, dilution effect which describes the influence of non-relevant information, framing effect which is the different valuation of two terms, and the disposition effect. This is measured by the influence of acquisition prices on the sell decision. For this purpose, an experiment with simulated situations of the stock exchange was developed. The subjects of the experiment had several response options that resulted in either rational, bounded rational, or irrational behaviour. The results of the theoretical part and of the experiment can refute an entire rationality of the stock exchange and the investment behaviour because every subject was influenced by at least one cognitive bias. Therefore, the experiment determined an influence of cognitive biases, although the strength and quantity varied individually. Besides, no correlation between the cognitive biases was determined, but it can be inferredfrom the experiment that the higher the willingness to assume the risk and the experience on the stock exchange market, the more rational investment behaviour will be. The results of this experiment give a first insight on how cognitive biases might affect rational behaviour on stock markets and how the theory of bounded rationality can explain these biases.