In literature, there are little evidence about interactions and respective roles of optimism and overconfidence on characteristic variables of cash-flows like mean and variance (Barberis and Thaler, 2003). If it seems obvious that the overconfidence (or underconfidence) bias decreases the risk, one can wonder whether an increasing risk means the absence of the overconfidence bias. Furthermore, if the optimism (pessimism) bias increases (decreases) the mean whatever the risk is, nothing is said about its influence on the risk. In order to clarify the respective roles of each bias on the mean and the variance, a methodology found on a simple binomial model has been chosen which allows us to take into account not only the direction of the trend (overconfidence bias) but also the volatility of asset value (optimism bias). The starting point of this paper consists in explaining the change between two dates of mean and variance of financial cash-flows as a result of two biases: optimism and overconfidence of investors. The main conclusion of this paper is the following one : we clarify the respective impacts of the overconfidence and optimism biases on the mean and variance variables. This result will be very useful in the experimental financial framework in order to foresee for instance the impact of psychological traits on the assessment of a security and then by aggregating these forecasts of the investors to evaluate the value of an asset and finally by aggregating the values of numerous assets to appraise the value of a portfolio of assets.

In the first part, the framework of the model is detailed. In a second part, the overconfidence bias is taken into account. In a third one, the optimism bias is introduced. In a next part, the overconfidence bias is combined with the optimism bias in order to have a more realistic model about investor's behavior. In an ultimate part, the decision-maker of the economic theory without any influence on the market equilibrium is given up in order to consider the case where only a part of investors are the victims of behavioral biases. It allows us to analyze other agent's behaviors like those of managers.