In Behavioral Finance it is observed that often individuals make mistakes in their decisions. Two of the most important phenomena analyzed in behavioral finance are overconfidence and under-confidence

Overconfidence occurs when individuals have excessive security and confidence in their judgment, knowledge and skills. They believe they can exploit all the information they are aware of, overestimating this information and increasing their self-esteem, if their decisions are confirmed at a specific event, attributing this positive result to their abilities. A consequence of over-confidence is an excessive trading activity that often leads to sub-optimal performance. In this regard, Barber and Odean (2000) conducted a study on 78,000 investors from a brokerage firm. The theorists have divided investors into five groups based on trading frequency and have observed that the group's most frequent annual return is around 6% less, net of transaction costs, of the group that trades less frequently . According to Barber and Odean, the low performance of the high level of trading can be explained by the error due to the too much confidence of the individual investor, which leads him to excessive trading. Investors fail to learn from mistakes made in the past and do not tend to correct them over time, but it usually happens that, faced with a substantial loss, regret aversion causes investors to justify the mistake made as a consequence of external factors and causes, unlike when decisions prove to be profitable.

Barberis and Thaler (2003) believe that the attitude of overconfidence generates in individuals too narrow confidence intervals that do not correspond to reality with regard to their estimates, since people underestimate the probability of error of their own evaluations. Furthermore, these people are often led to distort the likelihood of an event occurring, not taking into account the fact that external events occur more frequently than is expected. For example, an event with an 80% probability of realization is estimated as certain and an event with a 20% probability of realization is evaluated as impossible. The phenomenon of overconfidence does not only occur in the financial sphere, but also in legal, engineering or psychology sectors. Within the financial sector it can be used to explain numerous phenomena such as the existence of speculative bubbles or the large number of trades that can occur on a given security. It has been observed that overconfidence occurs more in males than in females and in young age, while it tends to decrease with the passage of time, as individuals with the acquisition of a wider experience develop a process assessment of one's abilities which is more objective. Moreover, empirical evidence has found that this phenomenon is more widespread in activities that do not offer immediate feedback and in those that require theoretical analysis rather than mechanical performance. Overconfidence is an orientation belonging to human nature and is a much more relevant and widespread phenomenon than under-confidence, which is the opposite attitude. Under-confidence occurs when investors show a lack of confidence in the reliability of their forecasts and often tend to underestimate their abilities. This lack of trust can occur especially in situations where the choice to be made is highly complicated or doubtful. These investors renounce making such choices, attributing very low probability of success. For this reason they are inclined to carry out conservative attitudes and to slowly adjust forecasts with the arrival of new information. The phenomena of overconfidence and under-confidence must not be confused with the terms of optimism and pessimism, in fact the excess or lack of confidence in one's choices does not necessarily imply optimism or pessimism about market prospects.

BARBER B. and ODEAN T. (2000). Trading is hazardous to your wealth: the common stock performance of individual investors. Quarterly Journal of Economics, 116, pp. 261-292.
BARBERIS N. and THALER R. (2003). A Survey of Behavioral Finance. Handbook of the Economics of Finance, Vol. 1B, Financial Markets and Asset Pricing. Elsevier North Holland.

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