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The validity of the classical theory of the efficiency of financial markets raises doubts about some hypotheses, since not always in the stock markets the price of a security corresponds to its fundamental value. In fact, a change in prices can depend not only on new information that becomes available, but also on other factors.

Criticism of the hypothesis of rationality
The idea that all investors who operate within a financial market are rational in their financing and allocation choices appears unrealistic. Most of these subjects make their own decisions based on reasonings that deviate from rational decision-making and make their choices in a non-rational way; the analysis of these aspects is often the object of study in psychology and sociology (see the item Behavioral Finance).
Fischer Black (1986) confirms the irrationality of investors through the existence of so-called noise traders; individuals who make their investment decisions by not evaluating and not rationally examining the information available, without having performed the technical or fundamental analysis of a given security, but in a completely irrational and even random manner. Such choices, even in the case in which the noise traders constituted only a minority with respect to the total of the investors, can cause distortions and changes in the prices of the stock and in their level of risk, making them different from those expected.
According to Kahneman and Riepe (1998) there are times when investors tend to deviate from the rational process. These deviations can be defined in three categories including the aptitude for risk, the different formation of expectations and the sensitivity of decisions to the structure of the problem, which do not allow to follow a rational path. A further problem for the sustainability of the efficient market hypothesis arises considering the fact that individual investors are not the only ones operating in the financial markets. Most of the funds are managed by professionals from financial institutions, which are subject to further distortions compared to those of individual investors, as they manage the money of others and have corporate goals to achieve (see Corporate Governance).

Criticisms of the absence of arbitrage
The theory of the efficiency of financial markets claims that in an efficient financial market the prices of securities completely reflect the information available. If irrational investors caused a change in prices, through their random strategies, arbitrageurs would intervene with the task of bringing prices back into equilibrium, thus annulling any kind of variation.
The criticism of the arbitrage hypothesis has been raised because empirical research has shown that arbitrage transactions in financial markets are not without risk, as the theory of the efficiency of financial markets claimed; it is precisely by virtue of the riskiness of the arbitrage strategies that the prices of the securities remain distant from their fundamental value for long periods. In these cases, arbitrage does not perform its function of price correction and fails to guarantee market efficiency.
Barberis and Thaler (2003) identify four different categories of risks related to arbitrage: fundamental risk, noise trader risk, implementation costs and model risk. The fundamental risk is when the publication of new information on a certain security can bring down the price, even if the stock was previously underestimated and far from its fundamental value. To defend themselves against this risk, arbitrageurs implement hedging strategies by negotiating securities that are considered substitutes for the previous one. However, the fundamental risk cannot be completely eliminated because, within the capital markets, substitute securities are hardly perfect.
The noise trader risk is the risk that the deviation of a share price from its fundamental value increases in the short term as a consequence of the behavior of irrational investors (for example due to a pessimism of noise traders, who decide to sell a security already underestimated, causing a further lowering of the price). If the arbitrageurs holding an underestimated stock and subject to such movements would adopt a long-term approach, they would wait for the price of the same to move closer to its fundamental value before selling it, thus realizing profits. However, arbitrageurs, who are often represented by financial institutions that manage other people's money, wait for the price to rise and adjust again to its fundamental value, since individual investors who rely on them do not accept initial losses. This means that the arbitrageurs sell the title even at a lower price than the purchase price, thus accepting the losses.
The third risk factor concerns implementation costs. To activate an arbitrage strategy, the presence of transaction costs (commission or bid-ask spread) must be assessed, which can limit the profits of the arbitrator. Often the subjects who apply the arbitration perform short sale or sale transactions in markets of several states; these transactions are subject to legal restrictions or even prohibited by some individuals (professionals of various investment funds). All the various implementation costs complicate the arbitration mechanism and make it more risky. Finally, with the model risk we underline the fact that arbitrageurs could use untruthful and inaccurate models that can lead them into error (for example estimating that a price of a security is far from its fundamental value, even if the two values ​​actually coincide).
Model risk can therefore cause strong uncertainty in the implementation of arbitrage strategies. The combination of the four risk categories, combined with other factors that are often realized in empirical reality, contributes to setting limits to arbitrage. The inexistence of a completely effective arbitration makes it impossible to correct market distortions, which is therefore inefficient. The theory of limited arbitrage shows that while irrational investors cause price deviations from the fundamental value of a security, on the other hand rational investors often do not have the power to correct such deviations.

Barberis N., Thaler R. (2003). A Survey of Behavioral Finance. In: George M. CONSTANTINIDES, Milton HARRIS, and Ren´e M. STULZ, eds. Handbook of the Economics of Finance: Volume 1B, Financial Markets and Asset Pricing. Elsevier North Holland, Chapter 18, pp. 1053–1128.
Black F.(1986). Noise. The Journal of Finance, Vol . 41, No. 3, Papers and Proceedings of the Forty-Fourth Annual Meeting of the American Finance Association.
Kahneman D., Riepe. (1998). The Psychology of non-Professional Investor. Journal of Portfolio Management, Vol. 24, No. 4.