To stipulate those prices and dividend are cointegrated is to claim a stable relationship between these two long-run variables.
In other words, these two series move together. So much so that there is no permanent gap between prices and dividends. In the long run, the error term of the relationship linking prices and dividends is zero.
If prices and dividends are not co-integrated, this means that there is a permanent gap between price and fundamental value in the future dividend rebate model.
Therefore, the price does not return to the base value, which can be interpreted as traces of inefficiency.
However, it should be noted that the integration between prices and dividends does not make it possible to draw a reliable conclusion about the efficiency of the markets.
As a matter of fact, in the context of efficiency, prices and dividends should form a stable relationship. But integration also means being able to predict from past dividends and prices that are hard to reconcile with productivity.
The sense of causality between prices and dividends is essential here. If prices do cause dividends, it is possible to predict dividends that remain consistent with efficiency relative to past prices and dividends.
However, if dividends cause prices, the outcome for the efficiency hypothesis remains unclear. As in the case of a return to mean, the results of integration tests between prices and dividends can lead to two opposing interpretations.
On the one hand, integration shows that there is no permanent difference between price and fundamental value, consistent with the efficiency hypothesis. On the other hand, integration encourages the existence of price predictability based on past dividends, which goes against the concept of efficiency.
Case Study Tests
In this second category, prices include not only all information about the history of prices and key variables, but also all publicly available information about the health of companies.
The purpose of event-based study tests is to determine whether prices quickly integrate this variety of publicly available information. Therefore, we test the market's response to publicly disclosed information by analyzing the rate at which the price adjusts to this information.
Much of the event research conducted on daily data shows that stock prices change rapidly based on any publicly available information. On average, prices seem to adjust within the day an event is announced.
It is concluded that the market is efficient in a semi-strong sense. However, the analysis shows that the market did not react quickly to the announcement, which seems to contradict efficiency in a semi-strong sense.
In this case of slow price adjustment, the problem of common hypothesis is highlighted, which is clearly aimed at improving the efficiency hypothesis.
In the face of the slightly different results of these observations and studies, it seems very difficult to come to a conclusion without uncertainty about the efficiency or effectiveness of the market in a semi-strong sense.
Special Knowledge Tests
This third and final category of information efficiency relates to the problem of private information: Are there investors who hold private information that is not reflected in prices?
If so, can these investors expect higher returns than agents without this knowledge?
In general, studies on productivity in a strong sense can be classified into three categories.
The first consists of studies on insider trading, the purpose of which is to determine whether investors with proprietary information are arbitrating.
The second category is based on the analysis of the performance of portfolios managed by professionals; The goal is to determine if they are making abnormal profits.
Finally, the third category consists of various tests, such as the results of experiments carried out in the laboratory, certain insider analysis, or wealth metrics.
Most studies often highlight that proprietary information is held by experts, insiders, and possibly mutual fund managers. Therefore, prices do not fully reflect all available information.
However, in order to reach a clearer conclusion in terms of efficiency, it is necessary to determine whether these investors, acting on the basis of this information, can beat the market, that is, whether they can make abnormal profits.
However, we rediscover the common hypothesis problem. Measuring abnormal returns requires a definition of the norm. In this case, it is impossible to come to a definite conclusion in terms of efficiency.
Adding to these theoretical challenges, we've seen that almost all of the results from productivity tests can be interpreted in two diametrically opposite ways, depending on whether one favors efficiency or not.
Faced with these uncertainties, new approaches to efficiency have been developed. What they have in common is that they are part of a dynamic perspective.
The first approach, the fractal market hypothesis, is based on the existence of differentiated horizons according to investors and gives a fractal structure to the market.
Other approaches focus on the preferences and behavior of market participants. This is particularly true in behavioral approaches to productivity, including the sociological approach and the evolutionary approach.