First of all, it should be emphasized that all productivity tests have one thing in common: any productivity test is a joint test of the efficiency hypothesis and an evaluation model.
At its most serious, the problem is to the extent that it concludes that efficiency cannot be directly tested. It must necessarily be tested in conjunction with a particular pricing model.
Therefore, testing efficiency through a simple random walk or martingale test is already a common test.
Because in this case it is assumed that the price formation model responds to a random walk or martingale type process.
An important consequence is that it is impossible to determine with certainty whether the rejection of the null hypothesis was due to market inefficiency or an incorrect determination of the valuation model used.
On the other hand, if we accept the null hypothesis, it means that the efficiency is accepted. Because in this case, we accept both the effectiveness and the validity of the evaluation model. The second includes the efficiency hypothesis.
Despite this fundamental problem, the results of these tests show that it is necessary and interesting to maintain test efficiency as market professionals change their vision and practice.
Poor Form Tests
Multiple tests of the predictability of returns suggest the need to distinguish between the short horizon and the long horizon. Short-term studies often highlight the presence of statistically significant autocorrelations. Thus, it shows the probability of estimating returns based on past values.
He concludes that, despite their statistical significance, these autocorrelations are economically insignificant in the sense that the existence of short-term autocorrelations does not permit the development of profitable strategies.
Here we are faced with a problem inherent in any productivity research. While econometric tests demonstrate the predictability of returns based on past values, efficiency advocates argue that knowledge of this phenomenon in no way questions efficiency.
Faced with this situation, various authors have tried to test the efficiency hypothesis by working on longer horizons.
One cannot draw conclusions in favor of efficiency by examining only short-horizon autocorrelations. With a simple example, he shows that we cannot observe short-term autocorrelation even if the process is autocorrelation.
To understand this autocorrelation, it is essential to study long horizons.
More specifically, it indicates that if the usual pattern of formation of prices discounting future dividends is confirmed, then we should observe negative autocorrelations over the long horizon.
This testifies to the phenomenon of returns to the mean (average revision) of returns. During the uptrend, returns will follow a decreasing trend to return to their average value. This existence of the mean reversal phenomenon has been confirmed by various authors.
What then does the mean of prices and the phenomenon of return mean for efficiency?
First of all, the return of prices to the fundamental value indicates that returns from past returns are predictable in the period when the mean reversal phenomenon occurs.
Therefore, prices do not follow a random walk and include a temporary static component. However, rejecting the random walk does not mean rejecting the efficient financial market hypothesis.
However, the presence of an average reversal component in prices necessarily causes a (more or less permanent) deviation of the price from the fundamental value.
This questions his hypothesis of equality in all institutions between both price and fundamental value.
Additionally, the longer the price deviation from the fundamental value, the longer the autocorrelations in returns are negative.
The more likely it is to create speculation rules to make abnormal profits. See the phenomenon of return to mean as a source of market inefficiency.
However, as in any discussion of efficiency, we naturally find that the opposite position, namely the phenomenon of return to average, does not at all testify to market ineffectiveness, but rather activity.
Therefore, it suggests that the negative serial correlation observed in long-term returns may be due to changes in expected returns over time.
However, the variability of these expected returns over time reflects the possibility of a variable interest rate incompatible with productivity.
Also, opponents of efficiency insist that the presence of an averaging component in price indicates a more or less permanent gap between price and fundamental value.
Proponents of efficiency, the tendency of the price to return to the fundamental value in this component leads to the confirmation of the long-term efficiency hypothesis.
Indeed, if prices return to the base value, the valuation model is validated in the long run. This model is based on the efficiency hypothesis, acceptance of the model leads to the acceptance of efficiency.
Faced with a rather sterile debate about the predictability of returns based on past returns, the authors focused on the study of the predictability of returns based on other economic or financial variables. These include in particular interest rates, dividend/price ratio.