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We examine four European stock indices and the prices of eight major German stocks for indications of psychological barriers. The frequency, (expected) returns, intraday volatility and trading volume of these assets are studied contingent on whether the prices lie within a certain range around round numbers. Our results indicate that psychological barriers do not exist on a consistent basis. It seems that some barriers have disappeared after these anomalies have been published. This discovery is consistent with current literature findings about disappearing stock market anomalies.

The answer to the question of whether there are psychological barriers in stock markets – prices' “exceptional” behavior whenever they are close to round numbers – depends heavily upon whom you ask. From market practitioners' and journalists' viewpoint, the existence of psychological barriers seems to be an obvious fact, as is daily noticeable in the markets. From an academic perspective the matter is much less obvious. Why should market participants' attention – or even excitement – be more intense at certain price levels than elsewhere? Donaldson (1990) and De Grauwe and Decupere (1992) demonstrate that in stock and foreign exchange markets, price levels near round numbers are of special importance to market participants. Donaldson and Kim (1993) ascertain that multiples of 100, and especially of 1000, mark a certain hurdle for the further movement of the Dow Jones Industrial Average Index. They furthermore state that traders interpret the upward movement rebound at such a resistance level as a “market weakness”, whereas breaking through the barrier is seen as a sign of a strong market (and vice versa in a downward movement). Another effect observed when prices break through a barrier is the so-called bandwagon effect, i.e. the phenomenon of prices quickly moving away from the barrier after it has been breached. The bandwagon effect can be explained by the fact that the demand by some market participants increases because others are already purchasing the relevant asset. It is therefore a type of herding behavior. Participants in financial markets try to reduce complexity with the help of simplifying heuristics in order to arrive at decisions even in very complicated situations. According to Mitchell (2001), one kind of simplification is the rounding of arbitrary rational numbers to integers, the so-called clustering. 1 Applied to stock markets, this means that a certain part of the asset pricing process is influenced by the number expressing the price itself. One consequence of clustering being made responsible for psychological barrier phenomena is the so-called grouping effect. 2 Grouping means separating numbers into different groups with the same leading figure. Due to this effect the difference between two numbers within the same group, e.g. 990 and 970, is perceived as smaller than the difference between two numbers of different groups, such as, e.g. 990 and 1010, although the difference is identical. In this view, psychological barriers – being multiples of powers of ten – lie exactly on the boundaries between the groups and are thus of special importance. Behavioral factors are not the only reason why barriers could exist. Option exercise prices also are usually round numbers. Delta hedgers frequently are most active when the option is at the money, i.e. the price of the underlying is close to the exercise price. Thus, purely technical reasons also cause additional trading activity in the underlying asset. From these considerations we can deduce that barriers may exist, but one cannot take their existence for granted a priori. Several studies from 1990 to date have empirically dealt with the question of psychological barriers in major stock indices (mainly the Dow Jones) and foreign exchange markets. However, these studies use daily close-to-close returns of FX rates or stock indices. None of these studies examine single stock prices. This is astonishing insofar as real stocks can be and are traded directly on stock exchanges, whereas stock indices are not immediately traded but rather by index futures and related instruments. Clearly, the existence of psychological barriers in the above sense is connected to the belief in the predictability of stock prices and thus may lead to the possibility of earning abnormal risk-adjusted returns, which is not compatible with the theory of efficient markets.3 Since thousands of articles and books have been written on the topic of efficient markets, we do not intend to review this discussion here.4 We would, nevertheless, like to state that psychological barriers' existence is contradictive to both the market efficiency hypothesis and the assumption of rational investors. From this point of view studies which find evidence for the existence of psychological barriers contribute to the literature on market anomalies. Again, we make no attempt to present a complete survey of this literature here. It deserves particular mention that current studies have documented the disappearance of many anomalies found by empirical researchers: Marquering, Nisser and Valla (2006) show that the weekend effect, the holiday effect, the time-of-the-month effect and the January effect have disappeared after these anomalies have been published. Our paper contributes new methodological aspects to the barrier literature as well as new empirical evidence from European stock markets, which have not been the main focus of earlier studies. Four European stock indices and the prices of major German stocks are examined with respect to the frequency with which they lie within a certain band around the barrier and also with respect to certain return characteristics and volume. Our concept is to use many different statistical approaches to find indications for psychological barriers in European Stock Markets. Some of our approaches are similar to the methods used in existing literature. Additionally, we pursue some new approaches in estimating the intraday variance and in using open, high, low and closing prices for our calculations. To the best of our knowledge, we also are the first to look for barrier effects in single stocks. The next section provides a short introduction to relevant papers on the issue of psychological barriers. Section 3 provides an overview of the data base and the methodology used in our study. Thereafter our study's results in respect of frequencies are presented in Section 4, and in respect of returns, intraday volatility and trading volume in Section 5. The paper is concluded with the presentation of the most important results and a discussion on disappearing anomalies in the last section.

To sum up the various findings of previous sections, stocks and stock indices behave very differently around possible psychological barriers. We are not able to identify systematic behavior by all assets at barriers. There is only scattered evidence, which is in no way at all consistent. Some evidence of psychological barrier's existence can be found in the Commerzbank stock for both barrier levels we examined. We see fragile traces of psychological barriers in all indices at the 1000s barrier level. There are indications of barriers at the 100s barrier level, too, except in the CAC index. In addition to the strong indications of the existence of barriers at the Commerzbank, we see evidence of barriers in the Henkel stock at the 10s level, and weak evidence in Adidas (100s and 10s level), HVB (100s and 10s level) and EON (10s level). The indications for the existence of psychological barriers are less weak for indices than for stocks (with the exception of Commerzbank and Henkel where the significance is stronger than in the CAC 40). This finding is surprising, because traders do have a direct influence on a share's value – contrary to the values of indices. If the fact that the price of an asset is close to a barrier has any influence on the market participants' behavior one would expect to see a stronger reaction in shares than in indices. This is not the case. A possible explanation for this phenomenon may be that only if an asset is widely and popularly followed one can expect to observe traces of barriers. This is the argumentation of Donaldson and Kim (1993). However, we do not find any systematic barrier effect for any barrier level. Thus our main result is there are no consistent barriers in European stock indices and stocks. Another important finding of our study is that some of the barriers found in previous studies seem to have disappeared. This is consistent with current literature findings about disappearing stock market anomalies: Dimson and Marsh (1999) examine the premier stock market anomaly (“small firm effect”) and show that the out-of-sample small-firm premium turned negative — the effect reversed after it was found. Marquering et al. (2006) use Dow Jones Industrial Average (DJIA) data in order to examine how the weekend effect, the holiday effect, the time-of-the-month effect, the January effect and the turn-of-the-month effect have changed over time since they were found for the first time. Most of these anomalies weakened substantially, some of them even disappeared completely. The weekend effect is also investigated by Kohers, Kohers, Pandey and Kohers (2004), who show that this anomaly was existent in 12 indices during the 1980s but it appears to have faded away in the 1990s. All these findings imply that the effects of many anomalies have disappeared. This may be due to increases in market efficiency: Trading oriented market participants, such as hedge funds, who perform statistical arbitrage, can have eliminated the anomalies by trading on them.21 In this regard the publication of certain anomalies is the initial point to the statistical arbitrageurs' activities. Due to the enormous quantitative and creative intelligence of such market participants one can also assume spillover effects to assets that have not been investigated in the initiating publications. In our case this could be the German stocks or the EURO STOXX 50. We believe that the weakening evidence is not mainly caused by the introduction of certain new instruments like ETFs on stock indices. Such instruments are very popular with private investors in Europe. But it is not clear ex ante whether the increasing use of such instruments would rather reinforce barrier effects due to the potential sensitivity of private investors to barriers or rather weaken these since the growing market completeness makes it easier to arbitrage barriers. Additionally the issue of data snooping cannot be overlooked in this context. We follow the argumentation of the disappearing-anomalies literature and see the reason of the disappearing of the psychological barriers in their discovery. In sum we provide a biased view on the evidence for psychological barriers. Although we employ a great number of empirical models in order to find evidence for barriers, the number of insignificant test statistics is by far greater than the count of the significant. Our significant results support psychological barriers, but these barriers are dissimilar in the different indices and stocks. At certain barriers and in some assets only the intraday variances are increased, at other assets and barriers we observe a clearly increased or, perhaps, decreased expected return. It is therefore not at all clear how to form a trading strategy to explore these market inefficiencies. We believe that our findings support market efficiency. The problem with empirical studies about market efficiency is that efficiency of capital markets can never be proven significantly, but only their failure can. Studies with significant results are more likely to be published; conversely, studies without such results are often not published. A lack of published studies with insignificant results could lead to a biased view of the existence of psychological barriers in asset prices and index levels. This problem is called the “publication bias” (or “file-drawer problem”). Psychological Barriers are stock market anomalies which seem to have disappeared in European Indices. Since we wanted to focus on European stock markets, we did not examine other international indices like the DJIA or the S&P. This may be a fruitful topic for future research. Finally, we hope that the reputation of studies without significant results will improve in future.