Post earnings announcement drift topic has been widely discussed since it was noted for the first time in 1968. Since then, many authors have tried to answer simple questions, e.g.why does it exist, or where the imperfection of the market which prevents equity prices from adjusting to earnings announcement immediately is, and so forth. There is no definite answer to these questions so far and I believe there never will be one as market is to me more of a "creature" reflecting dynamic human behaviour as a crowd and the technical description [1] of its functioning cannot cover every possible nuance.
I have several motivations for writing this thesis. Firstly, I would like review current and historic literature. It is important to understand how the knowledge has developed and how the perspective at the problem has changed. Considering it is well observed phenomenon and human mind has been always curious, the volume of papers that has been written is copious.
Secondly, given I am interested in exploiting new profitable and simple investment strategies, my next motivation is therefore different compared to majority of papers. I would like to scrutinize a method how the post earnings announcement drift can be harnessed in reality, without having to undergo complicated calculations and portfolio creation as suggested in most of papers (this is going to be discussed in more detail in the next chapter).Simply put, I am not asking why, but how. Such method of exploiting post earnings announcement drift is used by Dreman and Berry (1995). Dreman had been using this method already before the mentioned paper and is known as Low P/E investing or contrarian. Others use expression value investing, firstly introduced by Graham and Dodd.Basically, the question is whether I can use this strategy in connection with earnings surprises. I will get closer to the point in the next chapter as well.
Questions I want to answer are stated below:
Is the research done by Dreman and Berry (1995) still valid?
Can we use Low P/E equities with positive earnings surprise to enhance return of the portfolio?
Do stocks with different P/E ratios within same industry react asymmetrically to surprises in earnings announcements?
Do positive surprises for high-P/E stocks reinforce the market perception of "best," and negative surprises on low-P/E stocks reinforce the perception of "worst"? (Dreman and Berry 1995)
Is low P/E of an equity affecting analysts' ability to make unbiased earnings forecasts?
III. Key definitions, identification of the key variables (independent, dependent, confounding) if necessary
P/E
Earnings surprise
PEAD
Growth equity
Value equity
High P/E
Low P/E
Cumulative abnormal return
SUE
IV. A section demonstrating the significance of the research and the how the knowledge gap is being addressed
During the last decade we have witnessed turbulent times in world's financial markets, starting with a burst of dotcom bubble continuing with a credit crunch which now has resulted into sovereign debt crisis in countries with developed stock markets. Due to these circumstances many investors have earned small or close to zero, if not negative, return on their investments in equities and basic concept of diversification did not hold during the credit crunch in 2007-2008, when, regardless of asset class, prices collapsed. Therefore, by understanding investors' behaviour combined with contrarian investment strategy, my dissertation should provide better way of allocating resources into equities, hence more effectively preserving value of investment and offering higher returns with lower risk.
From the academic point of view, my dissertation will put into test findings of previous studies. It is vital to scrutinise, whether implications drawn from other studies are valid in a "real" environment, where investors usually don't behave in accordance with theories but are rather driven by fear and greed, e.g. investors like to hoard into equities which are currently "fashionable" and are causing exaggerated increase in prices of these assets. Also I would like to put into test study done by Dreman and Berry (1995).
Literature review
The purpose of this chapter is to summarise and discuss the literature on the Post Earnings Announcement Drift. It provides a general understanding of PEAD and a genesis how the knowledge gap has been addressed. At the beginning (mid 70s-90s) when Efficient Market Hypothesis "ruled" the world of finance, researches focused mainly on explaining the PEAD from technical perspective, i.e. wrong research models, effort to explain it within terms of CAPM model (actually by misspecification of this model), or transaction costs. But with time as new paradigm has emerged, behavioural finance, researches have begun to look at PEAD in; I would call it a psychological and "human" way, i.e. taking into account human behaviour, accepting possibility of inefficiency in the functioning of market.
The Nature of the Post-Earnings Announcement Drift
Ball and Brown (Autumn 1968) were the first authors to note on a sample extending back to the 1950s that after earnings are announced, estimated cumulative abnormal returns (CAR) continue to drift up for good news and down for bad news firms. This relation implies that earnings information already publicly available can be used to predict abnormal equity returns. This phenomenon is termed as a post-earnings announcement drift, or standardised unexpected earnings (SUE) effect. Bernard and Thomas (1989, 1990),Foster, Olsen, Shevlin(1984),Freeman, Tse(1989), andRendleman, Jones,Latané(1982) confirm findings of Ball and Brown(1968). Even most recent research (e.g. Liang(2003),Mendenhall (2004),and Narayanamoorthy(2003))continue to document this phenomenon. Hence post-earnings announcement drift (PEAD) became a statistically and economically significant anomaly.
However, there are several explanations why PEAD exists but none of them is definite. Ball(1992) suggests there are three, possibly related, explanations:
Inefficient information processing by the market.
Efficient information processing in the presence of significant transaction costs.
Misspecification in the measurement of abnormal returns.
He concludes that most likely explanation would be information processing costs or market inefficiency.Bernard and Thomas (1989) in their paper conducted series of tests on PEAD over the sample period 1974 to 1986, in which they provided evidence which casted doubt on CAPM misspecification as an explanation for PEAD. They assumed that CAPM misspecification may take several different forms:
Risk measurement.
Misestimation of systematic risk.
In other words it is misestimation of beta, which describes how equity price reacts to a risk unspecific to a company. Results of their study fail to support the Ball, Kothari, and Watts (1988) suggestion that beta shifts might explain a large proportion of PEAD. Their study also dissents with the BKW hypothesis that a strategy based on PEAD, long in good and short in bad news companies, would have a positive beta, hence performing poorly in bear markets. In fact, the standard unexpected earnings (SUE) strategy yielded consistently positive returns in both bull and bear markets.
Exclusion of risk factors other than systematic risk.
Bernard and Thomas were not able to find any evidence supporting the view that SUE strategy is risky and if it is, then there is little evidence surfacing in the form of losses whose cost could plausibly be commensurate with the value of the supposed risk premium.
Other misspecifications.
These could be a failure to allow for market imperfections such as taxes. If pricing is affected by difference between ordinary and capital gains tax rates, then a "dividend yield effect" would exist in stock returns. However, results of Bernard and Thomas (1989) study showed that differences in dividend yields between the high and low unexpected earnings companies are too low to possibly explain any significant proportion of the drift.
Another reason for a PEAD, again tested by Bernard and Thomas(1989), might be:
Transaction costs
If this is a reason for PEAD then the drift should not exceed transaction cost bounds, even for the most extreme values of unexpected earnings. Bernard and Thomas (1989) found that the drift appears to be limited by an upper bound that is approximately equal to roundtrip transactions costs for the individual investor. The bound also tends to vary across firm size in the same pattern as transaction costs do. On the other hand, Bernard and Thomas did not find strong evidence that abnormal returns to short positions in bad news stocks exceed the abnormal returns to long positions in good news stocks, as would be predicted if restrictions on short sales play a role in causing the drift.
Nevertheless, this explanation is difficult to support because it raises several difficult questions, according to Bernard and Thomas (1989).
Why does the trading continue throughout the post announcement period?
Why don't specialists or other market makers move the price to the "appropriate" level upon the first trade after the earnings announcement?
Why is the drift not eliminated by traders who face no commissions and can bypass the specialists' bid-ask spread?
Why would transaction costs necessarily cause underreaction to new information, as opposed to simply introducing noise in prices?
If transaction costs cause the drift, why is so much of it concentrated around the next quarter's earnings announcement?
Failure of market to recognize fully the implications of current earnings for future earnings.
Bernard and Thomas (1989) surmise that finding that the drift is concentrated around the next quarter's earnings announcement might be a reflection of market prices that fail to recognize fully the extent of serial correlation in seasonally differenced quarterly earnings. In other words, if a company announces surprise in earnings in quarter t, the market seems to be positively/negatively, depending on a nature of surprise, surprised in days surrounding an announcement for quarter t+1. Result is consistent with Foster (1977) evidence that estimates of unexpected earnings which ignore such autocorrelation [2] are more highly correlated with stock returns than proxies that do reflect the autocorrelation.
Bernard and Thomas conclude their research by expressing the possibility that market prices fail to reflect the full implications of current earnings for future earnings, but once such a discrepancy exceeds a certain threshold, there are sufficient incentives for speculators to trade until it is reduced. Coexistence of some traders who are either uninformed or unsure about whether the price fully reflects past earnings information, and informed speculators who can exploit the others only at some cost may be the precondition for this explanation.
As a follow up on the Bernard and Thomas (1989) paper, same authors (1990)put under scrutiny above stated hypothesis - market prices fail to reflect the full implications of current earnings for future earnings. Specifically, the hypothesis that prices fail to reflect the extent to which the time-series behaviour of earnings deviates from a naive expectation: a seasonal random walk, where expected earnings are simply earnings for the corresponding quarter from the previous year [3] . This would mean that market prices can be modelled; hence the reactions of prices to future earnings are predictable, just as the forecast errors of a naive expectation model are predictable (Bernard & Thomas, 1990). Their results confirmed this hypothesis to a high extent. They were able to predict with a significant degree of accuracy the three-day reaction to future earnings and information about the historical time-series behaviour of earnings. Furthermore, they were also able to relate the relative magnitudes of the future reactions to the autocorrelation structure of forecast errors based on the naive seasonal random-walk earnings expectations. Interestingly, Bernard and Thomas(1990) found a negative relation between unexpected earnings of quarter t and the abnormal returns around the announcement of earnings for quarter t + 4. This paper is significant, firstly, because it relates the signs and magnitudes of reactions to subsequent earnings announcements to the historical autocorrelation structure of earnings. Secondly, it creates several added obstacles to disagreements that the drift might be explained by flaws in the methodology used to estimate expected returns.
These two papers from early 90's basically summarise all the knowledge and research known at that time.
However, in a recent paper by Johnson and Schwartz (2000), they replicated study by Bernard and Thomas and documented that profit opportunities identified by them, which are connected with simple strategies (long good news, short bad news equities) designed to take advantage of the PEAD have been minimised. On the other hand, the drift still persists mainly among the smallest companies in the NYSE/AMEX. Reason for this is that:
Cost of arbitrage is high.
Little or no analyst follows them.
Low price.
Brown and Pope (October 1995) study wasn't able to entirely eliminate the possibility of forms of market irrationality, but it suggested for the first time that the drift phenomenon is at least partially related to risk and measurement error differences across unexpected earnings portfolios.
Kim and Kim (2003) argue that most of the PEAD observed in prior studies may be a result of using misspecified models and failing to appropriately adjust raw returns for risk. Using earnings data from I/B/E/S for the period 1984-1999, they constructed a risk factor related to unexpected earnings surprise and created a four factor model, which builds on the one proposed by Fama and French (1993, 1995) consisting of three factors [4] . By adding the fourth factor, there is a remarkable improvement in explaining PEAD, i.e. the cumulative arbitrage return over the 60 trading days subsequent to a quarterly earnings announcement is economically and statistically insignificant. However, those calculated by three factor model are still significant.
The risk factor is related to the notion that investors know that there will be a possible surprise compared to the expected earnings when the next period's earnings are announced. The degree of the risk of an unexpected earnings surprise is conditional upon the company's information environment, because the equity price response to the unexpected earnings surprise can be different according to the degree of information uncertainty (Kim & Kim, 2003). Proxy for the information environment is defined as a standard deviation of analysts' earnings forecasts for the most recent quarter. Companies with zero standard deviation are thought to be the most transparent ones. The risk factor is then calculated as follows: 5 portfolios are created based on standard deviations of earnings forecasts; then companies are reassigned into 3 groups based on type of earnings surprise (negative, zero, or positive); daily returns of each portfolio are then computed for the period starting two days after the quarters announcement day and ending one day after the next quarter's earnings announcement; in each of 5 groups return on the negative earnings surprise portfolio is subtracted from return on the positive earnings surprise portfolio; this is called by Kim and Kim zero-investment portfolio that represents the earnings surprise risk factor conditional on a given information uncertainty category, and average of such five portfolios is unconditional earnings surprise risk factor. Conditional earnings surprise risk factor is highest for companies with least information uncertainty (standard deviations of earnings forecast is zero) and is decreasing with increasing information uncertainty. According to Kim and Kim, the reason is that an investor is less prepared for the shock if there is some earnings surprise, because before an announcement there had been a uniform consensus.
Kim and Kim then use traditional way of measuring PEAD, i.e. constructing SUE (standardised unexpected earnings) portfolios. This way doesn't take into account actual forecasts by analysts, but uses a model based on a historical data for past 24 quarters before estimating earnings.
Exploiting the PEAD through contrarian investment strategies
Contrarian investment strategies are based on exploiting mispricing of equities through various market ratios.
Study by Berry and Dreman (1995) covers period from 1973 to 1993 and used earnings estimates from Abel Noser data base (not a SRW). They found that analysts' errors have an asymmetrical impact on high- and low- P/E equities. Dreman and Berry tested two sets of price response to earnings surprises. First, an event trigger: a positive surprise on a low-P/E equity, or a negative surprise on a high-P/E one. Second, a reinforcing event: a surprise which reinforces current perceptions of best and worst equities, which result in a lesser impact on equity price movements compared to event triggers. Positive surprises for "worst" equities (lowest P/E quintile) result in significantly above-market returns but have a far more moderate impact on "best" equities (highest P/E quintile). Negative surprises on best equities result in significantly below market returns, with only a minor impact on worst stocks. Berry and Dreman also identified PEAD and suggest that it takes at least five years for an equity price to revert to the mean, with low-P/E equities outperforming and the high-P/E equities underperforming the market. Their observations are consistent with the PEAD observed by researchers stated in above section. Their findings indicate that: "Equity prices, like analysts' forecasts, do not fully adjust to new information quickly. The price drift they observe may indicate a corrective reaction to significant mispricing. Thus, they believe that the mispricing or overreaction occurs prior to the measurement of the event occurrence (earnings surprise) and the corrective process or underreaction occurs following the event."Dreman and Berry called this idea a Mispricing-correction hypothesis (MCH). MCH also predicts that surprises should have a little net effect on the middle P/E quintiles.The MCH further suggests that the rationalityof investors is often suboptimal because of thestrong influences of behavioural phenomena in ahigh-risk and uncertain environment in whichinformation processing is complex.
Interestingly, Dreman and Berry showed evidence for the findings of Bernard and Thomas (1990), andAbarbanell and Bernard (1992), which claimed that analysts appear to underreact to recent earnings reports, based on positive autocorrelation in quarterly earnings surprises extending over three or four lags (Bernard and Thomas documented this positive autocorrelation only for the first 3 quarters). Dreman and Berry then inferred from Abarbanell and Bernard's results that this kind of outperformance would carry on possibly up to fourth quarter after the initial surprise.
Figure Nonannualized market-adjusted quarterly returns for positive and negative surprises (Berry & Dreman, 1995)
Dreman and Berry also examined whether the observed performance differential is attributable to analysts' tendencies to systematically misforecast earnings on one class of equities versus another, as being suggested byLakonishok, Shleifer, and Vishny (1994). The conclusion was a denial of the hypothesis.
Yalcin (2008) using ex post returns as a proxy for expected returns and size-controlled analyst coverage as a proxy for the rate of information diffusion, showed on a sample from 1980- 2004 that contrarian portfolio returns decline monotonically with increasing rates of information diffusion.
Yalcin also showed asymmetry that the impact of gradual information diffusion is more distinct among glamour equities (high P/E ratio)than value equities (low P/E ratio). He basically didn't find any significant cross-sectional return variation among value equities as grouped by different information diffusion level. On the contrary, analyst coverage seems to be more important among glamour equities, supporting the view that investors are more prone to decision biases when it comes to pricing hard-to-value glamour equities for which information is relatively more ambiguous (Yalcin, 2008). Furthermore, according to Yalcin growth equities with low rates of information diffusion have returns significantly lower than those with higher rates of information diffusion.Yalcin concludes that his paper gives weight to the idea that expectation errors may play a role in the way investors set security prices.
Another anomaly that has received a great deal of attention in the finance literature is the value/glamour anomaly. Many studies have found that a strategy of investing in value stocks (i.e. those with relatively low market-to-book ratios, P/E ratios or past earnings growth) produces higher returns than investing in growth stocks in the U.S. as well as in international markets. Researchers have offered a variety of reasons for this performance difference. Fama and French (1993) argue that higher average returns on value stocks merely compensate for the higher risk they bear; value stocks have positive loadings on a factor related to relative distress. On the other hand, Lakonishok et al. (1994) and other studies argue that value strategies earn higher returns because these strategies exploit the suboptimal behaviour of the typical investor. Investors irrationally extrapolate past earnings growth, thereby overvaluing companies that have performed well in the past, and undervaluing those that have performed poorly.
La Porta,Lakonishok, Shleifer, and Vishny (1997) showed that value stocks have significantly higher earnings announcement returns than glamour stocks for several years after portfolio formation.
Behavioural approaches
Before I discuss particular approaches in detail I would like to briefly introduce behavioural finance as a building block for this section. Behavioural finance is built on two main pillars. First, cognitive psychology which simply said means how people think, and second, limits to arbitrage. Furthermore, it admits that investors as group don't have to act rationally and that they don't necessarily maximize their utilizations. This is contrary to Efficient Market Hypothesis which has been used for numerous researches and is a building block of modern finance.
In the table below we can see most common objections to psychological and fully rational approach with regards to asset pricing.
Objection to psychological approach
Objection to fully rational approach
Alleged psychological biases are arbitrary
Rationality in finance theory requires impossible powers of calculation
Experiments that generate alleged psychological biases are not meaningful
The evidence we possess does not support rational behaviour
It is too easy to go theory fishing for psychological biases to match data ex post
It is too easy to go theory fishing for factor structures and market imperfections to match data ex post
Rational traders should arbitrage away mispricing
Irrational traders should arbitrage away efficient pricing
Rational investors will make better decisions and get richer
Irrational investors will bear more risk and get richer
Confused investors will learn their way to good decisions
Accurate investors will learn their way to bad decisions.
Apparent return predictability is spurious, so psychological models of predictability are misguided
Apparent return predictability is spurious, so rational models of predictability are misguided
Table Common objections to the psychological approach to asset pricing and parallel objections to the fully rational approach. Source: (Hirshleifer D. , 2001)
There are several cognitive biases, but I will briefly describe only those most often used in the literature as an explanation for PEAD.
Heuristics: rules of thumb. We use them to make the decision-making easier, but as things get complicated or change, they can lead to suboptimal investment decisions.
Overconfidence: people are overstating their abilities. For example when forecasting earnings.
Representativeness: underweighting long-term averages. Investors or people in general tend to put too much weight on recent experience. It is also known as the "law of small numbers." For example if an equity had several positive earnings surprises it could make someone believe that future earnings announcement will be again a positive surprise and as a result the prices gets inflated, P/E as well and if earnings surprise is not positive it may have a very adverse impact on the return.
Conservatism: people tend to be slow in adapting to changes. This cognitive bias is in contradiction with the previous one, because when the change occurs, investors might underreact (conservatism). But if this pattern occurs for long enough, then they will adjust and possibly overreact, because they underweight long-term average.
Moving forward, these cognitive biases are incorporated into behavioural models. They are usually divided into two groups; those based on beliefs and those on preferences.
Barberis, Shleifer, and Vishny (1998) built a model that incorporates two biases which contradicts each other: conservatism and representativeness. Firstly, when there is a positive surprise, investors react slowly and therefore later on, returns will be higher. This causes PEAD. Secondly, when there are numerous good earnings announcements in a row, people will overreact (representativeness). Naively, based on a small number of observations investors would begin to think that it is going to be like this forever and that a company is growing strongly. Unfortunately, such behaviour will bring lower returns and in the end a reversal, most probably triggered by a bad news.
To incorporate such ideas into a model, BSV assume that investors base their earnings expectation either on mean reverting regime or a trending regime. Mean reverting regime captures the conservatism bias and the trending regime capture representativeness bias.
Another model from this group was built by Daniel, Hirshleifer, and Subrahmanyam (1998) (2001). They looked closely at the interpretation of private information. They draw a connection between an investor who does his research on a company and overconfidence stemming from this. DHS then reason that PEAD arise because of self-attribution bias: public news which is in line with investor's research strengthens his confidence and adverse public news is given less attention and the investor's confidence is unchanged. Hence, on average overconfidence is followed by stronger overconfidence and as a result generating momentum.
Barberis and Shleifer (2003)built a model based on positive feedback trading. This means that investors are more keen to buy equities which have recently gone up, e.g. after a positive earnings surprise. Since investors are still buying after such a good price, the return keeps on moving in the direction of news. Subsequently, the return will be too low and reverse. This positive feedback trading is based on representativeness, because investors extrapolate few series of good/bad news.
I will not describe models based on preference as they are not used for explaining PEAD.
Further I chose several areas from behavioural perspective which aren't described by above stated models and I believe they should be treated separately.
Investor sophistication
Bartov, Radhakrishnan, and Krinsky (2000)(BRK) investigate in their study whether drift is a demonstration of inefficient processing of quarterly earnings by examining the relation between drift and investor sophistication. They hypothesise that PEAD in equity prices should be most pronounced for equities held mainly by unsophisticated investors who misperceive the process that underlies earnings to be a seasonal random walk. On the contrary, mispricing should be least pronounced for equities largely held by sophisticated investors who characterize correctly the process underlying earnings.
They used institutional holdings as a proxy for sophisticated investor. The reason is that they are experts in gathering and processing public information. On the other hand, other investors are unsophisticated as they primarily use information in the financial press and intuition rather than performing rigorous analysis of financial statements. According to BRK, using institutional investor holdings as a proxy for the holdings of sophisticated investors have two weaknesses. First, institutions that follow index investment strategies cannot be considered sophisticated investors (this problem tends to bias results of BRK study towards null hypothesis). Second, section 13(f) of the Security and Exchange Act of 1934 [5] applicable in the USA, does not cover holdings of insiders, individuals, raiders, arbitrageurs, brokerage firms, and corporations, hence their holdings are not included in BRK measure of institutional holdings. This fact raises the possibility that BRK's tests suffer from correlated omitted-variable problem.
Results of BRK's test on a sample of NYSE/AMEX listed equities during the period 1989-93 yield mixed results. They found that institutional holdings variable is important in explaining the drift and the price responses to subsequent earnings announcements. This variable is negatively correlated with equities' returns. Moreover, BRK also controlled for firm size and transaction costs. Their results show that explanatory power of institutional holdings variable is greater than control variable, i.e. firm size. Transaction costs turned out to be insignificant explanatory variable of the drift after incorporating institutional holdings variable. Presuming that institutional holdings is a valid proxy for investor sophistication, BRK's finding imply that the trading activities of unsophisticated investors should be a cause of the predictability of equity returns after earnings announcements. However, tests evaluating this idea yielded only mixed results, i.e. institutional holdings variable as a proxy for investor sophistication in terms of incorporating earnings information into equity prices in a timely fashion is not so strong. BRK conclude that this may be a result of liquidity or other constraints (e.g. diversification concerns) on the investing activities of many institutional investors. Underlining of this indefinite conclusion is work written by Hirshleifer, Myers, et al. (2002) in which they show on large database of individual investors' trades, that there exists no clear evidence that nonprofessional investors drive PEAD. On the other hand, e.g.Cai, Kaul, and Zheng (2002) and Griffin, Harris, and Topaloglu (2003) suggest that institutional investors might not be as sophisticated as expected, because high number of them are simply momentum chasers, i.e. not making investment decisions on fundamental basis.
Battalio and Mendenhall (2005)approached the topic of investor sophistication, or better to say how sophisticated investors process information, differently. Data they used was from the period between 1993 and 1996 and included equities traded on NASDAQ [6] . The main variable was an initial trade size around earnings announcement. Their results indicate that different investors, identified by a trade size, seems to make their buy and sell decisions on a basis of different information sets. Investors with small size appear to make their decisions on less sophisticated information than those opening large trades. Indirectly we could assume that institutional investors are those with large trades. Moreover, on average: "small traders ignore earnings signals based on analysts' forecasts and respond to signals of a less accurate time-series model. On the other hand, large traders use a more complete information set that incorporate time-series signals along with other information reflected in analysts' forecasts." (Battalio & Mendenhall, 2005).
Ke and Ramalingegowda (2005) improved BRK's research in a way that they focused on institutions which are having high portfolio turnover and highly diversified portfolio holdings - so called transient institutions. These should be able to exploit PEAD. Besides this type of institutions there are also dedicated and quasi-indexing. Both of them have long-term holding periods, i.e. low turnover. This doesn't mean they are not aware of PEAD, but they are not exploiting it.
Ke and Ramalingegowda found evidence on their sample from 1986-1999, that transient institutions earn significant abnormal returns by exploiting PEAD. In absolute terms an average quarterly abnormal return was 5.1% (22% p.a.) after transaction costs. Despite this high abnormal return, the PEAD arbitrage is not transient institutions' main trading strategy. It represents only 23% of return momentum-driven ownership changes.
Anyway, such activity helps to reduce PEAD. Ke and Ramalingegowda further conclude that "for firms where transient institutions trade most heavily to exploit PEAD, a larger portion of the implications of current earnings for future earning is immediately reflected in the contemporaneous stock price and a smaller portion of the implications of current earnings for future earnings is reflected in the returns around the subsequent four quarterly earnings announcements."
Capacity to process information
Another interesting point of view on processing of information from a human perspective was studied by Peng and Xiong (2006). It is well observed (e.g. Kahneman (1973)) that "attention is a scarce cognitive resource". If we want to focus on one thing we necessarily need to substitute cognitive resources from other tasks.
Given a vast amount of information being spout at investors every day and the inevitability of limited attention, investors have to process information selectively. This then creates space for inefficient information processing. Peng and Xiong (2006) built a model which showed that limited attention led to category-learning behaviour, i.e. "an attention-constrained investor tends to allocate more attention to market- and sector-level factor than to firm-specific factors". It may happen that investor totally ignores all the firm-specific data. For example, during the Internet bubble period, companies that had changed to dot.com name without any fundamental changes in strategies earned significant abnormal returns around their name change announcements (Cooper, Dimitrov, & Rau, 2001). It may also be a case for high P/E equities, when investors pile into high P/E firms just because they are in a fashion without considering firm-specific fundamentals and when negative news is being announced, e.g. lower earnings than forecasted, investors suddenly realise implications for their holdings and growth expectations.
This model built by Peng and Xiong capture three features of asset return co-movement observed.
Return correlations between firms can be higher than their fundamental correlations: this is, according to Peng et.al explained by the interaction of the investor's category-learning behaviour with his overreaction to the processed information.
Across different sectors, a negative relation exists between the average return correlation of companies in a sector and their equity price informativeness. If a sector has higher information processing efficiency, investor allocates relatively more attention to firm-specific information. Hence, the companies' equity prices are more informative about their future fundamentals
Over time, as information technology improves, investors' attention constraints become less binding and they can allocate relatively more attention to firm-specific information.
These three features have strong potential to explain the PEAD.
Experimental studies have shown that the trait of overconfidence is particularly severe in
those faced with diffuse tasks that require difficult judgments but provide only noisy and
delayed feedback (see Einhoen, 1980). The fundamental valuation of financial securities is
a good example of this type of difficult task, one that becomes even more challenging when
investors have limited attention. We model overconfidence as the investor's exaggeration
of her information-processing ability. As a result, the investor overestimates the precision
of her information, in a way consistent with other overconfidence models in the literature.3See, for example, Kyle and Wang (1997), Daniel et al. (1998), Odean (1998), Bernardo and Welch (2001),
Gervais and Odean (2001), and Scheinkman and Xiong (2003).
Herding
This part of behavioural approaches reflects behaviour of analysts therefore could be included in the part dealing with analysts, but given the nature of this explanation I believe it is better suited to be discussed within this section.
Olsen (1996) hypothesized that 'the positive bias and poor accuracy of published earnings estimates are attributable to the common, normal, and widespread human desire to conform, or "herd" '. According to Olsen, earnings tend to have a large random component, hence the quality of forecaster's estimates is difficult to appraise by comparing them with actual outcomes. Therefore he concludes that analysts tend to be judged more by the degree to which their forecasts conform to those of their colleagues.
Olsen suggests that herding has two distinct effects: it reduces the dispersion of the distribution of forecasts, and it increases the mean of the distribution. He also assumes that since herding creates positively biased earnings estimates, herding should lead to abnormally low returns when equity prices readjust to the negative earnings surprises. Additionally, perceived equity risk varies directly with the dispersion of analyst's earnings forecasts (see Malkiel and Cragg 1980 and Farrelly and Reichen-stein 1984).
Figure Distribution of Analysts' EPS forecast (Olsen, 1996)
With increasing forecasting difficulty the herding effects become more intense and so historical equity returns are expected to appear abnormally low for equities presenting more earnings forecasting difficulty.
Olsen studied overconfidence and herding by comparing actual earnings with forecasted distributions which tend to be tight as a result of overconfidence. If actual earnings fell into the tails of distribution with higher than normal frequency, it means that herding exists.
Olsen used 520 companies over the period 1985-87. Results of his study confirmed his hypothesis. He concludes that:
'Herding behaviour leads to more optimistically biased earnings forecasts and reduced perceptions of risk as earnings become more unpredictable. On balance, this relationship results in abnormally low returns for equities with more uncertain earnings stream.'
Two of the most well known recent studies using this approach are Barberis, Shleifer and Vishny(98) and Daniel, Hirshleifer and Subrahmanyam (98). The former uses the representativeness heuristic (tendency to view events as typical or representative of some specific class) and conservatism (slow updating of models in the face of new evidence) of investors to explain underreaction to earnings announcements and at the same time overreaction of stock prices over long horizons (debondt and thaler 85). The latter uses the so-called self-attribution bias to explain the same phenomena.
In another study by Cooper, Day, and Lewis (2001), they didn't exactly approach topic of herding, but conclusion serves well to support the idea of herding. They developed a ranking system of analysts' performance based on:
The timeliness of their earnings forecasts.
The abnormal trading volume associated with these forecasts.
Forecasts accuracy.
It is worth to mention that standard ranking approach is based on survey evidence. According to these authors, lead analysts, which were identified by their ranking system, have a greater impact on equity prices than follower analysts. Furthermore, they provide evidence that "analyst's forecast revisions are correlated with recent stock price performance, suggesting that security analysts use publicly available information to revise their earnings forecasts." (Cooper, Day, & Lewis, 2001). What this means is that, over time some analysts build up a reputation of being a leader, which stems from e.g. having better access to company information, being more accurate and in the end being timelier than others. Based on this other analysts, which are less good are following the leader and revise their forecasts in accordance with revisions of the leader.
Weakness of this research is that it was conducted only on companies in two industries:
High-tech companies that manufacture semiconductors and printed circuit boards
Low tech companies in the restaurant industry.
The clustering of analysts' forecasts following a forecast release by the lead
analyst is consistent with the reputation-based herding models of Graham
(1999) and Trueman (1994). Graham finds that investment newsletters herd
following the release of market timing advice in the Value Line Investment
Survey. Trueman shows that high qualityanalysts are more likelyto deviate
from the consensus, which is consistent with Stickel's (1990) finding that
Institutional Investor All-Stars are less likelytorelyon consensus forecasts than
other analysts. Similarly, Lamont (1995) finds that the magnitude of deviations
from consensus forecasts increases with a forecaster's age. He argues that
analysts with track records have less incentive to herd since their true ability
can be inferred more accurately.
Impact of analysts on PEAD
When we are researching PEAD we cannot omit impact of analysts as they are ones who provide investors with initial input on the basis of which investors make their decisions. I will firstly address the question if there's a difference in PEAD effect if we use e.g. SWR to estimate earnings or actual estimates by analyst. Later I will discuss whether analysts are actually reflecting implications of current earnings in their future forecasts.
Source of a forecast
Livnat and Mendenahall (2006)address in their paper following questions:
Are there differences in the magnitudes and patterns of abnormal returns generated in portfolios formed on competing measures of earnings surprise?
And, if so, what causes these differences?
They showed that PEAD effect is larger when using analyst forecasts and actual earnings from I/B/E/S than when using time-series models based on Compustat data (the source for almost all time-series PEAD studies [7] ). It is important to note, that all drift studies share a basic form for estimating the earnings surprise: actual earnings minus a forecast of earnings divided by a deflator.
This paper is important in a sense that if researches do not understand how the magnitude of the drift depends on the specification of earnings surprise, they are unlikely to understand the nature of the anomaly. For example, researchers exploring how firm-specific characteristics affect the drift's magnitude may be misled if they use a less than optimal measure of earnings surprise.
Furthermore Livnat and Mendehall (2006) showed that the drift is consistently and significantly larger when using analyst forecast errors from I/B/E/S. They also demonstrated that the pattern of returns around following earnings announcements is substantially different for analyst forecast errors than that previously documented for time-series errors, i.e. hedge returns (long positive surprises and short negative surprises) following a time-series forecast error are negative at the time of the fourth earnings announcement following the surprise [8] . This has made many researchers to conclude that the evident slow reaction to earnings announcements is due to a particular type of investor behaviour: overreliance on the seasonal random walk model of earnings. For analyst forecast errors, however, Livnat and Mendenhall (2006) do not observe negative hedge returns around the fourth announcement following the surprise. Livnat and Mendenhall propose that this result may be viewed as suggesting that some prior explanations for the drift, e.g. investor overreliance on SRW forecasts, may be premature and/or that analyst and time-series forecast errors capture somewhat different forms of stock market mispricing.
Analysts' behaviour
Overall, different studies conclude that analysts fail to fully incorporate information in earnings announcement, hence such underreaction contributes to the post earnings announcement drift. For example Bradshaw, Richardson, and Sloan (2001) show that financial analysts, considered to be sophisticated investors, do not fully incorporate the implications of current earnings for future earnings in their forecasts. Van Dijk and Huibers (2002) link momentum profits in European markets to analyst behaviour. Specifically, they find that analysts systematically underestimate earnings for strong price-momentum stocks, underestimate autocorrelation in earnings growth between consecutive years, and are in general too slow to adjust their earnings forecasts.
In quite a recent study by Zhang (2008), he argues that there exist two type of analyst underreaction to earnings announcements - underreaction in magnitude and underreaction in time. Typically, most of the literature focuses on underreaction in magnitude, allowing no specific role for when analyst forecasts are made. Zhang showed that analysts varied significantly in terms of their responsiveness to earnings announcements and that in general analyst responsiveness had increased steadily over the sample period [9] .In another study written prior to this one by Mikhail, Walther, and Willis (1997), they also document that analysts improved their forecast accuracy as they gain firm-specific experience. Furthermore, Zhang found that analyst responsiveness significantly increased the earnings response coefficient [10] in the event window [11] and significantly decreased the PEAD in the drift window [12] . This result, though, couldn't be explained by the effect of the determinants of analyst responsiveness or by analyst underreaction in magnitude.
Data
The database compiled by Aswath Damodaran who used data from Value Line is used to retrieve a list of companies and their market capitalisations [13] . Each company must be traded at NYSE, AMEX, or Nasdaq and the market capitalisation must be larger than lowest 20% of the sample at the beginning of each year (the market capitalisation data is available only for the beginning of a year). By this filter I exclude companies with small capitalisation, which may be illiquid and their price can be easier manipulated. From the Compustat database I obtained end of a quarter prices and twelve month trailing earnings per share required for calculation of a P/E ratio. The data covers period from January 2001 until December 2011 and yields total of 164 450 end of a quarter company related statistics observations. This number was further reduced by the filter:
Company must have fiscal year end in March, June, September, or December (146 239).
Company must be listed in I/B/E/S database, from which I retrieve mean analysts' forecasts and actual EPS.
In a quarter of a portfolio creation, a company must have a record of actual and expected earnings, as well as P/E ratio greater than zero.
After applying these filters, the highest number of companies involved in a one year holding period portfolio is 2168 and the lowest is 1312. Overall, the file consists of 108 094 end of a quarter observations which represents 3809 companies.
Regarding the choice whether to use actual EPS from Compustat or from IBES, there is certain ambiguity, as they are often not the same. Philbrick and Ricks (1991) came to the conclusion that mean analysts' forecast in IBES is more closely related to actual EPS in Compustat than to actual EPS in IBES. On the other hand however, more recent study by Rozhkov (2000) found out that mean analysts' forecast of EPS is more highly correlated with actual EPS from IBES than with EPS from Compustat. Since my research period begins in 2001 I will rely on Rozkov's conclusion and I will use actual EPS from IBES.
The research is demanding on the data availability and so it is crucial to have access to above stated databases. I overcame this problem by addressing people who were able to help me out with the access.
Methodology
Purpose of this section is to describe the methodology I used and also to emphasize reasons which made me chose one methodology over another. The way how this section is structured is equal to a top down analysis, in which I state what I chose and then become more granular in explaining the reasons.
The methodology is same as the one used by Berry and Dreman (1995) since one of the purposes of this thesis is to scrutinise their results in most recent conditions. The building blocks of the whole research are a calculation of an earnings surprise, and assigning companies into three P/E portfolios. Compared to other papers on PEAD which used statistical forecasting models (mostly ARMA) to estimate earnings from historical data, I used earnings estimates from actual analysts. I believe that this way the human behaviour is captured better as it is more dynamic in reflecting current situation compared to statistical models. And also analysts' forecast may be different from the ones obtained by using statistical models due to behavioural reasons, which I mentioned in Literature review chapter, i.e. herding, heuristics, representativeness, overconfidence, or conservatism. I will now further elaborate on this issue.
Rozhkov (2000) tested several ways of expressing earnings surprise and a significance of them in connection with equity prices reaction subsequently after earnings is announced (5 day period).
Typical way of expressing earnings surprise is through Standardized Unexpected Earnings (SUE). It is generally defined as
Where et stands for earnings announced at time t, Et-1(et) is an expectation of those earnings formed at time t-1, and σ denotes historical standard deviation of the difference between quarterly earnings and their expectation for a given company (usually measured over the previous eight years).
Earnings expectations are derived in various ways. The simplest approach is to assume that the investors expect earnings per share to follow seasonal random walk, which means that they expect a company's earnings in the current quarter to be exactly the same as its actual earnings one year ago. Using this way of estimating earnings expectations is slightly oversimplified as it assumes that investors form their expectations of earnings regardless of any information about the company that has become available during the previous four quarters.
Another approach to establishing earnings expectations, used also by Bernard and Thomas (1989), is to produce statistical forecast of earnings, based on univariate first order autoregressive model in seasonal differences (firstly used by Foster (1977). However, Bernard (1990) shows that there is no difference in results related to PEAD among the two above stated approaches.
To overcome the problems related to simplicity of the seasonal random walk model of expectations, we may use mean analysts' forecasts retrieved from I/B/E/S database. The problem of I/B/E/S database is that it has narrow coverage compared to Compustat. Included companies are mostly large ones Rozhkov (2000).
As Rozhkov points out, "...putting historical standard deviation of forecast errors into the denominator is a statistically reasonable thing to do and also makes intuitive economic sense, i.e. we expect rational agents to be a lot less excited by a 25% increase in earnings when the news comes from a company whose earnings have been historically highly volatile, than when it comes from a company with fairly stable earnings. Nevertheless, defining the earnings surprise in this way and thus implicitly expecting investors to fully and immediately incorporate all information contained in the SUE into the stock prices requires a rather high degree of sophistication from them." We may also see it in financial press when earnings announcement is reported as a change relative to the analysts' forecasts or previous year's performance. This is related by Rozhkov(2000) to known psychological behaviour that people tend to react to more salient news (e.g. big headline news of a massive jump in earnings) than to news that carry a lot of weight (SUE).
Taking into account this notion, I can then measure earnings surprise relative to the forecast or previous year's performance. Rozhkov in his essay put into regression analysis reaction of equity returns and different ways of earnings surprise calculation. It turned out that, using simple values (the ones mentioned at the beginning of this paragraph) in a denominator is much more statistically significant in explaining the reaction after the announcement than standardised values. Moreover, Rozhkov suggests that "... when confronted with two measures of earnings surprise of roughly the same saliency, investors correctly choose to pay more attention to one that has more weight. ..., analysts' forecasts incorporate more (and more recent) information about the firm than its earnings a year ago, and thus deviations from it are more important for re-evaluating the stock."
Relying on above stated evidence and in order to conduct my research in line with Dreman and Berry I express earnings surprises as a difference between actual and expected earnings relative to an estimate. This percentagemay also help me to check for the existence of different misestimating by analysts between companies with high and low P/E ratio.
Where et stands for actual earnings in time t and et*for analysts' estimate.
To create P/E portfolios, I divide the file of companies into quintiles. Middle three quintiles are grouped together as they shouldn't be, according to Berry and Dreman, demonstrating any anomalies and they represent 60% of the sample. This way I create three P/E portfolios: High, Low, and Middle. Furthermore, companies within each portfolio are sorted in regards to the type of surprise, i.e. negative, positive, or neutral. Berry and Dreman did not involve in their research results of a neutral portfolios as they assumed that there shouldn't be any visible effect.
For one year holding periods, I included as portfolio formation periods Quarters 1 to 40. Quarter 1 corresponds to January through March 2001, which means that I create portfolio at the end of March. Quarter 40 corresponds to October through December 2010. For five year holding periods, I used as portfolio formation periods Quarter 1 to 24.
Having created portfolios I proceed to calculate returns. For one year holding periods, I calculate quarterly annualised returns for each of four successive quarters. This way I measure the initial response to the earnings surprise. Returns for five year holding periods are used to examine long-term return behaviour. If a company subsequently shows a missing return it is excluded from the portfolio for the remainder of the holding period.
Results
This section is dedicated to a description of test results. In first part I will talk about general descriptive statistics where I want to check for any anomalies within the distribution. In the second part I will describe results in comparison with Dreman and Berry's research.
Descriptive statistics
In the first set of three tables, you may see descriptive statistics for three P/E portfolios without specifying type of a surprise, i.e. all three types of surprises are consolidated.
Total effect
Only High P/E portfolio is showing negative skewness for the forecast error, which suggests that overall, despite average being almost zero, if there is deviation from the forecast, it is mostly negative (actual result is lower than the estimate). Kurtosis for this portfolio and forecast error is also very high (~6), showing that forecast errors distribution is having fat tails, i.e. more data is lying further from the average. Range of forecast errors is in the middle among three types of portfolios.
Skewness of the total return is equal to almost zero, which means that the distribution around the average total return is well balanced. For the first two quarters it is negatively skewed reflecting tail of the distribution increasing from negative returns. And for the second two quarters, it is positively skewed. Kurtosis is slightly negative, which could mean that the distribution has very thin tails (in other words it is flat), hence higher probability that sample average return could fall further than three standard deviations.
Standard deviation of returns for each quarter is stable. Kurtosis has a tendency to stabilise, increasing from being negative to just above one. I would interpret this as returns are stabilising after the earnings announcement until they reach a return which is similar for all the equities with high P/E and they cluster around the average. On the other hand if I look at the range of returns for each quarter, then the range is smaller for first two quarters than the last two. It's quite puzzling what could be an explanation.
q1
q2
q3
q4
Total
forecast %
Mean
0.0160
0.0188
0.0228
0.0202
0.0648
0.0029
Standard Error
0.0197
0.0195
0.0218
0.0211
0.0406
0.0189
Median
0.0262
0.0179
0.0158
0.0185
0.0656
0.0157
Standard Deviation
0.1246
0.1236
0.1379
0.1333
0.2566
0.1198
Sample Variance
0.0155
0.0153
0.0190
0.0178
0.0658
0.0144
Kurtosis
-0.1928
0.1062
1.0765
1.2232
-0.2408
6.0695
Skewness
-0.4465
-0.3211
0.2490
0.1537
0.0976
-1.3952
Range
0.5332
0.5454
0.7221
0.7075
1.0987
0.7051
Minimum
-0.2846
-0.2895
-0.3054
-0.3038
-0.4650
-0.4832
Maximum
0.2487
0.2558
0.4168
0.4037
0.6338
0.2219
Sum
0.6398
0.7539
0.9122
0.8072
2.5934
0.1162
Count
40
40
40
40
40
40
Confidence Level(95.0%)
0.0398
0.0395
0.0441
0.0426
0.0821
0.0383
Table Descriptive statistics of 1 year holding period portfolio: High P/E + Total effect
The Mid P/E portfolio is exhibiting least extreme/volatile statistics. Forecast error is slightly positive skewed, with kurtosis edging towards 1. Standard deviation of the forecast error is negligible, only something below 5% compared to 11,98% for the High P/E portfolio, which also isn't very high number. The range is the lowest from the group.
Contrary to High P/E portfolio, skewness of Mid P/E return is negative throughout each quarter. On the other hand kurtosis is always positive, same as for High P/E, with growing tendency. Kurtosis of the total return is better than High P/E portfolio, in a sense that it is positive, hence lower chance of wide flat distribution.
Standard deviation of the total return is just below 20% (High P/E is ~25%). Same as for High P/E portfolio, standard deviation for each quarter is very stable. The range of return in first two quarters is, as in the High P/E portfolio, smaller than in last two quarters. But the difference between these ranges is not as significant as previously; in previous portfolio the maximum sample return exhibited large jump, which wasn't a case for the Mid P/E portfolio.
q1
q2
q3
q4
Total
forecast %
Mean
0,0227
0,0173
0,0165
0,0164
0,0621
0,0420
Standard Error
0,0152
0,0153
0,0161
0,0166
0,0312
0,0074
Median
0,0250
0,0134
0,0148
0,0156
0,0715
0,0428
Standard Deviation
0,0962
0,0968
0,1018
0,1051
0,1975
0,0470
Sample Variance
0,0093
0,0094
0,0104
0,0111
0,0390
0,0022
Kurtosis
0,4100
0,6785
0,9282
1,1488
0,5698
0,9292
Skewness
-0,3799
-0,3997
-0,2107
-0,0724
-0,1078
0,5484
Range
0,4653
0,4781
0,5287
0,5568
0,9549
0,2225
Minimum
-0,2483
-0,2599
-0,2568
-0,2574
-0,3948
-0,0533
Maximum
0,2170
0,2181
0,2719
0,2994
0,5601
0,1691
Sum
0,9075
0,6916
0,6610
0,6555
2,4829
1,6816
Count
