This study examines the relationship of stock price movement and earnings announcement surprises. More specifically, we examine how earnings surprise impacts stock price on the day of the earnings announcement, how stock price reacts immediately following earnings surprise announcements, and the post-earnings announcement drift phenomenon that follows the initial price movement. Our finding indicates that using signal theory; we can adequately predict the rough shape of the price curve prior to and following the earning announcement surprise. We believe that this work lays a sound foundation for further research in the future.

Introduction

There is a large body of research on the return pattern around and after earnings announcement. Most studies conclude that a surprise in the earnings announcement leads to abnormal returns in the period following the announcement. This period is most often the trading days from the day after the announcement up to a couple of months after the announcement. In the academic literature the abnormal return pattern is called post-earnings-announcement drift. The drift is in general positive for positive earning announcement surprises and negative for negative earnings announcement surprises. Therefore, studies claim that investors under-react to the information embedded in the earnings surprise. If investors would incorporate the information fully at the time of the announcement, no post announcement drift pattern should appear.

From earliest works of Ball and Brown (1968), numerous studies have been done on delays on a firm’s price responses to earnings announcement. However, specific studies on investor’s reaction appear in Bernard and Thomas’s seminal study (1989), which provides some explanation to the problem. Investors fail to understand the characteristics of the serial correlation in earnings. They prove that investor reliance on a naïve seasonal random walk earnings forecasting model provides some explanation for the post announcement drift. For the decile of stocks with the most negative surprise, they find an abnormal return of -2% up to 60 days after the announcement.

Mikhail, Walther and Willis (2002) find that the significance of the drift decreases with the aggregate experience level of the security analysts that cover the stock. Relating this to Bernard and Thomas, it could be argued that more experienced analysts understand the implication of the current earning on future earning to a higher degree than less experienced analysts.

Bernhard and Thomas also found a size effect in the drift. A smaller market capitalization leads to more significant drift. Controlling for this and other effects, Mikhail, Walther and Willis found that the effect from analyst experience was persistent.

Research has also been conducted on other announcement patterns. Bulkley and Herrias (2002) investigated the returns subsequent to profit warnings. They found no evidence of abnormal returns after the initial reaction.

Kvist and Åberg (2002) make use of the reliability theorem to explain and predict stock price reactions around profit warnings. The theorem states that investors will overstate the value of information with relatively low reliability while understating information with relatively high reliability. In their sample of Swedish stocks they find that most profit warnings leads to investor under reactions. They also find that proxies for information reliability can predict the return pattern subsequent to a profit warning to some extent. Due to the similarity between profit warnings and earnings announcement surprises, their findings is in line with the research on post-earnings-announcement drift.

The post-earnings-announcement drift is intriguing since it is one of the few persistent market anomalies that researchers have not been able to attribute to solely inadequate risk adjustment. In fact, Fama called the post-earnings-announcement drift the “Granddaddy” of market anomalies.

To our knowledge, there has been no academic study that investigates the entire shape of the return pattern around earnings announcements. Making use of signal theory we can characterize the return pattern around earnings announcement surprises by six parameters.

Signal Theory

The above equation taken from signal analysis theory, models the step response of a second order system.

The initial effect in the equation explains the initial period of drifting before the announcement actually occurs. Higher initial level variable denotes higher return from t-30 prior to the reaction actually begins.

The offset effect is the variable that explains how far apart the beginning of the reaction and the earnings surprise day is. The more negative the offset value is, the earlier the reaction started prior to the actual announcement date.

The magnitude effect is the actual size of reaction starting from the earning announcement date. The higher the magnitude effect is, the bigger the stock price reaction is.

Wn, Wn, and Zeta are all variables that explains the shape of the curve and how it oscillates. Wn is the natural frequency. Wd is the damped natural frequency. When Wn and Wd is higher, it denotes that the curve oscillation frequency will be higher before the curve finally settles down. Zeta is the dampening ratio that has to do with how quickly the curve flattens out, as well as the shape of the curve itself. The higher the zeta, the slower the curve will settle back into its true price.

These six variables together form the shape of our curve according to the signal theory. Together, they form the equation that hopefully depicts the curve that describes the relationship between stock price reaction and earnings announcement surprise.

Data

To collect our data we used FACTSET (predominantly the IBES Database) and Datastream.

Collection Methods

Our first challenge was to gather historical data on earnings surprises dating back to the mid-80s. We wanted to have data that stretched across a relatively long period of time, covering both up and down markets. We hold the untested belief that earnings
surprise reactions are effected by the economic environment (recession, boom etc.), and we felt that a wide time frame would neutralize this effect.

FACTSET's report wizard allowed us to compile earnings surprises for roughly 100 companies dating back to the mid-1980s, and provided critical identifies (ticker, exchange, surprise date) which we used as inputs for Datastream. As many companies have posted earnings announcement surprises at several occasions during this period, our data set is comprised of approximately 600 earnings announcement surprises.

Surprise %

Our definition of Earnings Surprise is the relative difference between a reported positive earning and the consensus estimate at the time of the announcement. We include data from companies that posted an earning surprise (reported earning/consensus – 1) in the range between 30% and 400%.

Negative surprises could also have been considered but we argue that the factors driving patterns around negative surprises might be different than factors that can explain patterns around positive surprises. We therefore chose to only study positive surprises. The surprise range was set so that we would capture substantial surprises while leaving out extreme data on the upside.

Dates

Once our list of surprises was collected we sought the price series surrounding each surprise date. We decided on a 30 day period both backward and forward to examine. Although other papers have examined longer time horizons, we felt that 30 days captured the surprise reaction that we are interested in. Longer periods would mean a higher risk of incorporating other events in the data window that significantly influence the stock price of the firm. The effect from the earnings surprise would then be more difficult to detect.

Regression Analysis

We chose the below list of explanatory variables to explain each parameter of our curve. Our hypothesis are listed below. Despite our reasoning we regressed our complete set of chosen explanatory variables on each coefficient.

Explanatory Variables

From Datastream and FACTSET, we sought explanatory variables. Factors which we believed could affect our co-efficients. Explanatory variables such as P/E, Beta, Volatility, Earnings Growth, # of Analysts etc. were collected for each earnings surprise incident. In the final regression we only used those explanatory variables for which we had adequate data. Many variables we would have liked to measure dropped out of our analysis such as # of Analyst Estimates

Variables that we used for our explanatory regression were:

1. 1-Year Share Price Growth

2. 10-Day Abnormal Return

3. Earnings Surprise $ Value

4. Earnings Surprise %

5. Price to Earnings Ratio

Offset

Offset is the time horizon difference between the start reaction time of our model and the actual earnings surprise date. We predicted that the magnitude of the actual earnings surprise will be a good predictor of this offset. The reason is that the bigger the surprise is, the less the market was able to foresee prior to the announcement. The less the market was able to forecast, the later the “chain reaction” that our model predicts will start, and the less the offset time will be.

Magnitude

We predicted that price to earning ratio and 10-day abnormal return will be good predictors for the magnitude of price reaction. The reason that price to earning ratio will be significant in predicting reaction magnitude is apparent with the definitely of price to earning ratio. For those stocks with high price to earning ratio, the magnitude of reaction is naturally higher because of the earnings surprise will change the valuation of the stock to a greater extent. In addition, the 10-days abnormal return is a useful indicator in predicting magnitude because whatever was already reflected in the market does not get reflected again. Therefore, the stocks with higher 10-day abnormal return are observed to have less of a magnitude of reaction after the actual earnings surprise occurs.

Wn

Wn is the natural frequency. It is a response variable that helps to determine the shape of the curve. Both the wn and wd has to do with how the curve oscillates. We do not believe that any of our predictor variables can sufficiently predict wn because of its complicated nature. The shape of the curve is highly non-linear, and our hypothesis is that our basic variables will not do a sufficiently good job in predicting the shape of the curve.

Wd

Wd is the damped natural frequency. We expect that those stocks with a higher surprise amount to have a higher damped natural frequency as well. The greater the actual surprise is, the bigger the market reaction will be. Following that, the market will naturally have a harder time finding the true price of the stock. Therefore, the curve oscillates more frequently. The surprise factor is what makes the stock price jump up and down more before settling down.

Zeta

Zeta is the dampening ratio that has to do with how quickly the curve flattens out, as well as the shape of the curve itself. The higher the zeta, the slower the curve will settle back into its true price. Zeta and Wd have many of the same functions, and actually their relationship is described by the equation . We conclude that our model’s predictability of the oscillation is insufficient, since there are too many Zeta’s with value of zeroes and ones. Although we do have quite a few significant variables that seem to be able to predict Zeta, we decided that the predictive power of these predictors comes from the extreme nature of our fit itself, and not the actual predictive power of the variables.

Results

Please see Appendix (i) for the Regression output summaries.

Our results were a bit disappointing overall however there were some interesting findings. While a number of our variables did seem to be significant. Low R-Squares plagued our results. We do not think that this was because of an inadequate curve fit. We think that our least squares curve fitting was actually very effective with average correlations of 80%. We do however realize that Earnings Surprises do not always have their expected effect. The market reacts in all sorts of different ways.

The table below summarizes what we feel are our significant findings.

Initial Level

Initial level was our least interesting parameter. It is simply the price level from t -30, to t. We expected the R-Square to be extremely high as there should be no abnormal return before the surprise. Indeed the R-square was 47%, and 2 explanatory variables were significant. There was a notably high t-stat caused by the 10-day abnormal return variable. However if there was little abnormal return, and a steady share price pre-surprise, we expect the significance for this variable to be very high.

Offset

Although the R-Square was low, the dollar earnings surprise amount did predict the offset. Per our original hypothesis this is indicative that the greater the surprise to the market, the later the reaction starts. Many observations had a negative offset. This we think is from whispers and rumors in the market, as analysts catch wind of what could be a surprise announcement. Negative offsets would mean less of a surprise amount come earnings time. This was adequately illustrated by our regression results.

Magnitude

Per our hypothesis, the 10-day abnormal return (market whispers) had a significant negative impact on the actual magnitude of price reaction. The greater the abnormal return leading up to the announcement the less the magnitude after the surprise announcement.

Contrary to our hypothesis earnings surprise percent was not significant.

The Price to Earnings Ratio was also significant in determining the Magnitude of the regression. It is difficult to say why this is so. Perhaps this has to do with the volatility and excitement caused by high growth stocks (with high P/Es). We were surprised by this significant find.

wn & wd

Per our hypothesis, we had a difficult time with wn & wd. However, Earnings Surprise % did have some significance when estimating wd. The Earnings Surprise Percentage influences the shape of the curve but there is no obvious and simple explanation for its exact effect. Wd however does impact Zeta. The higher the wd the higher the Zeta which means the longer it takes for the surprise to dampen and return to normal. Earnings Surprise % seems rightly correlated with wd in this respect.

Zeta

Zeta has to do with the dampening effect of the price shock. The higher the Zeta the longer the shock takes to dampen. We found that 1-year price growth, earnings surprise %, and Price to Earnings Ration were all significantly and positively correlated with Zeta. Our R-Square for this variable was a notable 4%.

Conclusion

Although our results were a bit disappointing we feel that it is worth examining the predictability of earnings surprises using the least squares method further. In this study we only scratched the surface.

Suggestions for further study

Below is a list of further work that could be pursued.

The explanatory regressions could be more rigorous. More variables could be gathered and different variables could be applied for the different coefficients.

One could also test the goodness of the least squares curve fit, and the predictability of the coefficients over time.

A larger sample could be taken. Our sample consisted of only the current S&P100 companies with earnings surprises after 1986. There are a lot more incidences of surprises readily available using FACTSET and other data providers.

New earnings surprise % could be used to collect the sample. One could test the effect of taking larger or smaller earnings surprises. Maybe also negative earnings surprise.

One could test predictability across industries.

Finally one could devise and test trading strategies. Because of the low R-Square and low curve predictability, Long/Short strategies would perhaps be the best bet.

Appendix (i) – Regression Summaries