Troy ShuSTAT 520 Small

December 19, 2010Final Project

Post Earnings Announcement Drift: Earnings Surprises and Intermediate Term Stock Returns

Introduction

Post earnings announcement drift is the tendency for a stock to drift in the direction of an earnings

surprise for several months—even years—following an earnings announcement. There have been several

academic analyses on this phenomenon (for example “The Extreme Future Stock Returns Following

IBES Earnings Surprises” by Doyle, Lundholm, and Soliman, 2004) and a strong association between

larger, more positive earnings surprises and higher future returns has been confirmed. We will examine

the post earnings announcement drift effect in the intermediate term, specifically the effect of earnings

surprises on returns during the 30 days after the earnings announcement.

Sample and Methodology

Sample

In this study we use the 500 stocks comprising the S&P 500, a subset of all stocks in the universe.

The S&P 500 is an index of 500 actively traded large capitalization stocks that vary across industries. Our

time frame is January 1, 1998 to January 1, 2009. Each data point in our sample is an earnings

announcement event for a stock in the S&P 500.

Data

Earnings release and median analyst estimate figures were obtained from IBES. Since our time frame

is January 1, 1998 to January 1, 2009, price data from January 1, 1997 to January 1, 2010 for each stock

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in the S&P 500 was downloaded from CRSP to ensure that past and future price metrics could be

calculated for any earnings release date between 1998 through the end of 2008. Also, price data for

^GSPC, the index symbol for the S&P 500, for the same timeframe (January 1, 1997 to January 1, 2010)

was downloaded from Yahoo Finance. GSPC’s price data was used to market-adjust returns as will be

explained in the next section. We will be using the terms GSPC and S&P 500 interchangeably.

Methodology

Our tentative multiple regression model is:

FutureReturn30 = β0 + β1ROC30 + β2Volatility30 + β3Surprise (1)

FutureReturn30 is the stock’s market adjusted return

(StockPrice30DaysFromNow/CurrentStockPrice – GSPCPrice30DaysFromNow/CurrentGSPCPrice)

over the next 30 days after its earnings announcement. ROC30 is the market adjusted rate of change of the

stock’s price 30 days prior to the earnings announcement date. Volatility30 is the price adjusted standard

deviation (SD(Last30Days’Prices)/CurrentStockPrice) of the stock’s price in the last 30 days. Surprise

for a stock on an earnings release date is the price adjusted difference between actual earnings per share

and analysts’ median earnings per share estimate, or (ActualEPS –

MedianEstimatedEPS)/CurrentStockPrice.

Analysis

Constructing the Model

Model (1) was constructed and a plot showing each data point’s Cook’s distance was drawn:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.014842 0.001595 9.308 < 2e-16 ***ROC30 0.030096 0.011114 2.708 0.00678 ** Volatility30 -0.097253 0.021259 -4.575 4.8e-06 ***

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Surprise 0.002179 0.005227 0.417 0.67679

We can see several high leverage points. After removing these points, the coefficients on our model’s

covariates became much more significant and Cook’s distance plot looked like the following:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.014924 0.001593 9.366 < 2e-16 ***ROC30 0.025014 0.011134 2.247 0.02468 * Volatility30 -0.098852 0.021310 -4.639 3.53e-06 ***Surprise 0.167108 0.060626 2.756 0.00585 **

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Plotting the component residual plot:

crPlots(regmodel,ylim=c(-1,1)) #component residual plots

We can see that a transformation of ROC30 and/or Volatility30 will allow our model to fit better.

Surprisingly, neither log nor polynomial transforming the above covariates had much of an effect on the

residual standard error of the model, but log transforming Volatility30 did decrease the residual standard

error of the model slightly from 0.1746 to 0.1745. After log transforming Volatility30, this is what the

resulting component residual plot looked like:

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Next, we checked the least squares regression assumptions:

We see that the mean model and the constant variance assumption hold reasonably well and that there

are no high leverage points. However, the distribution of the residuals does not seem to be normal. This

suggests that we use a nonparametric bootstrap test to estimate the confidence interval for the regression

coefficient of Surprise.

Inference and Interpretation

We are interested in examining if corporate earnings surprises have an effect on stock returns over the

next 30 days after the announcement.

Our current model is:

FutureReturn30 = β0 + β1ROC30 + β2 log(Volatility30) + β3Surprise (1)

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The null and alternative hypotheses are as follows:

H0: β3 = 0Ha: β3 ≠ 0

We build a nonparametric bootstrap test to obtain the 95% confidence interval for the regression

coefficient of Surprise (R code in appendix). The 95% confidence interval for β3 , or the coefficient of

Surprise, is:

lci.beta 2.5% 0.01393616 uci.beta 97.5% 0.3595436

(0.0139,0.3595). There seems to be a significant positive association between a higher Surprise and a

higher FutureReturn30. In other words, for every 1 point increase in Surprise is associated with a 0.0139

to a 0.359 point increase in FutureReturn30.

The interpretation of this confidence interval is tricky because since Surprise is price adjusted, we

must consider both the price of the stock and its earnings per share in order to make comparisons. The

values of Surprise were on the order of 0.001; so for a 0.001 increase in Surprise, the amount that

FutureReturn30 increases is 0.000139 to 0.00359. Using this information, consider an example:

Surprise Stock Price

Actual EPS

Median EPS

Surprise %

0.001 20 1.02 1 2%0.002 20 1.04 1 4%0.006 20 1.12 1 12%

In the above table we hold stock price and median earnings per share constant (all of them have a

price/median EPS ratio, or estimated P/E ratio, of 20) and vary the value of Surprise. The Surprise % is

then calculated for each stock so that we can better understand what a change in Surprise means in terms

of actual percentage EPS surprise. We can see that for stocks with an estimated P/E ratio of 20 that a

0.001 point increase in Surprise is equivalent to a 200 basis point higher surprise percentage. Using our

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confidence interval, this means that, ceteris paribus, a 20 P/E stock with an earnings surprise 200 basis

points higher than another 20 P/E stock will in general have a 1.4 basis point (0.014%) to a 36 basis point

(0.36%) higher 30-day return. In reality, earnings surprise percentages vary a lot more; let us compare a

20 P/E stock with a Surprise of 0.001 points to one with a Surprise of 0.006 points. In other words, we are

comparing a stock with a 2% earnings surprise to one with a 12% earnings surprise, respectively. Since

Surprise has increased by 0.005, the stock with the 12% earnings surprise will in general have a 1.4*5=7

basis point (0.07%) to a 36*5=180 basis point (1.8%) higher future 30-day return than a stock with a 2%

earnings surprise. Of course the relationship between percentage earnings surprise and 30-day returns will

vary based on the P/E ratio of the stocks being compared, but the positive association remains.

Let us look at a quantile regression:

qmodel=rq(Future30 ~ ROC30 + log(Volatility30) + Surprise,data=data2,tau=c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9));plot(summary(qmodel));

We can see that the positive association between Surprise and FutureReturn30 stays relatively

constant across the many different actual FutureReturn30 that each stock experiences.

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Conclusion

There is a significant association between larger, more positive earnings per share surprises and larger

returns that the stock experiences in the 30 days after the earnings announcement. We first removed

several high leverage points and transformed our original model to ensure that the mean model

assumption of least squares regression held. Our hypothesis that EPS surprise has a significant effect on

future returns was supported by a bootstrap test to find the 95% confidence interval for the regression

coefficient of Surprise and by a quantile regression of our model.

Researchers have proposed several explanations for the post earnings announcement drift effect. The

most widely accepted one is that market participants under-react to the long term effects of a unexpected

earnings growth surprise. Whatever the reasons, post earnings announcement drift is one of major market

anomalies that support the counterargument to market efficiency theory.

A consideration for future studies includes the observation that our model seems to behave differently

for positive Surprise than for negative Surprise as evidenced by the Surprise component residual plot.

Perhaps fitting a new model for positive only EPS surprises would allow us to examine the effect of

positive EPS surprises on future returns better than our generalized model for both negative and positive

EPS surprises. A future study could also incorporate more covariates into the model, such as a company’s

market capitalization, to control for effects outside the true influence of EPS surprise on future stock

returns.

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Appendix

#bootstrapdata = read.csv("C:\\Users\\Troy Shu\\Documents\\School\\Penn\\2010\\

courses\\stat520\\project\\java workspace\\STAT 520 PEAD\\finaldata.csv");

#removing high leverage pointsdata2 = data[-15405,];data2 = data2[-16955,];data2 = data2[-9373,];

#set number of bootstrap samplesnumboots = 500;#set the sample sizeN = length(data2$Surprise);#create vector to hold bootstrapped betasbetas = c(rep(0,numboots));

#for each bootstrap samplefor (i in 1:numboots) {

#sample with replacement from original student sampleindices = sample(1:N,replace=TRUE);

#regressregmodel = lm(Future30[indices] ~ ROC30[indices] + log(Volatility30)

[indices] + Surprise[indices],data=data2);

#get the beta for Surprise and storebetas[i] = coefficients(regmodel)[4];

}

lci.beta = quantile(betas,0.025)uci.beta = quantile(betas,0.975)

lci.betauci.betamean(betas)

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