Stock Price Reactions to Earnings Announcements
Maarten Alexander Smit University of Groningen
s1842943 Faculty of Economics and business
Oude Ebbingestraat 8 MSc. Finance
9712 HH Groningen Februari 2016
Stock Price Reactions to Earnings Announcements
ABSTRACT:
”More information always equates to less uncertainty, and it is clear that people pay more for certainty. Less uncertainty results in less risk and a consequent lower premium being demanded.” (Foster 2003)
In this quote Foster argues that an information increase results in a decrease of demanded risk premium. In this thesis I will follow this statement to analyze stock price movements surrounding quarterly earnings announcements from the largest Dutch listed companies in the period from 2008 to 2015.
JEL classifications: G12, G14
1. Introduction
Nichols and Wahlen (2004) describe a three step system how earnings announcements influence stock price. The first step is the assumption that current period earnings provide information to predict future period earnings. The second step links expected future earnings to expectations about future dividends. The third step is the intuition that stock price represents the present value of expected future dividends. I will use these three steps to show that earnings announcements information changes investors’ perception of dividends. However, this is not the real value of earnings announcements. The earnings announcements provide increased certainty in the prediction of the future dividends. This leads to a decreasing volatility and a lower discount rate. I will argue that this is the added value of earnings announcements.
The first step of Nichols and Wahlen (2004) states that quarterly earnings announcements contain information which can be used for future earnings predictions. For information to hold value it has to be accurate, trustworthy, timely and it must hold relevant content. In the past there have been several incidents where earnings announcements proved to be inaccurate, untrustworthy or even fraudulent. As a response to malicious reporting, authorities tightened the rules of accounting standards. In the United States, the Sarbanes Oxley Act (SOX) got introduced, and in Europe earnings announcements now have to be IFRS compliant. Since these rules are enforced, the announcements are perceived more trustworthy and thus the influence of earnings announcements has increased significantly. For the information to be timely, it is important that certain traders do not already have the information. The symmetry of earnings announcements has been extensively researched. If the information is asymmetric, i.e. known to some market participants but not to others, the information of the announcement will already be priced into the market price, the stock price reaction, if any, will be small.
already known to the public. If information has content, it is presumed to be timely. I will split this definition up into two new definitions: information quantity and information quality. First, the definition of information quantity: a firm’s earnings announcement is said to have information quantity if it leads to a change in investors assessments of the future returns (or prices), such that there is a change in equilibrium value of the current stock price. For information to have a good predictive value it has to be trustworthy and qualitatively good. Second, to describe the predictive value of information I will use the term information quality. I define information quality as follows: the measure in which new information contributes to investor perception about the precision of predicting a future event.
Figure 1 contains a typical graph of the volatility surrounding the publication of an earnings announcement. The spike at the event date shows a steep market reaction and therefore the earnings announcement is said to have information quantity. The graph in figure 1 also shows that the volatility after the event date is lower than the volatility prior to the event date. This supports the assumption that the announcement event contains quality information.
Figure 1. Return squared. The graph is a stylized figure of the volatility of the daily squared return of the data sample used in this thesis. t0 stands for the publication date of the earnings
announcement.
Ross (1989) theoretically predicted that in an arbitrage free market, an increase in information will lead to a decrease in uncertainty. Translated to the stock market, this means that more earnings information should decrease asset risk. This decrease in risk can be measured by a decrease in volatility. This prediction has been widely analyzed using earnings announcements as an information event. Rogers et al. (2009) do not unambiguously support this theory. They state that when management bundles the earnings announcement with management forecasts this
t-8 t-7 t-6 t-5 t-4 t-3 t-2 t-1 t0 t1 t2 t3 t4 t5 t6 t7 t8
increases volatility instead of decreasing it. Even though managers use these forecasts, trying to dampen volatility, it does not work. These findings contradict Billings et al. (2014). They find that earnings releases bundled with forecast guidance lead to exceptionally large post announcement reductions in volatility. Rogers et al. (2009) also find that when the earnings announcement deviates too far from analysts’ expectations, large earnings surprises will increase volatility. Finally, they conclude that negative earnings announcements will lead to more volatility. I argue that these contradicting conclusions are the result of regarding information as a one dimensional variable instead of a two dimensional variable. In this thesis I will test whether the daily volatility decreases after an earnings event in the Dutch market for the period 2008-2015.
The third step in this thesis is to link the decrease in volatility followed by earnings announcements to a decrease is the risk premium demanded by investors. Lambert, Leuz and Verrecchia (2007) explain this in the following way: earnings announcements containing more information do not affect cash flows per se, but affect the market participants’ assessments of the distribution of future cash flows. This increased information position will normally lead to a reduction in the assessed volatility of the firm’s cash flows. This will lead to a reduction of the firm’s cost of capital or induced risk premium and move this cost closer to the risk free rate. The reduction of the risk premium means that the future cash will be discounted at a lower rate. Therefore, the stock price will rise when the volatility decreases. Equation 1 shows the mechanics of this process. 𝑝𝑟𝑒 𝑎𝑛𝑛𝑜𝑢𝑛𝑐𝑒𝑚𝑛𝑒𝑡 𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒 − 𝑝𝑜𝑠𝑡 𝑎𝑛𝑜𝑢𝑛𝑐𝑒𝑚𝑒𝑛𝑡 𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒 = ∑ 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑡 (1 + 𝑝𝑟𝑒 𝑎𝑛𝑛𝑜𝑢𝑛𝑐𝑒𝑚𝑒𝑛𝑡 𝑟𝑖𝑠𝑘 )𝑡 ∞ 𝑡=1 − ∑ 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑡 (1 + 𝑝𝑜𝑠𝑡 𝑎𝑛𝑛𝑜𝑢𝑛𝑐𝑒𝑚𝑒𝑛𝑡 𝑟𝑖𝑠𝑘 )𝑡 ∞ 𝑡=1 (1)
This leads to the main question of this thesis: do investors pay for information through the process of calculating a lower discount rate after an increased information position?
volatility. The added value of this thesis is that I divide information in two seemingly unrelated dimensions: the information quantity and the information quality. I argue that information quantity is used by investors to form a perception about the expected future dividends. Information quantity has a direct restructuring effect on the predicted cash flows of an organization. I argue this effect will not have influence on the value of a well-diversified portfolio of stocks. The information quality, however, has influence on the discount rate, which cannot be absorbed by a portfolio. Theoretically, the change in stock price could be neutralized by arbitrage but market inefficiencies will allow for a measurable effect.
All prior empirical research has been done using US data samples. To my knowledge this thesis is the first empirical study on stock price reaction on earnings announcements outside of the US.
The remainder of this thesis is structured as follows: the next section is used to clarify the terminology; section three provides a review of the prior literature and derives the hypotheses; section four describes the data sample and the methodology; section five presents the results of the tests; section six provides a robustness check; section seven concludes this thesis.
2. Terminology and clarifications
In the literature many different terms are being used for the same basic principles. Depending on the point of view of the different academic fields, researchers sometimes argue from the company’s side and other articles are written from the investor perspective. On other occasions slightly different ways of calculating the same mechanism are used. To improve readability in this section, I would like to clarify some terminology and discuss the calculation methods.
For information measures I divide information content into two dimensions.
First, the information quantity (I) as defined above: a firm’s earnings announcement is said to have information quantity if it leads to a change in investors assessments of the future returns (or prices), such that there is a change in the equilibrium of the current market price. The information quantity has an influence on the expected dividends (equation 2).
I = ∆𝐷𝐸 (2)
𝑄 = ∆r = 𝑟𝑎− 𝑟𝑝 (3)
The discount rate (r) is the rate at which expected dividends are discounted. In this thesis I will use discount for two time frames: the discount rate prior to the earnings announcements (ra) and the discount rate after the earnings announcement (rp). The discount rate is split up into two kinds of risk, the risk free rate and the risk premium. This phenomenon is closely related to volatility.
To describe the value of the firm I will use the market price of the firm. The absolute size of the firm is not relevant to this thesis. Therefore I will use the price of a firm’s regular single stock as an indicator for the value of the firm. From here on revert to as stock price (P).
Return (R) is used to describe the change in stock price between two moments in time plus dividends. Stock returns can be calculated arithmeticly and logarithmicly. Ball and Shivakumar (2008) describe how log returns are more consistent with a linear regression between time periods of a different length. The downside of log returns is averaging them across a portfolio; log returns also exhibit some left skew. Arithmetic returns can be logically aggregated across securities, but not time. Arithmetic returns exhibit a considerable right skew. Ball and Shivakumar (2008) write that arithmetic returns are the conventional method for calculating stock returns. Therefore, in this thesis I will be using the conventional arithmetic returns. As a robustness check I will replicate my results using logarithmic returns (Rl).
backward and therefore I will use a historical volatility model rather than implied volatility. For the measure of volatility I use squared daily returns (R2).
In this thesis I used 10Q filings, quarterly and yearly earnings reports as proxy of information events. In this thesis, these are referred to as earnings announcements. In this thesis, all data is set to the earnings announcements being at t0.
An abnormally large shock in the stock price is called an earnings surprise. Earnings announcements are typically accompanied by these earnings surprises and are a proxy for information quantity. These earnings surprises are measured in R2.
Finally the expected dividends (DE) are all future dividends as expected by investors.
3. Theory and hypotheses
3.1 Information quantity
Information quantity has a direct effect on the perceived distribution of future dividends, the numerator in equation 4. To test the main question of this thesis, I assume that the perceived distribution of dividends for the data sample is constant. This is necessary to measure how the changed perception of risk after an earnings announcements, the denominator of equation 4, affects the stock price. This first part tests the assumption that expected future dividends can be treated as a constant. First I will describe the information quantity for a single stock.
∆𝑃 = ∑ ∆𝐷𝐸𝑡
(1 + 𝑟)𝑡 (4) ∞
𝑡=1
anticipated by the market. This would be a result of most of the information already being leaked into the market in the weeks prior to the moment the earnings announcement is published. They therefore say earnings announcements hold little information content. Both Ball and Brown (1968) and Nichols and Wahlen (2004) analyze the relative impact of an earnings announcement. As in equation 5, they calculated the relative information quantity (𝐼𝑦) by comparing the earnings announcements squared return to the sum of the returns of all other days.
𝐼𝑦 = 𝑅𝑡02
∑𝑛𝑡=1𝑅𝑡2
(5)
They therefore conclude that earnings announcements are only a small factor. Ball and Shivakumar (2008) also write that they only find evidence for very little information quantity being provided by earnings announcements. They argue that earnings announcements only account for a very small part of the yearly trading volume and stock price changes. They do see an increase of these parameters since 2000 which is especially steep in 2004 and 2005, the last two years of their sample. This research focuses on the relative importance of earnings reports to stock price over a year. It is clear that earnings reports only explain a small part of the yearly stock price movements. Information already leaked into the public domain and macroeconomic factors are a large factor. The research does provide evidence that the relative importance of earnings announcements is growing.
This being so, for this thesis the earnings announcements information quantity relative to the total yearly information quantity is not of interest. Of interest to this thesis is, however, the size of the information quantity of an earnings announcement day (𝑅𝑤2), relative to a normal trading day (𝑅𝑛2). For information content to be present, either the information quality or information quantity should be bigger than zero. I argue that information content as measured by Beaver (1968) is in fact a measure of information quantity. Equation 6 shows the formula used by Beaver to calculate information content. I will use it as a measure for information quantity.
I ≡𝑅𝑤2
𝑅𝑛2
This literature clearly shows that there is information quantity released with earnings announcements in the United States. My sample, however, consists of earnings announcements from the 29 largest Dutch companies for the period from 2008 to 2015. Therefore, generalizability across legislation and market efficiency is of interest to this study. All this prior research on the timeliness and information quantity of earnings announcements has been done on the US stock market. Most of the research was done on data samples from more than a decade ago. Therefore, they differ from this thesis in market culture, market regulations, and the ongoing importance of computing and communications capabilities. The idea is to confirm whether the theory also holds for this different sample. To test the hypothesis, I will use Beavers (1968) earnings surprise based method as a proxy of information quantity on the data sample.
H1: earnings announcements contain information quantity.
Hypothesis one can be written as equation 7.
1 < I ≡𝑅𝑤2 𝑅𝑛2
(7)
3.2 Information effects on price volatility.
(1999) research the theory or indeed the perception of risk follows this time pattern. They find the risk per unit of time, and thus the volatility, increases, when closing in on events whose timing can be predicted like earnings reports. Ross (1989) illustrates that the resolution of uncertainty helps investors plan for the future. From this perspective a more proximate information event is worth more than a more distant one. Following this train of thought, the ship’s financial claims should not only become more volatile but also become more pricy. In his paper Ross further argues that there is a link between stock price volatility and the flow of information content provided by the company. Ross argues that the changes in expected pay-out are arbitraged away. The effect is that information quantity is taken out of the equation. He focusses on the effect of information on the discount rate of a company. The discount rate is represented as the denominator in equation 8.
𝑅 = ∆𝑃 = ∑ 𝐷𝐸𝑡 (1 + 𝑟𝑎)𝑡− ∑ 𝐷𝐸𝑡 (1 + 𝑟𝑝)𝑡 (8) ∞ 𝑡=1 ∞ 𝑡=1
Ross concludes that in an arbitrage free economy, the stock price volatility is directly related to the rate of flow of information content to the market. Since the information quantity component is filtered out, his results are representative for information quality. Bushee and Noe (1999) use AIMR rankings as the measure for information quality. They find that when managers provide earnings announcements with a higher information quality, the subsequent stock price volatility will decline more than with lower information quality. Bushee and Noe provide a strong correlation between the AIMR earnings announcement quality ranking and the subsequent volatility change. This provides legitimization to use the volatility reaction as proxy for information quality. Therefore, in this thesis, I will divide the pre-announcement volatility (𝑅𝑎2) by the post-announcement volatility (𝑅𝑝2) as calculated in equation 9 as a measure for information quality.
𝑄 ≡𝑅𝑎2
𝑅𝑝2 (9)
cancel each other out. Earnings announcement quality, therefore, does not influence volatility. Rogers, Skinner and Van Buskirk (2009) find a decline in volatility from the period before the earnings announcement date to the period after the earnings announcement date. This result is consistent with the assumption of earnings announcements resolving investor uncertainty. They test specifically for the effect of guidance provided by managers bundled with the earnings announcements. Rogers, Skinner and Van Buskirk (2009) do find exceptions to the idea that earnings announcements result in a decline in volatility. When earnings announcements are accompanied by bad news guidance or when the earnings surprise is exceptionally large, they find an increase in volatility. This suggests a link between information quantity and information quality as shown in equation 10. This link contradicts my assumption that information quality and information quantity are two separate unrelated variables.
𝑅𝑎2
𝑅𝑝2 = 𝑄 = 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 + I
(10)
Billings, Jennings and Lev (2014), as well as Iselin and Van Buskirk (2015), describe that just before an earnings announcement is published, there is a steep increase in volatility. Both attribute this to pre-announcement investor uncertainty related to the topics discussed in the upcoming announcement, as described in the ship metaphor, and the likelihood this upcoming announcement is effective in resolving this uncertainty. These two issues are both positively correlated to the expected pre-announcement stock price volatility. This indicates that the perceived importance of an upcoming earnings announcement has influence on the resolution of uncertainty. This pre-announcement volatility is partly captured in equation 9. Billings, Jennings and Lev (2014) argue that managers combine guidance with earnings announcements to dampen volatility; they find that, contradictory to earlier research, guidance is a good instrument to lower volatility. They furthermore argue that the information quality of the guidance is the driver of volatility decline.
to the total volatility. Barth and So conclude from this that investors view earnings announcements as a source of uncertainty. Iselin and Van Buskirk (2015) further describe in their paper that when a firm’s earnings are volatile, an announcement has less impact on volatility and that firms covered by less analysts have more event specific uncertainty. The literature is not unambiguously supporting the view that earnings announcements lead to drop in volatility. I attribute this to the fact that information is seen as one dimensional. In my thesis, I argue that there are two information dimensions, information quantity and information quality. This leads to my next hypothesis.
H2: the size and direction of an earnings surprise is unrelated to the volatility change
Hypothesis two can be written as equation 11.
𝑄 ≠ 𝛽I + βDIRECTION (11)
3.3 The impact of information quality on stock price
Following the standard CAPM model, theory suggests, all else equal, that a decline in volatility should result in a decline in return. The CAPM model shows in essence the same relation as the product and the denominator in equation 8. This results in the notion that an announcement with high informational quality should lead to a low discount rate. This leads to a rise in stock prices and therefore to a high return.
𝑅 = ∆𝑃 = ∑ 𝐷𝐸𝑡 (1 + 𝑟𝑎)𝑡− ∑ 𝐷𝐸𝑡 (1 + 𝑟𝑝)𝑡 (8) ∞ 𝑡=1 ∞ 𝑡=1
Lambert, Leuz and Verrecchia (2007) use a model based on the CAPM model to predict the effect of earnings announcements on the induced risk premium. They argue that earnings announcements affect the risk premium by affecting the market participants’ assessment of the distribution of future cash flows, where a higher level of information content effects a firm’s real decisions, which in turn influences its expected value and covariance of firm cash flows. This theoretical model has not been tested empirically. Cohen, Dey, Lys and Sunder (2007) claim that an increased frequency of information content disclosure contributes to the decline in disclosure risk and with this a decline in the increased risk premium forgoing earnings announcements. None of these papers successfully links the announcement window return to the decline in risk premiums. This is consistent with hypothesis two.
Botosan and Plumee (2002) investigated the difference of change in risk premium between annual and quarterly announcements. For their study, due to data imprecision, they used quarter four announcements as being annual announcements. They find, as predicted, that the risk premium decreases with better quality information being disclosed at annual announcements. In contrast, they measure increasing risk premiums associated with quarterly announcements. This would mean that annual announcement reports have a high information quality where quarterly reports have low information quality. This seems consistent with Rogers, Skinner and Van Buskirk (2009) findings since annual announcement reports are usually accompanied with more guidance than quarterly reports.
quality. Barth and So (2014), like Bonsall, Bozanic and Fischer, find compelling evidence that investors anticipate earnings announcements to convey information content that increases market volatility. Barth and So suggest that investors pay a premium to hedge this non-diversifiable risk. These findings indicate that, although a large portion of the earnings announcement reaction is filtered away by arbitrage, there should be a small measurable reaction left.
Glinch and Verrecchia (2015) expected, following prior literature, that exogenous improvements in earnings announcements information content result in a reduced risk premium. In their paper they show that the association between increased endogenously motivated disclosure and the risk premium induced by changes in the underlying exogenous parameters in most circumstances is positive, and not negative like they expected. When examining the incremental effect of changes in information content disclosures following not exogenously motivated changes, they consider them as unexplained changes in information content disclosures, and they do find a decrease in risk premium.
Following this literature and the previous hypothesis I do not expect the event window returns to affect the volatility outside the event window. The direct resettling of investor beliefs about future dividends has a much larger effect on the stock price than the more subtle decrease in volatility. Within the event window, the information quality effect will therefore be unmeasurable in the information quantity noise. I, however, expect that the changes in volatility do have a measurable effect on the stock price outside the event window.
H3: information quality has a positive effect on stock price
Hypothesis three can be written as equation 12.
4. Data sample and methodology
4.1 Data sample
For the data sample this thesis uses a sample of publicly traded firms listed on Euronext Amsterdam. The sample is limited to firms who were part of the AEX-index between 2007 and 2015 and are still publicly traded in 2015. If they have dropped from the AEX-index to the Euronext-index or vice versa they are included in the sample. This leaves 29 firms who were traded some part of the time or the whole period. For obtaining the stock price information I made use of the Datastream database. To obtain earnings announcement release dates I used the dates provided by a calendar on IEX.nl. This provides 793 earnings announcement dates. Of these I deleted three samples because of acquisition announcements directly prior or after the earnings announcement dates. These acquisitions have much more information quantity than earnings announcements and therefore rendered the earnings announcements useless. For the remaining 790 earnings announcements I collected daily price information from 20 days prior to, and 20 days after the earnings announcement putting the announcement on day t0. Ball and Shivakumar (2008) came to the conclusion that arithmetic returns are the conventional method for calculating stock returns. In my review of the literature I came to the same conclusion. I have found no reason to divert from this convention and therefore calculate returns as in equation 13. As a robustness check, in part 6, I will redo the calculations using logarithmic returns.
R =𝑃𝑡−𝑃𝑡−1
𝑃𝑡−1 (13)
Using time in days (t) returns (R) of the stock price (P). This results in returns from 19 days prior to 20 days after the announcement date.
4.2 Information content
Landsman and Maydew describe relative change in stock prices as the cleaner measure. Both look at the announcement window squared returns and not at the change in volatility surrounding the announcement window. Therefore I will in this thesis use the earnings surprise as the measure of information quantity. The relative change in stock price is by definition the same as return. I will therefore use the squared daily returns (R2) to calculate the size of the relative change in stock price. In addition, I will test if the size of the firms return during the event window (𝑅𝑤2) is larger than the volatility of the stock price outside of this window (𝑅𝑛2). For the event window I will use the announcement day plus and minus one day. This three day window is the same measure Landsmen and Maydew use. For the normal or long term volatility I defer from their method. Landsmen and Maydew use for their measure of normal volatility the calendar year volatility, while I will only use the 37 day period surrounding the announcement event. As shown later, the results are the same and highly significant in both cases. Therefore I assume that this change in method doesn’t influence the result. Another deviation of this thesis from the method used by Landsmen and Maydew is that they correct firm volatility for market movements where I do not. These market movements should be random with a small upward drift (𝜀) and therefore have the expected sum of slightly positive, 𝜀 > 0. There is no reason to expect a larger upward drift during announcement windows and the sum should be constant. This means that with Landsman’s and Maydew’s method one should find a slightly larger earnings surprise. This leads to equation 14.
𝑅𝑤2
𝑅𝑛2 <
𝑅𝑤2−𝜀
𝑅𝑛2−𝜀
(14)
I do not expect this difference to influence the outcomes.
Figure 2. graph of squared returns. The size of relative change per day. The announcement event is on t0 and the event window stretches from t-1 to t1 .
Figure 2 visualizes the daily average of squared returns. It shows that the announcement window volatility (𝑅𝑤2 = 0.0014) is roughly triple the size of the normal volatility (𝑅𝑛2 = 0.0005). This is the same as predicted by Beaver (1968) as well as Landsmen and Maydew (2002).
To verify the first hypothesis, that quarterly earnings announcements contain information quantity, I will test whether the squared returns are equal. I will use a T-test for testing equality using equation 15.
0 = 𝑅𝑤2 − 𝑅𝑛2 (15)
From table 1 we can clearly conclude that earnings announcements hold information quantity. Ball and Shivakumar (2008) devised a measure to test for the amount of information quantity. The essence of the method is to use size of the event window volatility relative to the normal volatility. For this amount of information quantity (I), I will divide the event volatility by the normal volatility as defined in equation 16.
I ≡𝑅𝑤2
𝑅𝑛2 (16)
4.3 Expected dividends
Let us go back to equations 2, 3, and 4.This increase in information content can change the perception of either the expected dividends or the perception about the riskiness of the firm, or both. I = ∆𝐷𝐸 (2) 𝑄 = ∆r (3) ∆𝑃 = ∑ ∆𝐷𝐸𝑡 (1 + 𝑟)𝑡 (4) ∞ 𝑡=1
For an individual stock both will change substantially. For a portfolio of stocks the change in investors’ perception about future dividends will be diversified away. To test for this, the event window return should be marginally larger than zero for our sample of stocks. The sample contains measurements from 2008, when the AEX was trading at approximately 515 points, until 2015, when it closed at 442 points. This would suggest an average three day return slightly smaller than zero. The reason I expect a slightly larger announcement window return is that the frequency of our samples more than doubled since 2010. At the start of 2010, the AEX index was trading at 320 points. To filter this effect out all returns should be corrected for AEX returns. Correcting for AEX would be slightly more precise but the change is insignificant for the purpose of this thesis. To test for this I will use a T-test to test for equation 17, where 𝑅𝑤 is the announcement window return.
0 = 𝑅𝑤 = 𝑃𝑡1−𝑃𝑡−1
𝑃𝑡−1 (17)
4.4 Volatility reactions
Bonsall, Bozanic and Fischer (2013) show volatility reactions to earnings announcements cannot be diversified by using a portfolio of stocks. The logical explanation is that there is no pre-planned event that reduces information. There are events that increase uncertainty, the announcement of a lawsuit for instance, though the announcement dates of lawsuit announcements are not public knowledge. This leads to equation 18 and is empirically validated in section 3.2.
𝐼 ≡𝑅𝑤2
𝑅𝑛2 > 1 (18)
The next part of the theorem describes the reaction of stock price volatility outside of the event window to information content. According to theory, Hsieg, Jerris and Kross (1999), Ross (1989), Bushee and Noe (1999) Iselin and van Buskirk (2015) and others surmise that a release of information quality should lead to a decrease of volatility. This means that an earnings announcement leads to a volatility shift (𝑄) where the pre- announcement volatility (𝑅𝑎2) is lower or equal to the post- announcement volatility (𝑅𝑝2). This leads to equation 19.
1 ≤ 𝑄 ≡𝑅𝑎2
𝑅𝑝2≈ 𝛽I (19)
For the pre-announcement volatility I use squared returns of the time frame t-19 to t-2 and for the post-announcement volatility I do the same for the time frame t2 to t20. A volatility shift mean of 𝑄̅ = 1.14 indicates that the the sample still follows the theory.
extreme earnings surprises (𝐸𝑅). They argue that if the surprise is too large it will add uncertainty and therefore volatility will rise. To control for this, two categories in the form of two groups are constructed; the first group being the top five percent earnings surprises given the value one and the rest given the value zero. Putting the variables together, I look for a correlation between information quality and announcement window effects as follows in equation 20.
𝑄 = 𝛽0+ 𝛽1𝐼 + 𝛽2𝐷 + 𝛽3𝐸𝑅 (20)
All variables are highly insignificant. This regression has no explaining power at all. Where all independent variables are along the dimension of restructuring investor beliefs about the size of expected dividends, the dependent variable is an indicator of the resolvance of risk. The apparent independence of these two supports my assumption that these two should be treated separately. The restructuring of investor beliefs is the indicator of expected dividends where the resolvance of risk indicates the risk premium by which these beliefs are discounted.
The risk incurred by the restructuring of investor beliefs can be diversified away in a portfolio. This has as a result that information quantity has no value to a well-diversified portfolio. As Bonsall, Bozanic and Fischer (2013) describe, the shift in risk perception cannot be diversified away in a portfolio and investors have to pay a premium on derivatives to hatch for this phenomenon. This leads to investors demanding a risk premium prior to the announcement which they do not demand ex-post the earnings announcement.
4.5 Stock price reaction
dividends will be discounted. As described above, the expected dividends stay equal and as such the stock price should rise. This leads to equation 21.
∆𝑃 = ∑ 𝐷𝐸𝑡 (1 + 𝑟𝑎)𝑡− ∑ 𝐷𝐸𝑡 (1 + 𝑟𝑎− 𝑄)𝑡 (21) ∞ 𝑡=1 ∞ 𝑡=1
Assuming the expected dividends variable is a constant, the relationship between stock price and information quality can be simplified to equation 22.
∆𝑃 = 𝛽𝑄 (22)
To test this relationship, I use data quality variables as before. For the change in stock prices, I will use the pre and post announcement stock price periods and calculate their relative difference as shown in equation 23.
∆𝑃 =𝑃𝑝−𝑃𝑎
𝑃𝑎 (23)
Using these two variables, the regression analysis such as defined in equation 22, results in a confirmation of the hypothesis. There is a small but significant correlation between the two variables. This is a clear indication that information quality reduces volatility, a lower volatility leads to a lower demanded risk premium, this raises the stock price of a firm.
5. Results
Section 5.2 provides the results regarding to the announcement window return. This shows that information quantity is fully arbitraged away. Section 5.3 provides the results regarding information quality. This section shows whether the increased information position indeed leads to a lower volatility. This section shows that this lower volatility has no correlation with stock price reactions during the announcement window. Section 5.4 provides evidence that a decrease in stock price volatility leads to an increase in stock prices.
5.1 Information quantity
Table 1 shows the results of the test for information quantity. The test is a one-sided T-test and tests equality between the normal daily squared return and the announcement window daily squared return. The test contains 790 earnings announcements for the period between 2008 and 2015. For an earnings announcement to have quantity, the announcement window return should be larger than the normal daily return. In table 1 the returns are transformed into squared returns. Since the T-test is one-sided, the alternative hypothesis is that the difference is larger than zero. The T-test provides strong evidence that earnings announcements contain a significant level of information quantity. Table 1 clearly shows that the announcement window return is abnormal.
Table 1.
T-test information quantity.
The T-test provides evidence for information quantity in earnings announcements. The T-test tests whether the means of 𝑅𝑤2 and 𝑅𝑛2 are equal for 790 earnings announcement series during the period 2008-2015.
Variables 𝑹̅𝒘𝟐 𝑹̅
𝒏
𝟐 difference T-value Significance
𝑅𝑤2 − 𝑅
𝑛2 0.0014 0.0005 0.0009 5.46 < 0.0001
5.2 Announcement window return
Table 2 presents the announcement window return for 790 observations between 2008 and 2015. The null hypothesis (equation 17) states that earnings announcement windows wield no return.
0 = 𝑅𝑤 = 𝑃𝑡1−𝑃𝑡−2
𝑃𝑡−2 (17)
Table 2 shows that an average return of the announcement windows is slightly smaller than zero (𝑅̅𝑤 = −0.0011). The T-value is -0.45, for a sample of 790 observations. This translates to a p-value of 0.6544. This means the null hypothesis cannot be rejected, since the average return is not significantly different from zero. The sample value does not change significantly over the announcement event window. This indicates that, although individual stocks experience large price shocks as a consequence of an earnings announcement, a portfolio of stocks does not. Therefore information quantity has no effect on the sample value.
Table 2.
T-test announcement window return.
The T-test provides evidence that the information quantity in earnings announcements has no effect on the sample average stock price. The T-test tests whether the mean return of the announcement window is different than zero for 790 earnings announcement series during the period 2008-2015.
Variables 𝑹̅𝒉𝒚𝒑𝒐𝒕𝒉𝒆𝒔𝒊𝒔 𝑹̅𝒘 Std. Dev T-value Significance
𝑅𝑤 0.0000 -0.0011 0.069 -0.45 0.6544
5.3 Information quality
daily returns, divided by the squared returns of normal trading days. It is a measure for how much the earnings announcement diverts from investor beliefs about the distribution of future dividends. The direction variable (D) is constructed to form three equally sized groups which are selected by announcement day returns: a positive return group which is given the value one, a neutral return group which is given the value zero, and a negative return group which is given the value minus one. This variable is constructed to test whether negative earnings announcements have a different effect on volatility as compared to positive announcements. Last, the extreme returns variable (𝐸𝑅) is composed by giving the top five percent squared announcement day returns a value of one and the rest a value of zero. This variable is constructed to test whether extremely large earnings surprises have an effect on the volatility change.
First, the information quantity variable has a beta of 0.0021 and a T-statistic of 1.09, which indicates for a sample of 790 observations a p-value of 0.2788. This means that there is no apparent significant correlation between information quality and quantity. Second, the direction variable has a beta of 0.024 and a T-statistic of 0.48. For the sample of 790 observations this indicates a p-value of 0.6333. The assumption of a correlation between information quality and announcement window direction can therefore be rejected. The third variable is the extreme return variable: it has a beta of -0.010 and a T-statistic of -0.53. This indicates for a sample of 790 observations a p-value
Table 3.
Regression of announcement window effects on volatility.
The regression test for the influence of announcement information quantity (I), information window return direction (D) on the change in volatility surrounding the announcement window. Information quantity is measured as the squared return of the window. To test if extreme announcement window returns (𝐸𝑅) have an effect on the variable 𝐸𝑅, the top 5% squared returns is given the value 1 and the other measurements value 0. The variable direction is built up out of three equal groups where the most positive return group is given value 1, the intermediate group value 0, and the negative return group value -1. The dependent variable is the volatility of the 18 days prior to the announcement window divided by the volatility of the 19 days following the announcement window. The sample consists of 790 earnings announcement series during the period 2008-2015.
Variables 𝜷 Std. Error T-statistic Significance
Intercept 1.138446 0.042 26.60 < 0.0001
I 0.002139 0.002 1.09 0.2788
D 0.024010 0.050 0.48 0.6333
of 0.5978. This means that there is no significant correlation between extreme information events quantity and information quality.
The regression clearly shows that all announcement window volatility effects are constraint to the announcement window. All three variables are highly insignificant and therefore the null hypothesis that the announcement window effects have no influence on the volatility shift outside the announcement window cannot be rejected. This provides strong evidence that the restructuring of investors beliefs about future dividends leads to a price shock during the announcement window. Information quantity, however, has no effects on volatility outside of the announcement windows. These results confirm hypothesis two: the size and direction of an earnings surprise are unrelated to the volatility change.
5.4 Stock price
Table 4 shows how information quality affects stock prices for the period 2008-2015. This is an important part of the main question of this thesis. For the change in stock price, the arithmetic returns are calculated using the average stock price of the 19 days prior to the earnings announcement (equation 23). Information quality (Q) is measured by dividing the pre-announcement volatility by the post-pre-announcement volatility (equation 9).
Based on the theory, a small but significant positive relation between information quality and stock prices is expected. This small size can be mainly attributed to macroeconomic effects and arbitrage. Table 4 shows the beta of information quality is 0.013. This is the small positive correlation predicted by the theory. With a T-statistic of 4.08 for the sample of 790 measurements this relation is significant at the 1% level. This provides strong evidence that information quality has a positive effect on stock prices.
6. Robustness check
In the existing literature, arithmetic as well as logarithmic calculation methods are used to calculate returns. To exclude the possibility that the calculation method influences the results, I will use logarithmic calculations as a robustness check. All the tests will be exactly replicated as above. I diverge by using logarithmic returns (equation 24) for all calculations where in section five arithmetic returns where used.
𝑅𝑙 = 100 ∗ log 𝑃𝑡
𝑃𝑡−1 (24)
The results in this section are expected to be shifted slightly to the negative compared to the results in section five. This is due to the natural difference between arithmetic returns and logarithmic returns.
The next section provides the results regarding the extent to which earnings announcements hold information content. Section 6.2 provides the results regarding the announcement window return, this shows that information content is fully arbitraged away. Section 6.3 provides the results regarding information quality. This section shows that the increased information position indeed leads to a lower volatility. This section also shows that this lower volatility has no relation with stock price reactions during the announcement window; Section 6.4 provides evidence that a decrease in stock price volatility leads to an increase in stock prices.
Table 4.
Regression of information quality on stock price.
The independent variable is the information quality. This is measured by the volatility of the 18 days prior to the announcement window divided by the volatility of the 19 days following the announcement window. The dependent variable is the change in trading price surrounding the earnings announcement. This is measured using the arithmetic return of the average trading price. The periods used to calculate this return consist of the average stock price during 19 days prior to the announcement window and the average stock price during the 19 days following the announcement window. The sample consists of 790 earnings announcement series during the period 2008-2015.
Variables 𝜷 Mean Std. Error T-statistic Significance
Intercept -0.011 -0.011 0.006 -2.08 0.0381
6.1 Information content
To test for information content, the method described in section 4.2 is used for 790 observations from the period 2008-2015. In table 5 a one-sided T-test is used to compare the squared daily log return of the announcement window to the squared daily log return of normal trading days. The squared log return of the announcement window days is with 2.64 almost three times as large as the squared log return of a normal trading day, which is 0.94. This indicates that earnings announcements hold information quantity. This difference is, with a T-value of 7.16, significant at the 1% level. This confirms the results from part five.
Table 5.
T-test information quantity using logarithmic returns.
The T-test provides evidence for information quantity in earnings announcements. The T-test tests whether the means of 𝑅𝑙𝑤2 and 𝑅𝑙𝑛2 are equal for 790 earnings announcement series during the period 2008-2015.
Variables 𝑹̅𝒍𝒘𝟐 𝑹̅𝒍𝒏𝟐 difference T-value Significance
𝑅𝑙𝑤2 − 𝑅𝑙𝑛2 2.64 0.94 1.70 7.16 < 0.0001
6.2 Announcement window return
Table 6 presents the announcement window log returns (equation 25) for 790 observations for the period 2008-2015.
0 = 𝑅𝑙𝑤 = 100 ∗ log 𝑃𝑡1
𝑃𝑡−2 (25)
Table 6.
T-test announcement window return using logarithmic returns.
The T-test provides evidence that the information quantity in earnings announcements has no effect on the sample average stock price. The T-test tests whether the mean return of the announcement window is different from zero for 790 earnings announcement series during the period 2008-2015.
Variables 𝑹̅𝒉𝒚𝒑𝒐𝒕𝒉𝒆𝒔𝒊𝒔 𝑹̅𝒍𝒘 Std. Dev T-value Significance
𝑅𝑙𝑤 0.0000 -0.048 2.58 -0.53 0.5993
6.3 Announcement window effect
Table 7 shows the regression 𝑄𝑙= 𝛽0+ 𝛽1𝐼𝑙+ 𝛽2𝐷 + 𝛽3𝐸𝑅 and calculates the correlation between announcement window effects and information quantity. I recalculate the variables for a log information quantity (I𝑙) using equation 26 and log information quality (Ql) using equation 27.
𝐼𝑙≡ 𝑅𝑙𝑤2
𝑅𝑙𝑛2 (26)
𝑄𝑙≡ 𝑅𝑙𝑎2
𝑅𝑙𝑝2 (27)
First, the information quantity variable has a beta of -0.002 and a T-statistic of -0.26, which indicates a p-value of 0.7915 for a sample of 790 observations. This means that there is no apparent significant correlation between information quality and quantity. The arithmetic returns
calculation gave a positive indicator where the logarithmic have a negative beta. Both results are insignificant, which strengthens the assumption that there is no correlation between information quality and quantity.
Second, the direction variable has a beta of -.089 and a T-statistic of -0.95. For the sample of 790 observations this indicates a p-value of 0.3449. The assumption of a correlation between information quality and announcement window direction can therefore be rejected. The sign of the logarithmic direction beta is negative where in part five the direction was positive. This strengthens the assumption of no correlation.
The third variable is the extreme return variable; it has a beta of -1.058 and a T-statistic of -0.24. This indicates, for a sample of 790 observations, a p-value of 0.8077. This variable confirms the results of section five. All betas are lower than the betas in section five, this was expected by the assumption that logarithmic returns are skewed to the left where arithmetic returns are skewed to the right.
Table 7.
Regression of announcement window effects on volatility using logarithmic returns.
The regression test for the influence of announcement information quantity (Il), information window return
direction (D) on the change in volatility surrounding the announcement window. Information quantity is measured as the squared logarithmic return of the window. To test whether extreme announcement window logarithmic returns (𝐸𝑅) have an effect on the variable 𝐸𝑅, the top 5% squared returns is given the value 1 and the other measurements value 0. The variable direction is built up out of three equal groups where the most positive return group is given value 1, the intermediate group value 0, and the negative return group value -1. The dependent variable is the volatility of the 18 days prior to the announcement window divided by the volatility of the 19 days following the announcement window. The sample consists of 790 earnings announcement series during the period 2008-2015.
Variables 𝜷 Std. Error T-statistic Significance
Intercept 2.433 0.992 2.45 0.0145
I𝑙 -0.002 0.071 -0.26 0.7915
D -0.890 0.942 -0.95 0.3449
6.4 Stock price reaction
For the logarithmic change in stock price ∆𝑃𝑙, I recalculated the relative price using equation 28.
∆𝑃𝑙 = 100 ∗ log 𝑃𝑝
𝑃𝑎 (28)
Table 8 shows the results of the regression ∆𝑃𝑙 = 𝛽 + 𝛽𝑄𝑙. The regression confirms the results of section five. The information quality beta of 0.586 indicates that there is a small positive correlation between information quality and stock price. With a T-statistic of 4.138 the regression is significant at the 1% level. This provides strong evidence that investors demand a lower discount rate when information quality is released, and that stock prices rise as a consequence.
7. Conclusion
In this thesis, I expand on the existing literature by making a clear distinction between information quality and information quantity. The information quantity component has already been extensively analyzed. This can only be done by taking the information content as a variable. This thesis provides strong evidence that information content as calculated by Beaver is an unfit measure for informational value. The earnings surprise is a good measure for the resettling of investors’ belief about the upcoming dividends. It does not capture the resolution of uncertainty.
Table 8.
Regression of information quality on stock price using logarithmic returns.
The independent variable is the information quality. This is measured by the volatility of the 18 days prior to the announcement window divided by the volatility of the 19 days following the announcement window. The dependent variable is the change in trading price surrounding the earnings announcement. This is measured using the logarithmic return of the average trading price of the stock during this same periods. The sample consists of 790 earnings announcement series during the period 2008-2015.
Variables 𝜷 Mean Std. Error T-statistic Significance
Intercept -0.745 0.247 -3.013 0.0027
Information quality does capture the resolution of uncertainty. This is, through the mechanism of discount rate, measurable in the stock price.
I test three hypotheses in this thesis to answer the main question: do investors pay for information through the process of calculating a lower discount rate after an increased information position? With hypothesis one, earnings announcements contain information quantity, I show that earnings announcements hold information quantity. This implies earnings announcements can be used as a proxy for an increased information position.
Hypothesis two, the size and direction of an earnings surprise is unrelated to the volatility change, has implications for the second part of the main question. It clearly shows that the change in stock price is not due to the change in investors’ beliefs about the future dividends of the stock. This indicates that the change in stock price is not a result of the information quantity.
Hypothesis three, information quality has a positive effect on stock price, answers the final part of the main question. It provides a clear indication that the increase in stock price is driven by the increase information quality.
This leads to the conclusion: investors pay for information through the process of calculating a lower discount rate after an increased information position.
A shortcoming of this thesis is that it measures information quality directly from stock price volatility. This is the market’s perception of information quality and is proven by Bushee and Noe (1999) to be a good measure of information quality. To improve on the accuracy of the information quality measure, stock price movements should be corrected for index movements. As expected, the Dutch market follows the same patterns as the United States markets already covered in the prior literature. For further research, the results of this thesis should be replicated using the conventional databases of the US market. These are larger, more accurate, and cover the more relevant US market. These databases also cover more variables, thus eliminating some of the white noise that was inevitably part of the regressions used in this thesis.
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