Accounting conservatism and jump likelihood : is conservatism desirable?

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Accounting conservatism and jump likelihood: is conservatism

desirable?

Master’s thesis

Accountancy and Control

Amsterdam Business School

Faculty of Economics and Business, University of Amsterdam

2013 – 2014

Name: Lisette A. Lochtenbergh

Student number: 10000434

Supervisor: Dr. R.S. Boomsma

Date of final submission: June 23th 2014

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Abstract

The purpose of this research is to investigate to what extent the level of accounting

conservatism of a company influences the likelihood of a stock price jump of the company. Prior research provided this study with a theoretical foundation on which this paper’s main hypothesis is built (Jin and Myers, 2006; Hutton et al., 2009, Kim and Zhang, 2010; LaFond and Watts, 2008). Following the previously mentioned underpinnings, this study expects that conservatism would have a reducing effect on a company’s jump likelihood. This paper executes a logistic regression in order to examine whether there is a significant reducing effect of the level of conservatism on a company’s jump likelihood. The regression demonstrates that the hypothesis can indeed be supported. The study of Kim and Zhang (2010) found that accounting conservatism has a reducing effect on the crash likelihood of a company. Combining both results, accounting conservatism on one hand seems to help protect the company from possible costs associated with a stock price crash, but on the other hand it also seems to contribute in depriving the company from possible benefits associated with a stock price jump. Considering this, the desirability of accounting conservatism is not that easy to assess. Bearing in mind, however, that markets demand “more conservative earnings as a means of mitigating agency costs” (LaFond and Watts, 2008, p.476), this study tends to conclude that the benefits of having fewer crashes should outweigh the costs of having fewer jumps. This study, however, does advocate for further future research to determine whether information asymmetry and thereby costs as a whole indeed decrease because of accounting conservatism, because prominent accounting bodies like the FASB (2008) continue to distance themselves from the principle of conservatism. This study

contributes to existing literature by filling a gap in a certain branch of conservatism literature, which is a still somewhat new and emerging field of investigation. These papers all examined accounting conservatism as a control mechanism used by principals. Furthermore, this paper contributes to current conservatism debates by examining the desirability of accounting conservatism in order for better-funded opinions.

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Samenvatting

Het doel van dit onderzoek is onderzoeken in hoeverre conservatief boekhouden een effect heeft op de kans dat de aandelen van een organisatie een aandelenjump doormaken.

Voorgaand onderzoek biedt de theoretische basis waarop deze studie haar hypotheses heeft ontwikkeld (Jin en Myers, 2006; Hutton e.a.., 2009, Kim en Zhang, 2010; LaFond en Watts, 2008). Gebaseerd op de voorgaand genoemde studies, verwacht deze studie dat conservatief boekhouden een significant verkleinend effect heeft op de mogelijkheid van een

aandelenjump. Deze studie heeft dit onderzocht aan de hand van een logistische regressie. De statische resultaten tonen aan dat de hypothese inderdaad is bewezen. De studie van Kim en Zhang (2010) hebben aangetoond dat conservatisme een verkleinend effect heeft op de mogelijkheid van een aandelencrash. Als deze resultaten worden gecombineerd kan men afleiden dat conservatisme aan de ene kant een bedrijf probeert te beschermen tegen

mogelijke kosten van een aandelencrash, maar aan de andere kant een bedrijf ook mogelijke baten van een aandelenjump lijkt te onthouden. Daaruit volgt dat het niet eenduidig vast te stellen is of conservatief boekhouden wenselijk is of niet. Echter, uit de theorie van LaFond en Watts (2008) volgt dat conservatisme een markt gevolg is. Er is vraag naar conservatisme vanuit de markt, omdat conservatievere jaarverslagen leiden tot lagere informatie asymmetrie en daarmee lagere agency kosten. Derhalve neigt deze studie te concluderen dat de baten van lagere kosten door minder crashes zwaarder wegen dat de kosten van het mislopen van jump baten, omdat conservatisme een markt effect is dat zal leiden tot minder agency kosten. Desondanks pleit deze studie ervoor dat verder wordt onderzocht of de baten van minder crashes inderdaad zwaarder wegen dan de kosten van minder jumps, omdat prominente instituten zoals de FASB (2008) afstand blijven nemen van het principe van conservatisme. Deze studie draagt op verschillende manieren bij aan voorgaand onderzoek. Allereerst, draagt het bij door nog niet onderzocht gebied te onderzoeken binnen een opkomende tak binnen de conservatisme literatuur. Deze studies hebben conservatisme allemaal onderzocht in een breder of ander licht dan meer conventionelere theorieën zoals de contracting theorie. Zij zien conservatief boekhouden als een mechanisme dat door principalen wordt gebruikt om het opportunistische gedrag van agenten te kunnen corrigeren. Daarnaast draagt deze studie bij aan het hedendaags debat omtrent de wenselijkheid van conservatief boekhouden.

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Acknowledgements

I would like to thank Dr. R.S. Boomsma, my thesis supervisor, for his valuable and

constructive suggestions during the development of this thesis. Furthermore, I would like to thank Dr. J.J.F. van Raak for his additional assistance.

I would also like to express my great appreciation for my mother, who supported and encouraged me throughout my Master’s thesis and my academic study as a whole.

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Above average stock increases and decreases, hereafter jumps and crashes, are often the result of the disclosure of dramatic good or bad news to the market. With regard to the likelihood of a crash, research found that opaque financial statements significantly increase this likelihood (Hutton et al., 2009). Opaque financial statements are generally the result of earnings management, which encompasses the withholding of certain bad news and

disclosing good news as soon as possible, because managers hope that current bad news will be outbalanced by future good news. Managers manipulate earnings, because of (often short term horizon) opportunistic reasons like bonuses or career interests (Ball, 2009; Graham et al., 2005; Kothari et al., 2009). The bad news hoarding, however, cannot persist forever, as over time it becomes too costly or just practically impossible. Consequently, at a certain point in time the bad news hoarding reaches a tipping point resulting in a revelation of a great amount of bad news. This can potentially result in a stock price crash.

Hutton et al. (2009) found that financial statement opacity, caused by managers’ incentives for bad news hoarding, increases the likelihood of a stock price crash. The authors additionally examined this relation with regard to the likelihood of market jumps, but opacity has no effect on he likelihood of a stock price jump. This was as expected on beforehand, because managers are not likely to not have incentives to withhold good news. Accounting conservatism is a concept that can be seen as a correcting mechanism against the incentives of managers to withhold bad news, because conservatism encourages the exact opposite:

disclose bad news more rapidly and set higher requirements for recognizing good news. In this light, previous research wanted to examine if accounting conservatism decreases the likelihood of a stock price crash. Kim and Zhang (2010) indeed found evidence to support this hypothesis.

Following Kim and Zhang (2010) and Hutton et al. (2009), this study examines the possible effect that accounting conservatism could have on the likelihood of a stock price jump. As stated before, accounting conservatism works as a mitigating mechanism for bad news hoarding of managers. Generally, a manager is not likely to have incentives to withhold good news (Hutton et al., 2009). Accounting conservatism, however, works in both ways and also influences how managers have to deal with good news. A manager working in a more conservative company, is expected to recognize good news less easily as such as a manager at

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a less conservative company. Consequently, the release of a great amount of good news that could lead to a stock price jump is expected to occur less likely. Therefore, this research expects, other things equal, that accounting conservatism decreases the likelihood of future stock price jumps.

There are two types of accounting conservatism: unconditional accounting conservatism and conditional accounting conservatism. Unconditional accounting conservatism is news independent conservatism, which means that it is a system where expenses are systematically accelerated and revenues systematically deferred. Conditional conservatism is news dependent, which means that it asymmetrically reflects bad news over good news. Hence it reflects bad news on a timelier basis than good news, but it does not systematically result in a lower profit as with unconditional conservatism. When this study refers to accounting conservatism, it refers to the conditional form of accounting conservatism (Li, 2010; Kim and Zhang, 2010).

This paper contributes to existing literature in several ways. Above all, it fills a gap in a certain branch of conservatism literature by proceeding on papers like Jin and Myers (2006), Hutton et al. (2009), Kim and Zhang (2010) and LaFond and Watts (2008). The papers by Jin and Myers (2006), Hutton et al. (2009) and Kim and Zhang (2010) built their hypotheses on the notion that accounting conservatism acts as a contra mechanism for the opportunistic behaviors of managers. Additionally, LaFond and Watts (2008) found evidence for a reason, other than conventional ones like contracting, as to why accounting conservatism exists in line with the papers of Jin and Myers (2006), Hutton et al. (2009) and Kim and Zhang (2010). They found evidence for an actual market demand for accounting conservatism in line with the notion of principals wanting to correct for their managers’ opportunistic behaviors. This branch of conservatism literature is still a somewhat new and emerging field of investigation to which this study contributes. In particular, this study extends the study of Kim and Zhang (2010) by (i) again building on the previously described theory and by (ii) additionally examining the possible effect of accounting conservatism on the likelihood of a stock price jump next to its effect on the likelihood of a stock price crash. The results of this study complement the result of Kim and Zhang (2010) by showing that accounting conservatism, next to reducing the crash likelihood, also reduces the jump likelihood. Thereby, this study demonstrates that the desirability of accounting conservatism is not that easily assessed when considering both effects.

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As stated earlier, this study contributes to prior literaure in multiple ways. First, it contributes to current debates with regard to the desirability of accounting conservatism. In 2008, one of the leading accounting institutes, the FASB, declared that it no longer planned to incorporate accounting conservatism as a desirable feature in its accounting principles because they found that it increases information asymmetry. They stated that “the Boards concluded that describing prudence or conservatism as a qualitative characteristic or a desirable response to uncertainty would conflict with the quality of neutrality” (FASB, 2008, p. 28). According to the FASB, accounting conservatism interferes with neutrality, because the higher verification requirements for gains relative to losses allow a form of bias in the information of financial statement. This bias leads to information asymmetry between the company outsiders and company insiders, and this is seen as inconsistent with neutrality. With this statement, the FASB implies that accounting conservatism will be likely to undermine the quality of neutrality as the most important quality in order to provide the attainment of highest decision usefulness for investors.

However, academic literature (LaFond and Watts, 2008; LaFond and Roychowdhury, 2008) found evidence for an intrinsic market demand for conservatism, which suggests that conservatism actually contributes to decision usefulness of decision making of investors. Moreover LaFond and Watts (2008) found that their findings are more robust than the statements of the FASB. Therefore, according to LaFond and Watts (2008), if the FASB would succeed in minimizing conservatism, information asymmetry would actually increase instead of decrease. Despite these significant findings, with possibly great implications with regard to the recent movement of the FASB, the FASB and other accounting bodies continue to distance themselves from the concept of accounting conservatism and are increasingly moving towards the notion of fair value accounting. An important shift in a principle like this should be informed by extensive, in-depth and critical academic research like LaFond and Watss (2008). As stated before, this paper’s first contribution would be to contribute to current conservatism debates by examining the desirability of accounting conservatism in order for better-funded opinions. Inherently, this research’s second contribution is to provide new insights in the effect of accounting conservatism as a correcting mechanism of the optimism bias and whether conservatism increases or decreases information asymmetry. Third, it thereby contributes by discovering either a new advantage or a new disadvantage of accounting conservatism. Fourth, this is of importance for regulatory, accounting and

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economic bodies, because it improves their ability to better weight the advantages and disadvantages of incorporating accounting conservatism in regulations.

Fifth, although accounting conservatism is one of the main research areas of

accounting, current literature focuses its attention mainly on one aspect, i.e. explaining why conservatism exists (Watts, 2003b; Ball et al., 2000; Bushman and Potarski, 2006, LaFond and Watts, 2008). The positive and negative consequences of conservatism are however examined to a lesser extent. Some exceptions are Ahmed et al. (2002), Wittenberg-Moerman (2008), Zhang (2008) and Kim and Zhang (2010). This study would like to contribute to this relatively smaller sub area.

This remainder of this thesis is structured as follows. Chapter 2 reviews the key literature on the topic of accounting conservatism and hereby outlines (i) the more addressed conventional argumentation behind the reasons of its existence and (ii) a new, emerging theory about the reasons for conservatism. Chapter 2 also reviews some particular studies of interest in order for this study to develop its main hypothesis. In addition a second hypothesis is developed in order to give this study more depth by considering alternative interpretations. Chapter 3 outlines the sample selection process and research method. Chapter 4 describes the descriptive statistics and presents the statistics. In addition, chapter 4 present a discussion that further interprets the results by making use of the papers and theories introduced in chapter 2. Chapter 5 presents the conclusion.

2. Literature review and hypotheses development

2.1 Accounting conservatism

Conservatism in accounting is a subject within the major accounting research areas of the present-day (Scott, 2012). In 1997, Basu (1997) was the first to empirically examine accounting conservatism in financial reporting; his results mainly confirmed its existence. He used an earnings-relation model in order to assess the existence of conservatism. Basu found that bad news was reflected earlier in financial reporting than good news. Watts (2003a; 2003b) addressed the subject in two other seminal papers on accounting conservatism. “Part 1: Explanations and implications” developed a definition of accounting conservatism and, as the title implies, provided several explanation for conservatism (including contracting). With

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respect to its content, Watts’ (2003a) definition is similar to that of Basu (1997). Watts (2003a, p. 208) expresses accounting conservatism as the “asymmetrical verification

requirement for gains and losses”. Barth et al., (2013, p. 1) defines conservatism as “a larger response coefficient for negative return than for positive return in an earnings-return

regression”. Furthermore, the FASB (2008, p. 28) refers to conservatism, or as they propose “prudence”, as “that possible errors in measurement be in the direction of understatement rather than overstatement of net income and net assets”. In other words, accounting

conservatism encompasses that the mandatory requirements in order to recognize profits are higher than the requirements for recognizing losses, and thus indicates a more

reserved/conservative practice of accounting.

With regard to the different explanations for accounting conservatism, Watts (2003a) distinguishes four explanations of accounting conservatism, i.e. contracting, litigation, taxation and regulator. The two most addressed explanations in existing literature are

contracting and litigation (Watts, 2003a). According to Watts (2003a), there are three types of accounting conservatism under the contracting explanation: conservatism and debt contracts; conservatism and executive compensation contracts; conservatism and firm governance. The contracting explanation states that accounting conservatism exists, because of moral hazard problems caused by asymmetric pay-offs, asymmetric information, limited horizons and limited liabilities. A firm can protect itself from these problems by means of accounting conservatism. To illustrate, an example of the first type “accounting conservatism and debt contract” under the contracting explanation is provided. If a firm and a debt holder agree into a debt contract, the debt covenant, the debt holder is likely to include certain clauses that decrease the likelihood that a firm acts at the expense of the interest of the debt holder. For example, the debt covenant could prevent paying out liquidating dividends to shareholders or other clauses that discourage any behavior that may damage the firm’s ability to repay the loan. The litigation explanation states that, because the litigation costs of overstatements are considerably higher than the costs of understatements, firms tend to safeguard it by means of accounting conservatism (Watts, 2003a; Scott, 2012).

2.2 LaFond and Watts’ (2008) theory

A recent study on accounting conservatism by LaFond and Watts (2008) sheds another light on the reason why conservatism exists. Their finding is an extension of the already

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existing contracting theory, because it states that conservatism not only exists in order to reduce agency costs caused by debt contracts, compensation contracts and firm governance, but to reduce agency costs as a whole. LaFond and Watts’ (2008) finding, consequently, is related to the well-known agency theory.

LaFond and Watts (2008) found evidence in favor of an intrinsic demand for conservatism from investors themselves. This intrinsic demand stems from the fact that conservatism mitigates the so-called optimism bias. The optimism bias leads to information asymmetry. This information asymmetry is caused by incentives of managers to overstate the financial statements, because of for example opportunistic behavior. This information

asymmetry between the investor, principal, and the managers, agents, creates agency costs (e.g. over- or under investments). This is where accounting conservatism comes into play. When managers overstate assets or understate liabilities, accounting conservatism functions as a contra mechanism to adjust this downwards and thereby reduce information asymmetry and agency costs. So, investors demand “more conservative earnings as a means of mitigating agency costs” (LaFond and Watts, 2008, p.476). In other words, LaFond and Watts’ (2008) findings show that accounting conservatism is more than a means to reduce contracting costs, but that it is actually a market result caused by information asymmetry between the agent and the principal. LaFond and Roychowdhury (2008) also found evidence in line with a market demand for accounting conservatism. They find that the higher the separation of ownership and control, the higher the agency problems, and the higher the demand for conservatism as a mechanism to deal with these agency problems. This theoretical notion as to why

conservatism exists will be used later in this study as a means to interpret the results from the hypotheses.

2.3 Prior literature and hypotheses development

As stated earlier, this study would like to contribute to the sub area of the

conservatism literature that examines the possible consequences of accounting conservatism. Prior literature of this area found both advantages and disadvantages with regard to

conservatism. For example Barth et al. (2013) found that conditional conservatism is significantly negatively related to a lower information content of earnings. They found that conservatism results in (i) a delayed resolution of investor disagreement after an earnings announcement and (ii) higher economic costs caused by higher equity costs and higher

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dispersion of analysts’ forecasts after an earnings announcement. However, Li (2010) find that countries with relatively more conservatism companies have lower cost of debt and equity. Biddle et al. (2011a) found that both conditional and unconditional accounting conservatism mitigates bankruptcy risk, because of the informational role it plays in these types of critical situations. Conservatism can help in reducing debt costs and enhance

liquidity, because investors and lenders are more willing to cooperate with the company. They trust the company relatively more, because conservatism reduces overvaluing/hiding

behavior. Furthermore, Biddle et al. (2011b) found that both conditional and unconditional conservatism lead to lower operating cash flow downside risk, meaning a lower difference between the actual return and the expected return.

The studies of Hutton et al. (2009) and Kim and Zhang (2010) are particularly important for this research, because the theory used in order to develop their hypotheses is also used in this study. Hutton et al. (2009) examined the association between the opacity of financial statements, proxied by earnings management, and the likelihood of a stock price crash. They examined this by building on the following theoretical link. Managers of a company have incentives to manage earnings, because of for example opportunistic reasons. However, managing bad news is only possible until a certain tipping point is crossed, because it becomes for example too costly. Ones this point is crossed all the accumulated bad news will come out all at once resulting in a dramatic revelation of bad news, which could result in a stock price crash. Hutton et al. (2009) indeed found supportive evidence for this theory and found that opaque financial statements increase the likelihood of a stock price crash. The authors also examined the effect of opacity on the likelihood of price jumps, but found no effect. They predicted this on beforehand, because managers should have no incentives to manage/hide good news. In the same line of thinking, Kim and Zhang (2010) examined the effect of accounting conservatism on the likelihood of a stock price crash. Accounting conservatism reduces the incentives of managers to hide bad news, because of the

asymmetrical verification requirement for good news relative to bad news. Therefore, Kim and Zhang (2010) predicted that the tipping point that releases accumulated bad news is achieved less likely for companies that use conservative accounting practices, resulting in a lower likelihood of a stock price crash. The authors indeed found evidence for this, signifying that conservatism reduces the likelihood of a stock price crash. However, Kim and Zhang (2010) did not examine the effect of accounting conservatism on the likelihood of a stock

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price jump. Therefore, this research wants to contribute by addressing this gap in existing literature.

Hutton et al. (2009) demonstrated that opaque financial statements increase the likelihood of a stock price crash, and the study of Kim and Zhang (2010) demonstrated that accounting conservatism on the contrary decreases this likelihood because it works as a stimulant to recognize bad news sooner. The research of Hutton et al. (2009) also showed that opaque financial statements have no effect on the likelihood of a stock price jump.

Accounting conservatism can however have an effect on the likelihood of a stock price jump. Just like bad news is disclosed relatively sooner by conservative companies, good news is recognized less rapidly, because they set higher requirements. Consequently, a point where a great amount of good news is released in an instant, leading to a stock price jump, will occur not so readily with conservative companies as with less conservative companies. Building on the previously explained theoretical link, this research hypothesizes the following:

H1a: Accounting conservatism in financial statements reduces the likelihood of a

future stock price jump, ceteris paribus.

It is possible, to reason even further. Accounting conservatism could possibly work as a mechanism that not only reduces bad news hoarding (Kim and Zhang, 2010), but also increases good news hoarding. Accounting conservatism can slow down the recognition of good news to such an extent that it actually increases the likelihood of a stock price jump. Conservatism could even incentivize the “hiding” of good news until a certain tipping point is achieved where it is no longer possible to hide the good news, resulting in a stock price jump. On beforehand of the tests, however, this study deems this to be unlikely, because

conservatism can not be seen as the exact opposite of earnings management. Managers of conservative companies do not actually withhold good news, they only set higher

requirements before recognizing it as such (Hutton et al., 2009).

Another finding that could challenge hypothesis 1a is of Kim and Pevzner (2010). They found that the stock market reacts stronger (weaker) to good (bad) news of more conservative companies relative to less conservative companies. This would imply that conservatism would not have a reducing effect on the likelihood of a stock price jump,

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relatively more, which would balance out the effect. This study does not expect this to be of general significance, because (i) Kim and Zhang (2010) already demonstrated the reducing effect of conservatism on the likelihood of a stock price crash and (ii) Kim and Pevzner (2010) found somewhat weak evidence for this result. However, it is imaginable that the results of hypothesis 1a differs for high-conservative companies compared to medium- or low-conservative companies, because the stock markets are then generally aware of their accounting conservatism given its high level. Hence, in order to give this study more depth by considering another interpretation, it will additionally conduct a portfolio analysis that takes the study of Kim and Pevzner (2010) into account. It will examine whether the results of hypothesis 1a (significantly) differ for relatively high-conservative companies. Therefore, this study would like to examine the following hypothesis:

H1b: The possible reducing effect of accounting conservatism in financial statements

on the likelihood of a future stock price jump is neutralized for high-conservative companies, ceteris paribus.

3. Sample and research method

3.1 Sample

The sample of this study consists of data on all U.S. companies included in the north-American databases Compustat and the Center for Research in Security Prices. A description of all the variables can be found in Appendix A. The sample comprises the last ten years, from January 2004 to December 2013. Initially, this study’s intention was to comprise the years 1962-2013, but because of (i) the time scope of this master’s thesis and (ii) practical limitations the sample needed to be scaled down. During this study a sample year is expressed as a firm’s fiscal year.

After gathering all the needed data, certain selection criteria need to be met. First of all, observations with missing data were dismissed. Second, following Khan and Watts (2009), total assets and book value of equity needed to exceed $0,00 and the closing fiscal year share price needed to exceed $1,00. Third, also in line with Khan and Watts (2009), companies were dismissed if they fell in the top or bottom percentiles of earnings, annual returns, market value of equity, market-to-book ratio or leverage. The final sample consisted

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of 9741 company years. Table 1 presents the number of observations, i.e. company years, for each fiscal year. It is notable that the number of observations of 2012 and 2013 is relatively less. This may stem from the fact that not all information is gathered yet for these last two years, but this study did not find explicit confirmation for this.

Table 1

Number of observations, i.e. company years, per fiscal year Fiscal year N % 2003 1244 12,77 2004 1188 12,20 2005 1139 11,69 2006 1072 11,01 2007 1004 10,31 2008 892 9,16 2009 871 8,94 2010 841 8,63 2011 807 8,28 2012 362 3,72 2013 321 3,30 Total 9741 100 3.2 CSCORE model

This study uses the CSCORE model of Khan and Watts (2009) in order to measure the level of accounting conservatism of a company. The model of Khan and Watts (2009) is preferred over other conservatism models, because it (i) fits with the purpose of the hypotheses and (ii) represent a more sophisticated version of the widely used Basu (1997) model. It fits with the hypotheses), because it measures the conditional form of conservatism conservatism and because it measures conservatism on the firm-level. Moreover, selecting this model is in line with the related paper of Kim and Zhang (2010).

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As stated before, the CSCORE measure is based on the Basu (1997) model. The Basu model measures the extent of good news recognition relative to bad news recognition per company:

Xjt = β1t + β2tDjt + β3jtRjt + β4jtDjt * Rjt + εjt (1)

X refers to the earnings before extraordinary items divided by the market value of equity. j

represent the company and t the (fiscal) year. R is the yearly market return compounded from monthly returns, D is a dummy variable that equals one if R is beneath 0, and zero otherwise, and ε is the residual. The coefficient β3 measures the timeliness of good news recognition, β4 measures the level of conservatism (the timeliness of bad news recognition over good news recognition) and β3 + β4 together measure the timeliness of bad news recognition.

Khan and Watts enhanced the Basu (1997) model by replacing the coefficients β3 and β4 by functions that represent specific features that are consistent with the timeliness of good news recognition (β3) and with the level of conservatism (β4), respectively:

GSCORE = β3jt = µ1t + µ2tMKVjt + µ3tMBjt + µ4tLEVjt (2) CSCORE = β4jt = λ1t + λ2tMKVjt + λ3tMBjt + λ4tLEVjt (3)

In these functions MKV equals the natural log of the market value, MB is the market-to-book ratio, and LEV is the debt-to-equity ratio. By inserting the new functions in the former Basu (1997) model, the final empirical model can be written down as follows:

Xjt = β1t + β2tDjt + Rjt (µ1t + µ2tMKVjt + µ3tMBjt + µ4tLEVjt) + Djt * Rjt (λ1t + λ2tMKVjt + λ3tMBjt + λ4tLEVjt) +(δ1tMKV

+ δ2tMB + δ3tLEV + δ4tDjtMKV + δ5tDjtMB + δ6tDjtLEV) + εjt (4)

In order to measure the empirical model (function 4), five-year rolling panel regressions are employed. Then the resulting coefficients λ1, λ2, λ3 and λ4 are applied to the third function in order to compute the eventual CSCORE.

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This study uses a model developed by Jin and Myers (2006) in order to measure the jump likelihood of a stock. The model of Jin and Myers (2006) is chosen, because it again fits the hypotheses of this study very well. The model of Jin and Myers (2006) is able to measure the likelihood of a jump in stock prices per company per (fiscal) year, which suits the purpose of this study. Furthermore, related papers like Hutton et al. (2009) and Kim and Zhang (2010) also employed this jump likelihood model.

The empirical model’s basis is the expanded market model regression, which

measures the relation between a specific stock return compared to the value-weighted market index return:

rj,t = αj + β1jrm,t-2 + β2jrm,t-1 + β3jrm,t + β4jrm,t+1 + β5jrm,t+2 + εjt (5)

rj,t represents the stock return of stock j in week t and rm,t is the market index return in week t. After that the natural logarithm of the residual pus 1 is taken in function 6, which results in the eventual firm-specific weekly return (W):

Wj,t = ln(1+ εj,t) (6)

In order to measure the jump likelihood per company per fiscal year, the binary indicator JUMP is introduced. JUMP equals one if a company encounters more than one jump week per (fiscal) year, and zero otherwise. The firm-specific weekly return is denoted as a jump week if it is 3,2 standards deviations above the mean of the firm-specific weekly returns for the given fiscal year.

3.4 Empirical model (H1a)

Following Kim and Zhang (2010), this study employs the following empirical model in order to estimate the possible reducing effect of accounting conservatism (CSCORE) in year t on the jump likelihood (JUMP) in year t+1:

m

JUMPt+1 = α0 + α1CSCOREt + +

Σ

αq (qthControlVariablest) + εt (7) q=2

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The empirical model represents a logistic model. JUMPt+1 is a binary indicator that equals one if a company encounters more than one jump week in year t+1, and zero otherwise. α1 is expected to be below zero, which indicates the expected reducing effect of CSCORE on JUMP (negative relation).

To control for external factors known to influence jump likelihood, the following control variables are included in the logistic regression: SIZE and DTURN. First, firm size is included as a control variable in order to control for the size effect (Hutton et al., 2009; Kim and Zhang, 2010). Firm size is proxied by the natural logarithm of sales instead of the natural logarithm of market value, because of possible multicollinearity problems. Hence, market value is one of the important variables in order to compute the CSCORE measure. Second, DTURN is included, because it controls for investor heterogeneity. The variable definitions of the control variables can all be found in Appendix A.

In a latter regression, MB, LEV and ROE are also incorporated as control variables. This is not done, however, in the primary regression. MB and LEV are important components of computing the CSCORE. Consequently, incorporating them in the primary logistic

regression could result in minor results because of multicollinearity. Following Hutton et al. (2009), contemporaneous ROE is also included in the latter regression as a control variable in order to mitigate the possible effects of a company’s profitability on its jump likelihood. ROE is proxied by income before extraordinary items divided by the book value of equity.

Therefore, ROE is only used in the latter regression for the same reasons of multicollinearity, because the book value of equity is also used in order to compute the MB variable.Initially, this study wanted to incorporate the control variables SIGMA, RET and NCSKEW as well, because this would have been in line with related papers (Kim and Zhang, 2010; Hutton et al., 2009; Chen et al., 2001). These variables would not have been incorporated in the main logistic regression, but in the latter regression as well. The three control variables are based on the variable W, which is also the basis for the JUMP variable. Therefore, these three control variables would again not have been incorporated in the initial logistic regression because of multicollinearity problems. SIGMA controls for weekly return volatility; RET controls for past one-year average weekly returns; NCSKEW controls for negative skewness. However, taking into account the possible multicollinearity problems and given the time

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scope of this research and other practical limitations like the needed skills and experience with statistical software, this study chose to let these measures alone for this study.

3.5 Portfolio analysis (H1b)

In order to examine whether the jump likelihood differs for high-conservative companies relative to medium- or low-conservative companies, this study compares the logistic results (H1a) of companies with low to high levels of accounting conservatism. In order to conduct this portfolio analysis, the sample is first split into three percentile groups (from low=1 to high=3) based on their level of conservatism (=CSCORE). Second the likelihood results associated with each group are calculated using equation 7 and then compared.

4. Descriptive statistics, results and interpretation

4.1 Descriptive statistics

Table 2 presents the descriptive statistic of the main variables. These variables are used in the final empirical model, i.e. equation 7. They include the dependent variable JUMP(t+1), the independent variable of key interest CSCORE and the control variables. The mean of JUMP(t+1) of 0,6095637 indicates that 60,96% of the companies experienced one or more jump weeks per fiscal year. This is above the average of jump weeks that can be found in relating papers, i.e. 25-35% (Hutton et al., 2009; Chung, 2013; Wang, 2012). However, to the knowledge of this paper, this paper followed the same practice to come to this. The standard deviation also seems quite high. Therefore, this study believes that the smaller sample size or possibly outliers cause the relatively higher mean and standard deviation. Additionally, calculating the jump likelihood based on this exact methodology has not been don extensively, which could mean that the actual averaged mean might indeed lie higher than 25-35%. Finally, this study based its jump likelihood on the mean plus 3,2 times the standard deviation, whilst for example Hutton et al. (2009) maintained a standard deviation of 3,09. The CSCORE mean and median are a smaller than the means found in related papers like Kim and Zhang (2010) or Khan and Watts. However, this is possibly due to again a smaller sample size. Moreover, this study had to deal with a small amount of multicollinearity during the calculation of CSCORE. Given the time scope and knowledge limitations of this

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study, this study chose to not correct for this multicollinearity. Moreover, the correlations between the CSCORE measure and other variables are generally very well in line with relating papers (see table 3). Lastly, the other descriptive statistics are all very well in line with relating papers. The means, medians and standard deviations of all the control variables seem to be constructed accordingly.

Table 2 Descriptive statistics

Variable Mean Std. Q1 Median Q3 N

JUMP(t+1) 0,6095637 0,4878773 0 1 1 8365 CSCORE 0,0196971 0,0188821 0,0064443 0,0190496 0,0326033 8195 SIZE 6,775931 2,285423 5,343659 6,890083 8,415277 8133 DTURN 0,0062065 0,1604104 -0,0181034 0,0030604 0,0314372 6505 ROE 0,0617019 0,5461075 0,0331303 0,1012792 0,1695068 8195 MB 2,886754 3,578136 1,343489 2,022222 3,171888 8195 LEV 0,1129471 0,387583 0,0003819 0,0144073 0,0649292 8195 Appendix A provides a complete overview of all the variables and their definitions.

Table 3 presents the correlation matrix of the key variables. The correlations are all in line with related papers like Kim and Zhang (2010), Hutton et al. (2009), Chung, 2013 and Wang, 2012, which supports the reliability of this study. The one noticeable difference lies in the correlation between (i) SIZE and CSCORE. This is an evident negative correlation, which is in line with Kim and Zhang. However, -80,15% lies above the correlation found by for Kim and Zhang (2010) of -40%. The exact reason behind this difference is not exactly clear, but it could be possibly due to the multicollinearity factor in the CSCORE measure or again the relatively smaller sample size.

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Table 3 Correlation matrix

Variable JUMP(t+1) CSCORE DTURN ROE SIZE MB LEV

JUMP(t+1) 1.0000 CSCORE 0.0553 1.0000 DTURN -0.0050 -0.0321 1.0000 ROE -0.0250 -0.1354 0.0025 1.0000 SIZE -0.0878 -0.8015 0.0478 0.1304 1.0000 MB -0.0011 -0.3601 0.0015 -0.0023 -0.0398 1.0000 LEV -0.0374 0.1047 0.0459 -0.0475 0.0817 -0.1047 1.0000 Appendix A provides a complete overview of all the variables and their definitions.

All in all the descriptive statistics and correlations between the key variables seem to be constructed well and seem to be in line with the related papers. The most noticeable difference lies mainly in the mean and median of the jump likelihood, but (i) because of the previously mentioned reasons and limitations like for example the smaller sample size and (ii) because of the fitting correlations this is let alone for this thesis.

4.2 Results H1a

Table 4 presents the logistic regression, i.e. equation 7, which predicts the jump likelihood. All the coefficients of the variable of key interest her, the CSCORE, are negative. This is in line with the main hypothesis that accounting conservatism has a reducing effect on the likelihood of a jump event. In the first model, model a, a plain logistic regression is executed in which only the size effect is controlled for. The coefficient of CSCORE is indeed negative, but not yet significant. The P-value here equals 11,5%, which already provides some evidence for a reducing effect, but it’s not clearly significant. In model b, the control variable DTURN is added. This does affect the coefficient of CSCORE to become significant, but the P-value of DTURN is highly insignificant. In model c, ROE, MB and LEV are added as control variables. As explained in chapter 3, these variables are expected to cause

multicollinearity effects. The P-values range from 5-20%, which means that they seem to improve the model, but not significantly. This study expects this to be due to the

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Finally, model d is constructed, which includes all the control variables of model c except for the highly insignificant DTURN variable. This model provides the most significant

coefficient of CSORE and the other variables (and constant) are also of significant or strong influence. Taking into account that the relatively higher P-values of ROE and LEV could be due to multicollinearity, model d provides this study with the best results for further

interpretation.

As stated before, the coefficients of CSCORE in all four models are negative. This indicated a reducing effect of accounting conservatism on the jump likelihood, which is in line with hypothesis 1a. When looking at model d in particular, the coefficient of CSORE equals 1,1%. This indicates a high significant reducing effect of accounting conservatism on the jump likelihood. Therefore, this study found significant evidence for the main hypothesis, hypothesis 1a.

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Table 4

Predicting the jump likelihood: logistic regression of JUMP(t+1) on CSCORE(t)

*** p<0.01, ** p<0.05, * p<0.1

Appendix A provides a complete overview of all the variables and their definitions.

Model a Model b Model c Model d

Variabl es Coefficie nt P-value Coefficie nt P-value Coefficie nt P-value Coefficie nt P-value CSCOR E -3.668212 0.115 -5.31964 0.041** -8.746236 0.014** -7.99579 0.011** SIZE -.1000088 0.000** * -.1210819 0.000** * -.1416086 0.000** * -.1266142 0.000** * DTURN -.0055313 0.975 .0107194 0.951 ROE -.075458 0.204 -.0864994 0.125 MB -.0201207 0.053* -.0239685 0.012** LEV -.1257904 0.136 -.0987617 0.214 Constant 1.521535 0.000** * 1.651146 0.000** * 1.936271 0.000** * 1.873616 0.000** * N 7237 5680 5680 7237 Prob. > chi2 0.0000 0.0000 0.0000 0.0000

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4.3 Results H1b

Table 5 presents the portfolio analysis, which is executed in order to examine hypothesis 1b. This portfolio analysis is based on model d, because this study perceives model d to fit further examination best (see section 4.2). For the portfolio analysis, this study distinguishes three groups based on their conservatism scores, i.e. low-, medium- and high conservative. When looking at the coefficient of CSORE for all three groups, it seems that a downward trend may be found. For group 1, the coefficient of CSCORE equals 4,95,

indicating a positive effect. For group 2, the coefficient of CSCORE decreased relative to its coefficient of group 1. It equals 0,81, which seems to go in the direction of zero indicating a somewhat neutral effect. For group 3, the high conservative group, the coefficient continues to decrease even further to -22,95. This trend is in line with hypothesis 1a that the level of conservatism has a reducing effect on the jump likelihood. However, given the high insignificant coefficients of group 1 and 2, a real trend cannot be affirmed. The declining coefficients are, however, noticeable when taking into account the overall result of hypothesis 1a. Especially given the fact that the coefficient of the CSCORE measure of group 3 is both very negative and highly significant.

Turning to hypothesis 1b, however, it seems that the portfolio analysis does not

support this hypothesis. The expected result of hypothesis 1b would be a significant or at least stronger negative coefficient of CSCORE for group 2 and a more neutralized coefficient of CSCORE for group 3. This was based on the finding of Kim and Pevzner (2010) that

investors react stronger (weaker) to good (bad) news of more conservative companies relative to less conservative companies. When looking at table 5, this appears not to be the case. Therefore, this study found no evidence in favor of a neutralized effect of conservatism on the jump likelihood and hypothesis 1b is rejected. The coefficients only seem to move in line with hypothesis 1a.

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Table 5

Portfolio analysis of three conservatism groups, i.e. low-, medium- and high conservative.

*** p<0.01, ** p<0.05, * p<0.1

Appendix A provides a complete overview of all the variables and their definitions. Group 1 = low Group 2 =

medium

Group 3 = high Variables Coefficient P-value Coefficient P-value Coefficient P-value CSCORE 4.953935 0.513 .8131176 0.942 -22.94539 0.000*** SIZE -.0793621 0.112 -.0992068 0.035** -.1391557 0.001*** ROE -.0781929 0.278 -.2181922 0.174 .04801 0.692 MB -.009311 0.477 -.0268395 0.278 .0358283 0.333 LEV -.0132821 0.935 -.382324 0.031** .053167 0.634 Constant 1.33562 0.005*** 1.667271 0.001*** 2.36736 0.000*** N 2459 2444 2334 Prob. > chi2 0.0196 0.0080 0.0000

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4.4 Interpretation of results

The aim of this section is to further interpret the statistical results by means of the theoretical underpinnings of the hypotheses. As concluded from the statistical tests, this study found significant evidence that supports the main hypothesis that accounting conservatism in year t has a reducing effect on the jump likelihood in year t+1. The evidence for this result is a negative, significant coefficient of the CSCORE measure in the logistic regression on JUMP(t+1), see table 4. Hypothesis 1b is rejected, because the evidence of the portfolio analysis only seems to further support the main hypothesis. A neutralized effect has not been found for the high-conservative group, see table 5.

The theoretical underpinnings of the main hypothesis of this study flow from a

theoretical link first developed by Jin and Myers (2006). Managers have incentives to release as much as good news as possible to the investors on the market. By releasing good news (or not releasing bad news) a manager may for example receive bigger bonuses because of the positive reactions of investors on the market to the good news. Hence, the manager starts to hoard bad news as much as possible. However, this bad news hoarding can only go on until a particular tipping point is crossed, because the hoarding becomes too costly for example. Subsequently, all the hidden bad news is released to the market all at once, which could result in a stock price crash. Accounting conservatism reduces these incentives of managers to hide bad news, because of the stronger verification requirements for good news relative to bad news. Subsequently accounting conservatism could work as a mechanism to control for these incentives of managers, because the accounting mechanism incentives the relative sooner release of bad news. Therefore, Kim and Zhang (2010) predicted that accounting

conservatism has a reducing effect on the crash likelihood of a company. Kim and Zhang (2010) indeed found evidence for this. This study extended the study of Kim and Zhang (2010) by applying the same line of thinking on the likelihood of a stock jump. Conservative companies disclose bad news relatively sooner and good news is recognized less rapidly, because they set higher requirements. Consequently, a point where a great amount of good news is released in an instant, leading to a possible stock price jump, will occur not so readily with conservative companies as with less conservative companies. Therefore, this study predicted that accounting conservatism also has a reducing effect on the likelihood of a stock price jump. As stated before, the results indeed indicate a reducing effect of accounting conservatism on the jump likelihood of a company.

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Building on the previously described theory and papers, the results seem to implicate that accounting conservatism indeed works as a contra mechanism for the opportunistic incentives of managers to hoard bad news, but it also works as a mechanism that reduces the release of good news. On one hand it reduces the incentives of managers to hoard bad news, because of the asymmetrical requirements to recognize bad news as such relatively sooner, which results in a lower crash likelihood (Kim and Zhang, 2010). On the other hand it also reduces the release of good news, because of the higher requirements to recognize good news as such. As can be found in tables 4 and 5, this results in a lower jump likelihood. In short, accounting conservatism seems to help protect the company from possible costs associated with a stock price crash, but it also seems to contribute in depriving the company from possible benefits associated with a stock price jump. Considering this, the desirability of accounting conservatism is not that easy to assess. This study attempts to further interpret the results in order to see whether accounting conservatism seems desirable or not based on the theory introduced in chapter two of this study of LaFond and Watts (2008).

LaFond and Watts (2008) found evidence for a market demand for accounting conservatism, which extends the frequently addressed explanation for conservatism, namely contracting. Investors demand conservatism, because it reduces agency costs caused by information asymmetry, which in turn is caused by the optimism bias. The optimism bias refers to the incentives of managers to overstate the financial statements, because of for example opportunistic behavior. In other words, LaFond and Watts’ (2008) findings

demonstrate that accounting conservatism is more than a means to reduce contracting costs, but that it is actually a market means that reduces agency costs caused by information asymmetry. When considering the findings of LaFond and Watts (2008), the results of this study seem to imply that the jumps of conservative companies are preferred by the market, because the jumps, even if they occur less, contain relatively less optimism bias.

Subsequently the lower optimism bias results in lower information asymmetry, which in turn reduces agency costs. Considering this, it seems that the benefits of conservatism by

protecting against possible crash costs should outweigh the costs of missing out on possible benefits associated with more jumps, because the market demand found by LaFond and Watts (2008) indicates that agency costs as a whole will decrease.

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When considering the standpoint of the FASB on the contrary, the results could possibly also implicate that the relatively lower jump likelihood of conservative companies stems from an interference with the quality of neutrality of accounting. Subsequently the information asymmetry actually increases leading to increased agency costs. LaFond and Watts (2008), however, demonstrated that their findings are more robust than the statements of the FASB (2008). Therefore, this study tends to conclude that conservatism is a desirable accounting principle with regard to its effects on stock fluctuations and information

asymmetry and agency costs, based on the results of the paper of Kim and Zhang (2010) and the results of this paper. However, this study suggests that more in-depth future research is needed in order to thoroughly determine (i) to what extent accounting conservatism is desirable or not and in specific (ii) whether the reduced effect on jump likelihood should be seen as an advantage or as a disadvantage.

5. Conclusion

The purpose of this research was to investigate to what extent the level of accounting conservatism of a company influences the likelihood of a stock price jump of the company. Prior studies like Jin and Myers (2006), Hutton et al. (2009), Kim and Zhang (2010) and LaFond and Watts (2008) provided this study with theoretical foundations on which the following main hypothesis was built: “accounting conservatism in financial statements reduces the likelihood of a future stock price jump, ceteris paribus”. An empirircal research method was employed in the aim to examine this hypothesis. This study extended the paper of Kim and Zhang (2010) in order to examine the effect of conservatism on the jump likelihood next to Kim and Zhang’s (2010) findings about the effect on the crash likelihood. In addition a second hypothesis was developed in order to give this study more depth by considering alternative interpretations. This study first set the background by explaining accounting conservatism and outlining the more addressed conventional argumentation behind the reasons of its existence and the newly emerging theoretical findings by LaFond and Watts (2008). Hereafter, particular studies of interest were further conceptualized in order for this study to develop its main hypothesis. In addition a second hypothesis was developed in order to give this study more depth by considering that investors are capable to take into account a company’s conservatism level when assessing the release of good or bad news.

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The empirical analysis of this study found evidence for hypothesis 1a, indicating that conservatism in fact has a reducing effect on the jump likelihood of a company’s stock in the following year. The empirical analysis did not found evidence for hypothesis 1b, implying that investors don’t seem to react stronger (weaker) to good (bad) news of more conservative companies relative to less conservative companies. The portfolio analysis actually further supported the main hypothesis, hypothesis 1a.

Building on the main theoretical link, the results seem to implicate that accounting conservatism indeed works as a mechanism that reduces the release of good news resulting in a lower jump likelihood. When combining the result of this paper with the results of Kim and Zhang (2010), it is not really possible to determine the desirability of accounting

conservatism, because it on one hand help protect the company from possible costs associated with a stock price crash, but it also seems to contribute in depriving the company from

possible benefits associated with a stock price jump. Bearing in mind, however, that investors demand “more conservative earnings as a means of mitigating agency costs” (LaFond and Watts, 2008, p.476), this study tends to conclude that the benefits of having fewer crashes should outweigh the costs of having fewer jumps. This study, however, does advocate for further future research to determine whether information asymmetry and thereby costs as a whole indeed decrease because of accounting conservatism, because prominent accounting bodies like the FASB (2008) continue to distance themselves from the principle of

conservatism.

Initially this study intended to include multiple robustness checks. For example this study wanted to calculate the CSCORE again based on annual cross-section regressions and this study intended to include an alternative measure for the jump likelihood. Unfortunately, this study did not manage to include robustness checks because of the time scope of the thesis in combination with the somewhat limited knowledge of the author with statistical software. Another possible limitation of this study was its sample size. Initially, this study’s intention was to comprise the years 1962-2013, but because of (i) the time scope of this master’s thesis and (ii) practical limitations the sample needed to be scaled down. A further limitation is that this study came across a few multicollinearity difficulties between certain components of the CSCORE measure. The study did not correct for this, because of the limited time and

knowledge of the author. An important note, however, is that the correlations of the CSCORE fitted with related literature. A last possible limitation is that it was not able to include the

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control variables RET, SIGMA and NCSKEW, because this would have been in line with related papers (Kim and Zhang, 2010; Hutton et al., 2009; Chen et al., 2001). These control variables would have been based on the variable W, which is also the basis for the JUMP variable. Therefore, these control variables would again not have been incorporated in the initial logistic regression because of multicollinearity problems. Although this study had to cope with some time and expertise limitations, the purpose of this research is evident. It contributed to a rather new and emerging branch of the conservatism literature and the implications of this study are worth deeper investigation. Moreover, the current distancing of accounting and economic bodies like the FASB from the concept of accounting conservatism should encourage further in-depth future research. This may be especially important given the recent economic crisis and the reducing effect of accounting conservatism on stock crashes (Kim and Zhang, 2010) and the possible reducing effect of accounting conservatism on agency costs as a whole.

As stated before, the results of this paper are worth to be further investigated. For example an in-depth analysis that compares the costs associated with crashes to the benefits associated with jumps could help demonstrate the possible desirability of accounting

conservatism. An interesting future research question could be whether accounting conservatism has a reduced effect on the total costs associated with crashes and jumps. A positive answer to this question would then seem to support the findings of LaFond and Watts (2008); accounting conservatism reduces information asymmetry and thereby agency costs. A negative answer to this question would then seem to support accounting bodies like the FASB (2008); accounting conservatism increases information asymmetry and thereby agency costs. Further it would be interesting to additionally conduct this research on a longer term instead of only a short term. It is imaginable that a longer research window offers more or even better insights, because a shorter window for example might not clearly demonstrate to what extent costs or benefits persist over time.

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Appendix A Variable definitions

X is proxied by the earnings before extraordinary items divided by the market value of equity. R is proxied by the yearly stock return compounded from monthly stock returns.

D is a dummy variable that equals one if R is beneath 0, and zero otherwise. MKV is proxied by the natural log of the market value of equity.

MB is the market-to-book ratio, which is proxied by the market value of equity divided by the book value of equity, where the market value of equity equals common shares outstanding multiplied by the annual fiscal closing price.

LEV is the debt-to-equity ratio, which is proxied by the book value of total liabilities divided by total assets.

rj,t represents the stock return of stock j in week t, which is proxied by the weekly stock

returns compounded from daily stock returns, where the daily stock return is equal to ((daily stock price/daily adjustment factor) * daily total return factor )[t] /(daily stock price/daily adjustment factor) * daily total return factor))[t-1]-1)*100)

rm,t represents the market index return in week t, which is proxied by the weekly market

returns compounded from daily market returns.

W is the firm-specific weekly return, which is proxied by the natural logarithm of the residual of the expanded market index regression (see equation 5) plus 1.

JUMP is a binary indicator that equals one if a company encounters more than one jump week per (fiscal) year, and zero otherwise. The firm-specific weekly return is denoted as a jump week if it is 3,2 standards deviations above the mean of the firm-specific weekly returns for the given fiscal year.

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JUMPt+1 is a binary indicator that equals one if a company encounters more than one jump

week in year t+1, and zero otherwise.

CSCORE represents the conservatism score based on the measure of Khan and Watts (2009) (see equations 1-4).

SIZE is proxied by the natural logarithm of sales.

DTURN is proxied by the average monthly share turnover per fiscal year t minus the average monthly share turnover of t-1, where monthly share turnover is proxied by the monthly trading volume divided by total number of shares outstanding during the month.

Accounting conservatism and jump likelihood : is conservatism desirable?