Conservatism and stock return skewness DEVENDRA KALE*, SURESH RADHAKRISHNAN, and FENG ZHAO Naveen Jindal School of Management, University of Texas at Dallas, 800 West Campbell Road, Richardson, Texas 75080 Abstract In this paper, we study the association between conservatism and stock return skewness. Existing literature has studied how conservatism is associated with stock return distribution in terms of mean returns as well as return volatility. The literature is relatively silent on how conservatism influences stock return skewness. Conservatism implies higher verification threshold for gains versus losses, thereby creating an asymmetry or skewness in reported earnings. Given that earnings and prices are highly correlated, we expect to find an association between conservatism and stock return skewness. Following recent literature, we use returns on skewness assets, which are designed to be long skewness, as a measure of stock return skewness. Every month, we sort our sample into quintiles, based on the conservatism score, and find that the returns on the skewness assets increase monotonically across conservatism quintiles, consistent with our expectation. In additional tests, we find that a dollar-neutral trading strategy with a long position in quintile 5 firms (highest conservatism) and a short position in quintile 1 firms (lowest conservatism) yields significant returns, after adjusting for priced risk factors. * Corresponding Author Email addresses: devendra.kale@utdallas.edu (Devendra Kale), sradhakr@utdallas.edu (Suresh Radhakrishnan), feng.zhao@utdallas.edu (Feng Zhao)
Section 1: Introduction In this paper, we study the association between conservatism and stock return skewness. Empirical evidence documents the association of conservatism with contemporaneous and future average stock returns as well as stock return volatility (Penman & Zhang [2002], Khan & Watts [2009], Penman & Zhang [2014]). However, the literature is relatively silent on whether and how, conservatism influences stock return skewness. Conservatism implies a higher degree of verification to recognize good news as gains than to recognize bad news as losses (Basu 1997). It therefore implies that expected losses are immediately recognized in earnings, whereas expected gains are recognized into earnings only after detailed verification and a fair amount of certainty that the gains will materialize. Conservatism thus, creates an asymmetry or skewness in earnings. Given that stock prices are discounted values of expected earnings, stock returns can be impacted by the skewness in expected earnings 1. Consequently, we expect to see an association between conservatism and the skewness of stock returns. To conduct our tests, instead of using the 3 rd moment formula, we use skewness assets constructed using a combination of stocks and options following Bali & Murray (2013) 2. These assets are long skewness, implying that any increase in the skewness of the underlying stock return distribution, should be associated with an increase in the returns on these skewness assets. As a result, we test our hypothesis using the returns on these skewness assets, as a measure of stock return skewness. Using these assets has two advantages. Firstly, these assets are constructed as delta and vega neutral 3. As a result, any changes in the mean returns or volatility of the underlying stock return 1 Basu (1995) also provides evidence of an association between conservatism and stock return skewness 2 We explain more about the skewness assets and other aspects of the research design later in the paper 3 Please see Appendix E to understand how these assets are delta and vega neutral
distribution do not impact the returns on these assets. This allows us to isolate the impact of skewness of stock returns. Secondly, the traditional skewness formula (3 rd moment formula) is not tradable. The skewness assets are a combination of options and stocks, which makes these assets tradable, allowing us to test our hypothesis in the capital markets setting. We use the three skewness assets from Bali & Murray (2013). Every month, we sort our sample into quintiles based on the conservatism score, and find that the returns on the two skewness assets increase monotonically across quintiles. This result is consistent with our expectation. This result is robust to several robustness tests, thereby providing support to our results. In additional tests, we show that a trading strategy which involves a long position in quintile 5 firms (highest conservatism firms) and a short position in quintile 1 firms (lowest conservatism firms), generates statistically and economically significant excess returns, which are not explained by well-known risk factors. A related paper to our study is Kim & Zhang (2016), where the authors use the negative conditional skewness of weekly stock returns over the next year, as a measure of crash risk. They show that conservatism is negatively associated with crash. Our results are consistent with theirs, which further lends credibility to our results. However, our study differs from theirs in a few aspects. Firstly, the authors in their paper use the 3 rd moment formula, whereas we use skewness assets, and analyze our results in a trading strategy as well. Secondly, they look at annual data, whereas our paper focuses on more frequent, monthly data. Thirdly, by using the skewness assets, we are able to control for the impact of contemporaneous stock return changes as well as changes in the volatility of the underlying stock return distribution, which can be correlated with stock return skewness. Our paper contributes to the literature in several ways. Firstly, we contribute to the literature on conservatism by providing evidence on how conservatism can influence stock return skewness. In
addition, our results can be tested in the capital market by means of a trading strategy. We also contribute to the capital markets literature by documenting conservatism as a determinant of stock return skewness. To the best of our knowledge, this is the first paper to conduct a detailed test of association between conservatism and stock return skewness as well as the first paper to use skewness assets as a measure of skewness as associated with an accounting variable. The rest of the paper is organized as follows: Section 2 discusses the background and hypothesis development; section 3 discusses research design, sample selection and descriptive statistics; section 4 discusses main results, robustness tests and additional analyses; section 5 concludes. Section 2: Background and Hypotheses development The conservatism principle has been widely studied in the accounting literature. Basu (1997) noted conservatism as accountants tendency to require a higher verification for gains vs losses. Extant literature has studied determinants as well as consequences of conservatism from the perspective of multiple stakeholders, including company s board, managers, debtholders, suppliers, analysts, shareholders as well as stock market participants. Ahmed & Duellman (2007) show that conservatism is associated with board characteristics; LaFond & Roychowdhury (2008) document the effect of managerial ownership on financial reporting conservatism. They state that separation of ownership and management gives rise to agency problems, and financial reporting conservatism is one potential mechanism to address this issue. In addition, Hui et al. (2012) show how a firm s suppliers and customers can influence accounting reporting practices, in terms of accounting conservatism. Hui et al. (2009) document a negative association between accounting conservatism and the frequency, specificity and timeliness of management forecasts. Zhang (2008) finds that
more conservative borrowers are more likely to violate debt covenants following a negative price shock, and that lenders offer lower interest rates to more conservative borrowers. Mensah et al. (2004) find accounting conservatism to be associated with higher analyst forecast errors and forecast dispersion. These studies document the impact of conservatism on stakeholders, both within and outside the firm. Another area of research in the conservatism literature is its association with and impact on the stock market. Existing studies have proven the association of conservatism with stock returns as well as stock return volatility. Penman & Zhang (2002) find a positive association between conservatism and future raw and size-adjusted stock returns. They suggest this is due to investors inability to understand conservatism in the financial statements. In addition, Khan & Watts (2009) show a positive association between conservatism and stock return volatility. They suggest that firms with high uncertainty tend to have higher agency costs, higher potential shareholder losses thereby increasing the likelihood of shareholder litigations, as well as higher unverifiable future gains. All these factors generate a higher demand for conservatism. Penman & Zhang (2014) also document a similar intuition. They suggest that conservative accounting considers the uncertainty in future gains before recognizing those in the financial statements. As a result, the higher the uncertainty of the future cash flows, the more conservative the financial statements would be. The authors document a positive association between conservatism and future stock returns (which they term as the required return, due to the uncertainty of the cash flows). Consequently, they suggest a positive conservatism and future volatility. The literature, though, is relatively silent on whether and how conservatism influences skewness in stock return distribution. Conservatism implies a higher degree of verification to recognize good news as gains than to recognize bad news as losses (Basu 1997). What this means is expected losses are recognized into earnings much faster (without extensive verification) than
expected gains (after extensive verification). This asymmetric verification threshold or asymmetric recognition of expected cash flows into earnings, creates an asymmetry or skewness in earnings 4. Given that prices are highly correlated with earnings, this skewness in earnings should impact skewness in stock returns as well. As a result, we hypothesize that conservatism would influence stock return skewness. However, we don t make an ex-ante prediction as to the direction of the association. Consequently, we write our hypothesis in the null form as follows: H1: Conservatism is not associated with stock return skewness Section 3: Research design, Sample selection and description We test our hypothesis using two methods. In the first method, we sort the sample every month into quintiles based on the conservatism score. We then calculate average return on each of the skewness assets within each quintile every month 5. We assess whether there is a monotonic trend in the returns on the skewness assets across quintiles, and whether the difference in the returns between the top quintile and bottom quintile is significant. In the second method, which is a robustness test to the first method, we run an OLS regression, regressing the skewness asset returns (our skewness measure), on conservatism, including control variables, used in the existing literature, along with suitable fixed effects. This provides robustness to our results from the sorting 6. We explain the two methods in detail here. 4 Basu (1995) states that conservatism creates a negative skewness in earnings. 5 We calculate equal weighted average for each quintile 6 In additional analyses, we also study excess returns on a dollar-neutral trading strategy with long position in quintile 5 firms (highest conservatism) and short position in quintile 1 firms (lowest conservatism).
FIRST METHOD: In the first method, we sort the sample every month into quintiles based on the conservatism score calculated using the Khan & Watts (2009) methodology. Quintile 1 captures those firms that have the lowest conservatism score whereas quintile 5 includes firms with the highest conservatism score in that month. Once we sort the sample into quintiles, we calculate average returns on each of the skewness assets for each quintile. We also calculate excess returns, measured as difference in the average return of each skewness assets in top quintile and bottom quintile. We assess if the excess returns are statistically significant. Stock return skewness measure: To measure stock return skewness, instead of using the traditional 3 rd moment formula, we use the returns generated by skewness assets documented in Bali & Murray (2013). The authors call these as Put Asset, PutCall Asset and Call Asset 7. To maintain consistency with their paper, we use the same names in our paper. As mentioned before, these assets are long skewness, implying that their returns increase with an increase in the skewness of the underlying stock return distribution. As a result, the skewness assets are a good measure of stock return skewness. Secondly, these assets are a combination of stocks and options, which makes these assets tradable, and allows us to test our hypothesis in a capital markets setting by way of a trading strategy. Moreover, these assets are constructed in a way that small changes in the returns (delta) or volatility (vega) of the underlying stock return distribution do not impact the returns on the asset 8. Consequently, we are able to isolate the effect of skewness in the underlying stock return distribution to test our hypothesis. 7 Appendix D provides a brief overview of how the three assets are constructed 8 Delta (vega) refers to a change in the return on these assets caused by a change in the price (return volatility) of the underlying stock
Following Bali & Murray (2013), we use options with a one-month expiry cycle for constructing these assets because the one-month options are usually the most active. Options with an expiry cycle longer than one month can lack sufficient trading volume. This can either reduce the sample or bias the results. The skewness assets are set up every month on the 2 nd trading day after the monthly options expiry cycle. Options usually expire on the third Friday of every month. Consequently, the assets are usually setup on the Tuesday following the monthly options expiry. However, if the Monday following the options expiry is a holiday, the 2 nd trading day is the Wednesday following options expiry, and the assets are set up on that Wednesday for that month. 9,10 Conservatism measures We use two measures of conservatism to test our hypothesis. Our primary measure of conservatism is based on Khan & Watts (2009). We also use Penman & Zhang (2002) measure for robustness 11. As per Khan & Watts (2009), we run the modified Basu regression (equation 4 in their paper) every month, and use the coefficients to calculate conservatism. Since every month, at least some of the firms report their quarterly financial statements, using the Khan & Watts (2009) methodology allows us to have an updated conservatism score every month for every firm 12. The financial and accounting data for calculating the conservatism score come from the company s 9 In Bali & Murray (2013), the authors use the 2 nd trading day, because they develop the test signal of their study, on the 1 st trading day after options expiry. Since in our study, we don t have that restriction, we can also use the first trading day after expiry to set up the assets. Our results do not change if we setup the skewness assets on the 1 st or 2 nd trading day after options expiry. 10 We don t construct the assets on the day of options expiry since volatility is very high. The expiry of the current options cycle can create a lot of noise in the options market, thereby biasing our results. 11 Please see Appendix B for a summary of how the two measures are calculated 12 Although we use an updated conservatism score every month, we also run our tests by calculating the score at the end of each fiscal year (quarter) and keeping the score constant for the next year (quarter) for each firm. The results do no change whether we use the monthly updated measure or keep the measure same for the next fiscal year (quarter).
quarterly financial reports. We use the latest available quarterly data for each company every month until new quarterly information is furnished by the company. Our alternate measure is based on Penman & Zhang (2002). Their methodology allows us to calculate a firm-specific measure which is not subject to data of other firms. Since some of the variables used for calculating this conservatism score are not available in the Compustat quarterly data, we use the latest available annual data for each company every month, till the company provides new annual financial data. We use the natural log of the conservatism measure calculated under Penman & Zhang (2002) methodology, because in our sample, the raw conservatism measure was slightly skewed 13. In further analyses, we also test if these excess returns calculated above still hold after controlling well-known risk factors. This is important for testing our hypothesis in the capital markets by way of a trading strategy. If the excess returns are explained away by the risk factors, then they just capture some of those known priced risk factors. Following existing literature, we use the Fama- French-Carhart 4 risk factors 14. The data for the tests comes from multiple sources. Data on Options comes from OptionMetrics database. Financial and accounting information is taken from Compustat. Data on stock returns and prices is downloaded from CRSP. Our sample covers the period 1996 to 2015. This is because the earliest data available in OptionMetrics database is Jan 1996 and the latest is March 2016. We calculate the skewness asset returns following data adjustments in Bali & Murray (2013). Accordingly, we remove observations with missing bid price or offer price, a bid price less than 13 Our results don t change whether we use the natural log measure or the raw measure. However, since the natural log measure reduced the skewness of the conservatism in our sample, we used the natural log measure for the test. 14 Li et al (2014) use the FFC4 factor model to test if a dollar-neutral strategy based on macro vs micro exposure of firms generates significant returns. In addition, Bali & Murray (2013) also use FFC4 factor model. To maintain consistency with these papers, we also use the 4 factor model for known risks. However, using the Fama French 3 or 5 factors does not change the results
0, offer price less than or equal to the bid price, a spread (offer-bid) less than the minimum spread ($0.05 for options with prices less than $3.00, $0.10 for options with prices greater than or equal to $3.00). We also remove options where the special settlement flag 15 in the OptionMetrics database is set, and options where there are multiple entries for a call or put option with the same underlier/strike/expiration combination on the same date. Options with missing or bad Greeks or implied volatilities are removed, as the Greeks (delta and vega) are necessary to create the skewness assets. An example of that would be observations where the vega is negative 16. Another example would be of a call option with a negative delta or a put option with a positive delta 17. Option price is calculated as the average of bid and ask prices. We also exclude observations of options that violate basic arbitrage conditions. For calls, we exclude observations where the bid price is equal to or higher than the spot price or where the offer price is less than the spot price minus strike price. For puts, we exclude observations where the bid price is equal to or higher than the strike price or offer price is less than the strike price minus the spot price. We winsorize the three return variables at 1% on both tails in order to control for the effect of outliers. For the two conservatism measures, we follow the respective methodology in the given papers. 15 Special settlement flag refers to non-standard settlement (the number of shares to be delivered may be different from 100; additional securities and/or cash may be required; and the strike price and premium multipliers may be different than $100 per tick; the option may have a non-standard expiration date) 16 Vega is the change in the price of a derivative asset caused by a change in the volatility of the distribution of the underlying asset. Consequently, vega should always be positive. 17 Delta is the change in the price of a derivative asset caused by a change in the price of the underlying asset. Since call option is an option to buy, delta for a call should always be positive. Whereas a put option is an option to sell, the delta for a put option should always be negative.
SECOND METHOD: This test is a robustness test to our earlier results. Here, we run the below pooled OLS regression: Skewness it = β 0 + β 1 Conservatism i,t 1 + β 2 Size it 1 + β 3 BTM it 1 + β 4 Market_RET it + β 5 Leverage it 1 + β 6 ROA it 1 (1) + β 7 Earnings dummy it 1 + β 8 Litigation it 1 + β 9 CGOV it 1 + ΣIND FE + ΣYEAR FE + ΣMonth FE + ε it The measures of skewness and conservatism remain the same as explained earlier. Summary Statistics Tables 1 and 2 present descriptive statistics as well as correlations among the variables used in our tests. As seen in Table 1, the average size is 8.20, with median of 8.22, which translates to market capitalization of ~USD 3.7 billion. This is expected; since we use options to construct the skewness assets, our sample is generally tilted towards larger firms. The average book to market ratio is 0.39 and the median is ~0.29 18. Leverage has a similar distribution as in Khan & Watts (2009), with mean leverage higher than the median. Average conservatism score is -0.0139 and the median is - 0.0049. The conservatism scores are not significantly skewed and can be used in our tests without any adjustment 19. The three skewness assets all exhibit negative returns on average. This is consistent with Bali & Murray (2013) 20. 18 The distribution of MTB (1/BTM) is consistent with that seen in Khan & Watts (2009). 19 The conservatism score calculated using Khan & Watt2 (2009) has a skewness of 0.125 20 The distribution of all 3 skewness assets is consistent with Bali & Murray (2013). For the Put asset, the mean return is higher than the median return. For the remaining two assets, the mean return is lower than the median return.
Table 2 shows the correlations among the variables used. All the skewness asset returns are positively correlated with one another, except for the spearman correlation between the Put and PutCall assets. Size and MTB are positively correlated, consistent with existing literature. Conservatism is negatively correlated with size and MTB. This is expected. As mentioned earlier, the Khan & Watts (2009) methodology is based on predicting a conservatism score using coefficients from cross-sectional regressions. The coefficients on size and MTB have a negative sign, implying a negative correlation with Conservatism 21. The correlation among the assets is also seen in Figure 1. The figure graphs average returns for each of the three skewness assets across firms, every month. The graphs show that the return patterns for the three assets are quite similar, especially for Put and PutCall asset. The returns are also similar for Call asset except for some peaks and troughs not seen for the other two assets. As seen in the graphs, Call asset has a maximum monthly return of ~12% as compared to ~7% for the other two assets. In addition, the minimum monthly average return for the Put and PutCall assets is approximately -27%, whereas the minimum monthly return for the Call asset is approximately -18%. These differences slightly weaken the correlation of Call Asset with the other two assets. However, barring these few exceptions, overall trend is quite similar for the three assets. Section 4: Empirical results 4.1 Base results Using Conservatism sorts 21 This result is consistent with Khan & Watts (2009). They also have a negative sign on the size and MTB coefficient, used for calculating the CSCORE (their name for the conservatism measure).
Our first method to prove our hypothesized association between conservatism and stock return skewness is by sorting the sample based on conservatism and assessing if there is a monotonic trend in average skewness asset returns across quintiles (from quintile 1 [lowest conservatism] to quintile 5 [highest conservatism]). The results are shown in Table 3, Panel A. As seen in the table, there is a monotonic increase in average skewness asset returns for the Put asset as well as the PutCall asset. In addition, the excess returns (quintile 5 minus quintile 1 average returns, captured by the Q5-Q1 row) are positive and significant. The Call asset, however, does not show any monotonic trend. In Table 3, Panel B, we use the same methodology, except that we replace quintile sorts with decile sorts. The results in panel B remain qualitatively similar, implying that the sorting method does not influence our results. In unreported tests, we re-ran the above test using the alternate measure of conservatism (Penman & Zhang 2002. Our results remain qualitatively similar. The results in Table 3, therefore, provide initial evidence of the hypothesized association between conservatism and stock return skewness. As a robustness test, we also tested the hypothesized association in the regression framework. We regressed the skewness asset returns on the raw conservatism measure and other control variables (equation 1), using both measures of conservatism. Tables 4 and 5 present the results from the regression using the two alternate measures of conservatism. In both the tables, we see that conservatism is positively and significantly associated with returns on two of the three skewness assets (Put and PutCall assets). Return on the Call asset does not generate any statistical significance with regard to conservatism. This is consistent with our results in Table 3, where the skewness assets showed no trend for the Call asset, and the Q5-Q1 excess return wasn t statistically significant.
Removing extreme years Figure 1, panels A-C graph out the average monthly returns on all the three assets during the sample. All three assets show a rather uniform pattern. However, as we can see, there are a few months when the assets have generated very high or very low returns. So, to dispel the possibility that these extreme returns may drive our results, we ran our main regression (equation 1) after excluding the 3 extreme negative return months. We then re-run the regression excluding the 3 extreme positive return months. In the third test, we exclude the 3 extreme positive and negative return months, and re-run the regression. The results are shown in Table 6, panels A-C. Panel A shows the results after excluding the 3 extreme negative return months; Panel B shows the results after excluding the 3 extreme positive return months; Panel C shows the results after excluding the 3 extreme positive and negative return months. The results are qualitatively similar to those in Table 4. This proves that the monthly fluctuations in the returns on the three assets do not drive the main results. In other (unreported) robustness tests, we also re-ran the main regression by excluding the 3 extreme negative and/or positive return years. The results remain qualitatively similar. In additional robustness tests, we also ran the regressions separately for each of two groups split on the basis of the size of firms 22. In our paper, since we use options data in our sample, our sample can be skewed towards larger firms. Also, using the Khan & Watts (2009) methodology, conservatism has a linear correlation with size, since size is one of the factors used in measuring conservatism. In addition, extant literature has proved an association between conservatism and 22 This test splits the sample into two groups on the basis of the median NYSE market capitalization as well as 75 th percentile of the NYSE market capitalization for each month, and using either of the two classifications does not change the results.
size of the firm. The above factors necessitate the use of this robustness test. Our results are qualitatively similar and do not change based on size split. The results shown so far help us prove that conservatism is, indeed, associated with stock return skewness. 4.3 Further analyses Trading Strategy All of the preceding tests document the association between conservatism and skewness of stock returns. As mentioned earlier, we don t use the traditional skewness formula (3 rd moment), and instead use a combination of options and stock to construct skewness assets because skewness, in its traditional form, is not tradable. Using the skewness assets as documented in the literature, allows us to go one step further and establish a trading strategy based on the results. The next test is thereby focused on documenting the excess returns from a dollar-neutral trading strategy. To test this, for each of the three skewness assets, each month, we set up a dollar-neutral hedge portfolio by taking a long position in the skewness assets for companies exhibiting high conservatism (quintile 5) and taking a short position in the skewness assets of companies with low levels of conservatism (quintile 1). This strategy is followed each month. To test whether the trading strategy provides genuinely excess returns, we regress the returns from each portfolio (quintile 1 to quintile 5, as well as hedge portfolio of quintile 5-quintile 1) on the known risk factors. Following existing literature, we use the Fama-French-Carhart 4 risk factors. We run the following regression: PortRet it = β 0 + β 1 SMB it + β 2 HML it + β 3 MKT it + β 4 Mom it (2)
where the subscript i refers to the portfolios and t to the particular month 23. PortRet refers to the average return generated from each of the three skewness assets, on a particular portfolio. Our coefficient of interest is β 0, which captures excess returns (return on the hedge portfolio, Q5-Q1) after adjusting for known priced risk factors 24. The results are discussed in Table 7 panel A. As we see, even after controlling for the priced risk factors, there is a monotonic increase in the average risk-adjusted returns as we go from quintile 1 to quintile 5. The dollar-neutral trading strategy generates statistically and economically significant excess returns, not explained by the priced risk factors. As we can see, the average excess monthly return on the Put asset is ~1.8%, whereas that on the PutCall asset is ~1.3%. The Call asset does not see any significant excess return, given the lack of association with conservatism in the first place. The results discussed in Table 7, panel A are based on quintile sorts. However, existing literature generally uses decile sorts to run such excess return tests. As a result, in our next test, we show that our results don t change whether we use quintile sorts or decile sorts. Similar to the quintile sorting, we sort the sample each month into deciles based on the conservatism measure. Then, we run the regression equation 2, this time on each decile portfolio, as well as on the hedge portfolio (long decile 10 and short decile 1). Table 7, panel B shows the results of this test. As we see, the results are qualitatively similar. The returns on the D10-D1 portfolio continue to be positive and significant for the Put and PutCall assets even after adjusting for the priced risk factors. Although we don t see a monotonic increase from decile 1 to decile 10 for these two assets, there is still a very visible increasing trend across the deciles. Panel C shows the decile wise average returns for 23 There are 6 portfolios; 5 quintile sorted portfolios and one hedge portfolio capturing the excess return between the top and bottom quintile. 24 The results are robust to using Fama French 5 risk factors or 3 risk factors.
each of the three skewness assets graphically. As we can see, both Put and PutCall assets exhibit an increasing trend. The Call asset, however, fails to exhibit any such monotonic trend. This is consistent with the earlier tests and results. The results in Panels B & C provide robustness to our results of the hedge strategy. Although our results are robust to using decile sorting, we use quintile sorts in our main analysis. This is because quintile sorting allows us to have relatively higher number of observations in each quintile each month such that the average return for the quintile in that month is not very sensitive to extreme returns. For example, there are 9 observations in quintile 5 in the month of Jan 1996 whereas there are 5 observations in decile 10 in the same month. Having a higher number of observations reduces the impact of an extreme observation when we calculate the average return in each sort. Consequently, we use quintile sorts for our main results. Section 5: Conclusion In this paper, we study the association between conservatism and stock return skewness. Since conservatism creates a skewness in reported earnings, we expect that to influence the skewness in the stock returns as well. We find that our results are consistent with our expectation. We also find that our results are robust to an alternate measure of conservatism, after removing the impact of periods of extreme returns (both positive and/or negative), as well as after controlling for the size of the firms. We also sort the sample every month, based on the conservatism score. We document that the average return on each skewness asset increases monotonically across quintiles. Further analyses show that a dollar neutral strategy, with long position in the skewness assets of firms with high conservatism and short position in the skewness assets of firms with low conservatism generates significant returns, not explained by well-known risk factors.
Our results contribute to the broad literature focusing on conservatism. We show that the skewness in earnings created by conservatism also influences skewness in stock returns. In addition, by using the skewness asset returns as a measure of stock return skewness, we document the impact of our study in a capital markets setting, by way of a trading strategy. Our study also contributes to the capital market literature by documenting conservatism as a determinant of stock return skewness.
Table 1: Descriptive Statistics Variable N Mean Median Std Dev p25 p75 Skewness Asset Returns Put Asset 53528-0.0137-0.0176 0.1901-0.0670 0.0530 PutCall Asset 53528-0.0166-0.0055 0.1604-0.0642 0.0554 Call Asset 53528-0.0176 0.0100 0.1859-0.0895 0.0763 SIZE 53528 8.2083 8.2284 1.2122 7.3215 9.1601 Conservatism 53528-0.0139-0.0050 0.1205-0.0779 0.0598 BTM 53528 0.3900 0.2881 0.5424 0.1656 0.4649 Leverage 53528 0.2625 0.0999 0.6066 0.0054 0.2862 Market_Ret 53528 0.0000 0.0001 0.0005-0.0003 0.0003 ROA 53526 0.0137 0.0168 0.0446 0.0052 0.0303 This table presents the descriptive statistics of some of the variables used in the analysis. Conservatism is calculated monthly using the Khan & Watts (2009) methodology. Size is the natural logarithm of market capitalization at the end of the previous month. BTM is book value to market value of equity. Leverage is short term and long term debt divided by market value of equity. Market return is the value weighted market return for the month. ROA is income before extraordinary items dividend by total assets.
Table 2: Correlation Matrix A B C D E F G H I J K L A 1 0.5883-0.1218 0.0374-0.0213-0.0064 0.0163 0.0044-0.0065 0.0006-0.0009 0.0071 B 0.8381 1 0.5823-0.003 0.0136 0.0139 0.0168-0.0162-0.0121 0.0142-0.0086 0.0006 C 0.1998 0.6114 1-0.0399 0.0345 0.0176-0.0101 0.0217-0.0068 0.0149 0.0051-0.0062 D -0.0162-0.0182 0.0051 1-0.5091-0.1805 0.1073-0.0304 0.0492-0.126-0.0625 0.1172 E 0.0273 0.0271-0.0027-0.4835 1 0.2677 0.0968-0.0229-0.1554 0.1199-0.0137-0.0295 F 0.0111 0.017 0.0086-0.1295 0.1975 1 0.4757 0.034-0.3855 0.0978-0.2717 0.0487 G 0.0061 0.0061-0.0041-0.0109 0.2327 0.3653 1-0.0241-0.4782 0.1081-0.3878 0.1167 H 0.0238 0.0364 0.0336-0.0249-0.0235 0.012-0.0195 1-0.0125 0.0222 0.0179 0.0078 I -0.0168-0.0193-0.0152 0.1691-0.1141-0.0353-0.0642-0.0123 1-0.5476 0.0985-0.0329 J 0.0258 0.0245 0.0089-0.2346 0.1421 0.0317 0.0674 0.0234-0.6057 1 0.0412-0.0274 K 0.0195 0.0079-0.0034-0.1207 0.0007-0.1291-0.1979 0.0186-0.094 0.145 1-0.1047 L -0.0063-0.0029 0.0007 0.118-0.0283 0.0095 0.0244 0.005-0.0138-0.0274-0.1047 1 This table presents correlations between the variables used in this analysis. The top triangle shows the Spearman correlation, while the bottom triangle shows the Pearson correlation. Due to shortage of space, we have used letters to represent the variables. The interpretation of these letters is given below. Conservatism is calculated monthly using the Khan & Watts (2009) methodology. Size is the natural logarithm of market capitalization at the end of the previous month. BTM is book value to market value of equity. Leverage is short term and long term debt divided by market value of equity. Market return is the value weighted market return for the month. ROA is income before extraordinary items dividend by total assets. Earnings dummy is an indicator variable equal to 1, if Income before extraordinary items is less than zero, 0 otherwise. Litigation is an indicator variable, equal to 1 if the firm operates in one of the industries represented by the following SIC codes (2833 2836, 8731 8734, 3570 3577, 3600 3674, 7370 7374, 5200 5961), 0 otherwise. CGOV is a proxy for corporate governance. It is an indicator variable equal to 1 if the CEO holds the position of Chairman, 0 otherwise Letter Variable represented A Put Asset Return B PutCall Asset Return C Call Asset Return D Size E Conservatism F BTM G Leverage H Market_Ret I ROA J Earnings Dummy K Litigation L CGOV
Table 3: Average returns on the three skewness assets by quintiles Panel A: Using the Khan & Watts (2009) conservatism measure, and using quintile sorts of the conservatism measure Skewness Asset Returns Put PutCall Call Quintile 1-0.0247-0.0247-0.0157 Quintile 2-0.0222-0.0233-0.0181 Quintile 3-0.0185-0.0225-0.0239 Quintile 4-0.0161-0.0223-0.0242 Quintile 5-0.00791-0.0109-0.0144 Quintile 5 Quintile 1 0.0166 ** 0.0142 *** 0.00175 * t-stat (3.816) (4.024) (0.556) Panel B: Using the Khan & Watts (2009) conservatism measure, and using decile sorts of the conservatism measure Skewness Asset Returns Put PutCall Call Decile 1-0.0265-0.0256-0.0155 Decile 2-0.0251-0.0245-0.0165 Decile 3-0.0229-0.0242-0.0211 Decile 4-0.0218-0.0236-0.0176 Decile 5-0.0228-0.0267-0.0256 Decile 6-0.0159-0.0202-0.0245 Decile 7-0.0225-0.0254-0.0237 Decile 8-0.0110-0.0208-0.0267 Decile 9-0.00654-0.0120-0.0160 Decile 10-0.00915-0.0101-0.0124 Quintile 5 Quintile 1 0.0173 ** 0.0156 *** 0.00350 * t-stat (2.633) (3.243) (0.644) This table presents the results from regressing skewness asset returns on the average conservatism score within each quintile. The table also documents whether the difference between quintile 5 average return minus quintile 1 average return is statistically significant. The sample is sorted every month into quintiles based on the conservatism score.
Table 4: Regression of skewness asset returns on conservatism (equation 1) Skewness Asset Returns VARIABLES Put PutCall Call Intercept -0.0239-0.0193-0.0117-0.0118-0.00726-0.0233 (-0.755) (-0.633) (-0.555) (-0.533) (-0.455) (-1.028) Conservatism 0.0490 *** 0.0568 *** 0.0353 *** 0.0407 *** -0.00726 0.00473 (6.710) (5.597) (5.806) (4.876) (-1.077) (0.565) Size -0.0175 0.00932 0.00233 ** (-0.171) (0.107) (2.192) BTM 0.00294 0.00506 ** 0.00637 ** (1.195) (2.214) (2.549) Leverage -0.00141-0.00342 ** -0.00429 * (-0.829) (-2.266) (-1.716) Market_Return 4.152 * 7.553 *** 11.71 *** (1.681) (3.653) (4.679) ROA 0.00588-0.0115-0.0668 * (0.182) (-0.399) (-1.675) Earnings Dummy 0.00961 *** 0.00613 ** -0.00286 (2.897) (2.194) (-0.752) Litigation 0.0126 *** 0.00776 * 0.00179 (2.732) (1.953) (0.472) CGOV 0.147 0.194 0.0489 (0.718) (1.111) (0.266) Industry FE Yes Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes Yes Month FE Yes Yes Yes Yes Yes Yes N 36,632 36,632 36,632 36,632 36,632 36,632 Adj R2 0.608 0.826 0.739 0.982 0.309 0.476 This table presents the results of regressing skewness asset returns on conservatism. It show the association of conservatism with stock return skewness, as measured by the returns on the skewness assets. Conservatism is calculated monthly using the Khan & Watts (2009) methodology. Size is the natural logarithm of market capitalization at the end of the previous month. BTM is book value to market value of equity. Leverage is short term and long term debt divided by market value of equity. Market return is the value weighted market return for the month. ROA is income before extraordinary items dividend by total assets. Earnings dummy is an indicator variable equal to 1, if Income before extraordinary items is less than zero, 0 otherwise. Litigation is an indicator variable, equal to 1 if the firm operates in one of the industries represented by the following SIC codes (2833 2836, 8731 8734, 3570 3577, 3600 3674, 7370 7374, 5200 5961), 0 otherwise. CGOV is a proxy for corporate governance. It is an indicator variable equal to 1 if the CEO holds the position of Chairman, 0 otherwise. Fixed effects are included by way of dummy variables. Two-digit SIC code is the industry definition used. We use standard errors, clustered at firm level.
Table 5: Regression of skewness asset returns on conservatism, using Penman & Zhang (2002) measure Skewness Asset Returns VARIABLES Put Put PutCall PutCall Call Call Intercept -0.0210 0.0559-0.0380 0.0132-0.00809-0.0114 (-0.701) (0.214) (-0.200) (0.695) (-0.0599) (-0.520) Conservatism 0.00139 *** 0.00166 ** 0.00721 ** 0.0011 *** -0.00162 *** -0.00119 ** (2.690) (2.452) (2.516) (3.613) (-2.705) (-2.041) Size -0.00300 *** -0.00190 ** 0.00216 ** (-3.279) (-2.441) (2.215) BTM 0.00308 0.00543 ** 0.00654 *** (1.239) (2.308) (2.600) Leverage 0.000751-0.00199-0.00409 * (0.470) (-1.345) (-1.671) Return -0.00759-0.00997-0.0153 (-0.758) (-1.078) (-1.161) Market_Return 1.327 5.221 ** 11.35 *** (0.511) (2.425) (4.395) ROA 0.00948-0.156-0.683 * (0.0291) (-0.542) (-1.706) Earnings Dummy 0.0105 *** 0.00670 ** -0.00263 (3.158) (2.370) (-0.688) Litigation 0.0122 *** 0.00751 * 0.00180 (2.625) (1.901) (0.478) CGOV 0.00158 0.00180-0.00752 (0.767) (1.027) (-0.0407) Industry FE Yes Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes Yes Month FE Yes Yes Yes Yes Yes Yes N 46,995 35,476 46,995 35,476 46,995 35,476 Adj R2 0.816 1.03 1.10 1.36 0.447 0.643 This table presents the results of the regression of skewness asset returns on the alternate measure of conservatism. The dependent variable is the return on skewness assets. Conservatism is calculated every month, using firm annual data, using the Penman & Zhang (2002) methodology. Size is the natural logarithm of market capitalization at the end of the previous month. BTM is book value to market value of equity. Leverage is short term and long term debt divided by market value of equity. Market return is the value weighted market return for the month. ROA is income before extraordinary items dividend by total assets. Earnings dummy is an indicator variable equal to 1, if Income before extraordinary items is less than zero, 0 otherwise. Litigation is an indicator variable, equal to 1 if the firm operates in one of the industries represented by the following SIC codes (2833 2836, 8731 8734, 3570 3577, 3600 3674, 7370 7374, 5200 5961), 0 otherwise. CGOV is a proxy for corporate governance. It is an indicator variable equal to 1 if the CEO holds the position of Chairman, 0 otherwise. Fixed effects are included by way of dummy variables. Twodigit SIC code is the industry definition used. We use standard errors, clustered at firm level.
Table 6: Regression of skewness asset returns on conservatism excluding months with extreme returns Panel A: Excluding top 3 months with extreme negative returns Skewness Asset Returns VARIABLES Put PutCall Call Intercept 0.00239 0.0180-0.00946 (0.0843) (0.901) (-0.423) Conservatism 0.0338 *** 0.0197 ** -0.00548 (3.462) (2.466) (-0.660) N 35,964 35,989 36,228 Adj R2 0.670 0.912 0.370 Panel B: Excluding top 3 months with extreme positive returns Skewness Asset Returns VARIABLES Put PutCall Call Intercept -0.0173-0.00997-0.0153 (-0.646) (-0.379) (-0.600) Conservatism 0.0447 *** 0.0482 *** 0.0107 (4.510) (5.664) (1.271) N 36,014 36,081 36,056 Adj R2 1.09 1.03 0.515 Panel C: Excluding months with top 3 extreme negative and positive returns Skewness Asset Returns VARIABLES Put PutCall Call Intercept 0.00384 0.0201-0.00120 (0.153) (0.846) (-0.0481) Conservatism 0.0257 *** 0.0267 *** 0.000256 (2.661) (3.314) (0.0308) N 35,346 35,438 35,652 Adj R2 0.704 0.952 0.401 This table presents the results of regressing skewness asset returns on conservatism, by excluding months with extreme returns, both positive and negative. Panel A excludes the months with 3 extreme negative returns; panel B excludes months with 3 extreme positive returns, and panel C excludes months with extreme positive as well as negative returns. Dummy variables for industry, year and month are included. Control variables are not shown for brevity. Standard errors are clustered at firm level.
Table 7: Average skewness asset returns, by quintile sorts of conservatism, controlling for FFC4 risk factors Panel A: Sorting Conservatism score into quintiles Skewness Asset Returns Put PutCall Call Quintile 1-0.0259-0.0250-0.0157 Quintile 2-0.0223-0.0237-0.0191 Quintile 3-0.0193-0.0234-0.0250 Quintile 4-0.0168-0.0232-0.0252 Quintile 5-0.00790-0.0110-0.0141 Quintile 5 Quintile 1 0.0178 *** 0.0139 *** 0.0021 t-stat (3.816) (4.024) (0.498) Panel B: Sorting Conservatism score into deciles Skewness Asset Returns Put PutCall Call Decile 1-0.0265-0.0256-0.0155 Decile 2-0.0248-0.0242-0.0163 Decile 3-0.0228-0.0241-0.0210 Decile 4-0.0216-0.0235-0.0176 Decile 5-0.0226-0.0266-0.0256 Decile 6-0.0158-0.0201-0.0244 Decile 7-0.0225-0.0254-0.0237 Decile 8-0.0109-0.0206-0.0265 Decile 9-0.00651-0.0120-0.0159 Decile 10-0.00909-0.0100-0.0123 Decile 10 Decile 1 0.0173 *** 0.0156 *** 0.00350 t-stat (2.633) (3.243) (0.644) This table presents the results from regressing average monthly portfolio returns on Fama-French_Carhart 4 risk factors. The portfolios are formed by sorting the sample each month on the basis of conservatism score. An additional portfolio, the dollar-neutral trading portfolio (long quintile 5 and short quintile 1) is also formed, the results of which are shown in the last row (Q5-Q1 or D10-D1).
Panel C: Graph depicting the average returns on skewness assets by decile sorts of conservatism
Figure 1: Panel A: Monthly average return on Put Asset
Figure 1 Panel B: Monthly average return on PutCall Asset
Figure 1 Panel C: Monthly average returns on Call Asset
Appendix B: Conservatism measures used in the paper Khan & Watts (2009) The first measure of conservatism we use in this paper is based on Khan & Watts (2009). The methodology is based on Basu (1997) measure of asymmetric timeliness. Under this methodology, we run the following cross-sectional regression for every month & year combination 25. The regression has been reproduced as is from the mentioned paper: X t = β 1 + β 2 D i + R i (μ 1 + μ 2 Size i + μ 3 M B i + μ 4 Lev i ) + D i R i (λ 1 + λ 2 Size i + λ 3 M B i + λ 4 Lev i ) + (δ 1 Size i + δ 2 M B i + δ 3 Lev i + δ 4 D i Size i + δ 5 D i M B i + δ 6 D i Lev i ) + ε i The coefficients from the above regression are then used to measure conservatism: CSCORE = λ 1 + λ 2 Size i + λ 3 M B i + λ 4 Lev i. The empirical estimators of λ i, i = 1 4 are constant across the firms for the particular period for which they are estimated in the regression above. However, they vary over time (month-year combination) since the coefficients are estimated from month-year regressions. Penman & Zhang (2002) 25 As mentioned earlier, our results do not change whether we use a monthly updated conservatism score, or calculate the score for each fiscal year (quarter), and keep the measure constant for the next fiscal year (quarter).
The second (alternate) measure of conservatism we use is based on Penman & Zhang (2002). This is an annual measure of conservatism, and is firm-specific, unlike the Khan & Watts (2009) measure, which is a measure relative to the particular time period, for which the original regression is estimated. The measure is calculated as given below C it = (INV RES it + RD RES it + ADV RES it )/NOA it, where INV RES it equals the LIFO reserve reported in the financial statement footnotes. We draw this number from Compustat (LIFR variable) RD RES it is calculated as the estimated amortized R&D assets that would have been on the Balance Sheet if R&D had not been expensed. R&D is capitalized using the industry coefficient estimates documented by Lev & Sougiannis (1996). AD RES it, similar to RD RES it is the estimated amortized advertisement expenses that would have been on the Balance Sheet if advertisement expenses had not been expensed in the year of outlay. Advertisement expenses are amortized using a sum of years digits method over two years, based on Bublitz & Ettredge (1989) and Hall (1993), who indicate that advertisement expenses have a typical life of about 1-3 years. The authors choose the above three components because these components because the accounting treatment for the above three components is relatively immune from managerial discretion after the expenditures has occurred. For instance, bad debt allowances can be a good indicator conservatism. However, allowance for bad debts can be high either because of an accounting policy of carrying net receivables at a conservative level or because there was a temporary rise in estimate of bad debts to reduce current income and increase future income.