* Corresponding Author

Email addresses: devendra.kale@utdallas.edu (Devendra Kale), sradhakr@utdallas.edu (Suresh

Radhakrishnan), feng.zhao@utdallas.edu (Feng Zhao)

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.

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 earnings1. Consequently, we expect to see an association between

conservatism and the skewness of stock returns.

To conduct our tests, instead of using the 3rd 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

neutral3. 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 (3rd 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 3rd 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 earnings4.

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 month5. 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

sorting6. 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 3rd 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 Asset7. 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 asset8. 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 2nd 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 2nd 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 robustness11.

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 firm12. The

financial and accounting data for calculating the conservatism score come from the company’s

9 In Bali & Murray (2013), the authors use the 2nd trading day, because they develop the test signal of their study, on

the 1st 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 1st or

2nd 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 skewed13.

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 factors14.

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 flag15 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 negative16. Another

example would be of a call option with a negative delta or a put option with a positive delta17.

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:

𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠𝑖𝑡 = 𝛽0 + 𝛽1𝐶𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑠𝑚𝑖,𝑡−1 + 𝛽2𝑆𝑖𝑧𝑒𝑖𝑡−1 + 𝛽3𝐵𝑇𝑀𝑖𝑡−1

+ 𝛽4𝑀𝑎𝑟𝑘𝑒𝑡_𝑅𝐸𝑇𝑖𝑡 + 𝛽5𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖𝑡−1 + 𝛽6𝑅𝑂𝐴𝑖𝑡−1

+ 𝛽7𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑑𝑢𝑚𝑚𝑦𝑖𝑡−1 + 𝛽8𝐿𝑖𝑡𝑖𝑔𝑎𝑡𝑖𝑜𝑛𝑖𝑡−1 + 𝛽9𝐶𝐺𝑂𝑉𝑖𝑡−1

+ 𝛴𝐼𝑁𝐷 𝐹𝐸 + 𝛴𝑌𝐸𝐴𝑅 𝐹𝐸 + 𝛴𝑀𝑜𝑛𝑡ℎ 𝐹𝐸 + 휀𝑖𝑡

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 ~0.2918. 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 adjustment19. 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.

(1)

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 Conservatism21.

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 firms22. 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 75th

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 (3rd 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:

𝑃𝑜𝑟𝑡𝑅𝑒𝑡𝑖𝑡 = 𝛽0 + 𝛽1𝑆𝑀𝐵𝑖𝑡 + 𝛽2𝐻𝑀𝐿𝑖𝑡 + 𝛽3𝑀𝐾𝑇𝑖𝑡 + 𝛽4𝑀𝑜𝑚𝑖𝑡 (2)

where the subscript i refers to the portfolios and t to the particular month23. PortRet refers to the

average return generated from each of the three skewness assets, on a particular portfolio. Our

coefficient of interest is 𝛽0, which captures excess returns (return on the hedge portfolio, Q5-Q1)

after adjusting for known priced risk factors24.

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. Two-

digit 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 combination25. The

regression has been reproduced as is from the mentioned paper:

𝑋𝑡 = 𝛽1 + 𝛽2𝐷𝑖 + 𝑅𝑖 (𝜇1 + 𝜇2𝑆𝑖𝑧𝑒𝑖 + 𝜇3

𝑀

𝐵𝑖+ 𝜇4𝐿𝑒𝑣𝑖)

+ 𝐷𝑖𝑅𝑖 (𝜆1 + 𝜆2𝑆𝑖𝑧𝑒𝑖 + 𝜆3

𝑀

𝐵𝑖+ 𝜆4𝐿𝑒𝑣𝑖)

+ (𝛿1𝑆𝑖𝑧𝑒𝑖 + 𝛿2

𝑀

𝐵𝑖+ 𝛿3𝐿𝑒𝑣𝑖 + 𝛿4𝐷𝑖𝑆𝑖𝑧𝑒𝑖 + 𝛿5 𝐷𝑖

𝑀

𝐵𝑖+ 𝛿6𝐷𝑖𝐿𝑒𝑣𝑖) + 휀𝑖

The coefficients from the above regression are then used to measure conservatism:

𝐶𝑆𝐶𝑂𝑅𝐸 = 𝜆1 + 𝜆2𝑆𝑖𝑧𝑒𝑖 + 𝜆3𝑀

𝐵𝑖+ 𝜆4𝐿𝑒𝑣𝑖. The empirical estimators of 𝜆𝑖, 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

𝐶𝑖𝑡 = (𝐼𝑁𝑉𝑖𝑡𝑅𝐸𝑆 + 𝑅𝐷𝑖𝑡

𝑅𝐸𝑆 + 𝐴𝐷𝑉𝑖𝑡𝑅𝐸𝑆)/𝑁𝑂𝐴𝑖𝑡, where

𝐼𝑁𝑉𝑖𝑡𝑅𝐸𝑆equals the LIFO reserve reported in the financial statement footnotes. We draw this

number from Compustat (LIFR variable)

𝑅𝐷𝑖𝑡𝑅𝐸𝑆is 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).

𝐴𝐷𝑖𝑡𝑅𝐸𝑆, similar to 𝑅𝐷𝑖𝑡

𝑅𝐸𝑆 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.

Appendix C: Variable definitions

Variable Name Description

BTM Book Value to Market Value of equity

CGOV A proxy for corporate governance; an indicator variable, equal to 1 if the

CEO of the company also holds the position of Chairman, 0 otherwise

Conservatism Conservatism score, as calculated using either Khan & Watts (2009)

methodology or Penman & Zhang (2002) methodology

FFC4 factors 4 factors that explain cross sectional variation in stock returns, as documented

by Fama & French (1993) & Carhart (1997). These include SMB (size factor,

short for Small minus Big) HML (value factor, short for High minus low),

MKT (market factor) and Mom (momentum factor, to capture momentum in

stock returns)

Industry FE Industry dummy variables using two-digit SIC code

Leverage Short term and long term debt, scaled by market value of equity

Lit26 An indicator variable set equal to 1 if the firm operates in the following

biotechnology (2833–2836 and 8731–8734), computer/electronics (3570–

3577, 3600–3674, and 7370–7374), or retail (5200–5961) industries, and 0

otherwise

Market_ret Value weighted market return for the month

Size Natural logarithm of market capitalization

26 Based on Francis, Philbrick, and Schipper (1994) and Kerr & Ozel (2015)

Small An indicator variable, equal to 1 if the market capitalization of the firm in

that month is less than the 2nd tertile of market capitalization of all firms in

NYSE at the start of that month, and 0 otherwise27

Year FE Year dummy variables using calendar years

27 Robust to using median NYSE market cap. However, using median market cap reduces the sample size of the

‘small’ group drastically. This is expected since we use options data. To avoid any bias arising from the small

sample, we use the 2nd tertile of market cap of NYSE firms

Appendix D: Description of the skewness assets used

This section briefly describes the construction of the skewness assets that we use for our tests. The

methodology follows BM paper. For the purposes of all the assets, OTM (out of the money) put

(call) option contract is that contract with a delta closest to -0.1 (0.1). Similarly, ATM (at the

money) put (call) option contract is that contract with a delta closest to -0.5 (0.5). Also, please note

that ∆𝑃,𝑂𝑇𝑀 refers to the delta of the OTM put contract, and 𝜐𝑃,𝑂𝑇𝑀 refers to the vega of the OTM

put contract. We can define other terms analogously for ATM as well as call contracts. The three

assets are described below. Please note that we use the same terminology as in BM, to make it

easy to read the other paper

Put Asset

𝑃𝑂𝑆𝑃,𝑂𝑇𝑀𝑃 = −1 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑂𝑇𝑀 𝑃𝑢𝑡

𝑃𝑂𝑆𝑃,𝐴𝑇𝑀𝑃 =

𝜐𝑃,𝑂𝑇𝑀

𝜐𝑃,𝐴𝑇𝑀𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝐴𝑇𝑀 𝑝𝑢𝑡

𝑃𝑂𝑆𝑆𝑃 = −(𝑃𝑂𝑆𝑃,𝑂𝑇𝑀

𝑃 ∗ ∆𝑃,𝑂𝑇𝑀 + 𝑃𝑂𝑆𝑃,𝐴𝑇𝑀𝑃 ∗ ∆𝑃,𝐴𝑇𝑀) 𝑠ℎ𝑎𝑟𝑒𝑠

PutCall Asset

𝑃𝑂𝑆𝐶,𝑂𝑇𝑀𝑃𝐶 = 1 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑂𝑇𝑀 𝐶𝑎𝑙𝑙

𝑃𝑂𝑆𝑃,𝑂𝑇𝑀𝑃𝐶 = −

𝜐𝐶,𝑂𝑇𝑀

𝜐𝑃,𝑂𝑇𝑀𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑂𝑇𝑀 𝑝𝑢𝑡

𝑃𝑂𝑆𝑆𝑃𝐶 = −(𝑃𝑂𝑆𝐶,𝑂𝑇𝑀

𝑃𝐶 ∗ ∆𝐶,𝑂𝑇𝑀 + 𝑃𝑂𝑆𝑃,𝑂𝑇𝑀𝑃𝐶 ∗ ∆𝑃,𝑂𝑇𝑀) 𝑠ℎ𝑎𝑟𝑒𝑠

Call Asset

𝑃𝑂𝑆𝐶,𝑂𝑇𝑀𝐶 = 1 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑂𝑇𝑀 𝐶𝑎𝑙𝑙

𝑃𝑂𝑆𝐶,𝐴𝑇𝑀𝐶 = −

𝜐𝐶,𝑂𝑇𝑀

𝜐𝐶,𝐴𝑇𝑀𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝐴𝑇𝑀 𝑐𝑎𝑙𝑙

𝑃𝑂𝑆𝑆𝐶 = −(𝑃𝑂𝑆𝐶,𝑂𝑇𝑀

𝐶 ∗ ∆𝐶,𝑂𝑇𝑀 + 𝑃𝑂𝑆𝐶,𝐴𝑇𝑀𝐶 ∗ ∆𝐶,𝐴𝑇𝑀) 𝑠ℎ𝑎𝑟𝑒𝑠

The construction of the above assets makes the assets delta and vega neutral. That is, small changes

in the price or volatility of the underlying stock are controlled for, so that we can focus on the

change in the value of the asset driven purely by the change in the skewness of the underlying

distribution.

Appendix E: Explanation on the delta and vega neutrality of the skewness assets

Here, we take the example of the PutCall asset to explain how the assets are made to be delta and

vega neutral

The PutCall asset is created as follows:

1. 𝑃𝑂𝑆𝐶,𝑂𝑇𝑀𝑃𝐶 = 1 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑂𝑇𝑀 𝐶𝑎𝑙𝑙

2. 𝑃𝑂𝑆𝑃,𝑂𝑇𝑀𝑃𝐶 = −

𝜐𝐶,𝑂𝑇𝑀

𝜐𝑃,𝑂𝑇𝑀𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑂𝑇𝑀 𝑝𝑢𝑡

3. 𝑃𝑂𝑆𝑆𝑃𝐶 = −(𝑃𝑂𝑆𝐶,𝑂𝑇𝑀

𝑃𝐶 ∗ ∆𝐶,𝑂𝑇𝑀 + 𝑃𝑂𝑆𝑃,𝑂𝑇𝑀𝑃𝐶 ∗ ∆𝑃,𝑂𝑇𝑀) 𝑠ℎ𝑎𝑟𝑒𝑠

Let’s suppose the vega of the OTM put option is 0.6 and the vega of the OTM call option is 0.9.

That means, in step 2 above, we short 0.9/0.6=1.5 contracts of the OTM Put.

Now, in step 1, we go long 1 OTM call option, which increases the vega by 0.9. To offset this, we

short 1.5 contracts of the OTM put, which will reduce the vega by 1.5 * 0.6 = 0.9. Thus, the vega

exposure in step 1 is removed in step 2. On similar lines, step 3 removes the delta exposure of the

position when we take a long/short position in the stock equal to the delta-weighted average

positions from steps 1 and step 2.

REFERENCES:

Ahmed, Anwer S., and Scott Duellman. "Accounting conservatism and board of director characteristics:

An empirical analysis." Journal of accounting and economics 43, no. 2 (2007): 411-437.

Bakshi, Gurdip, Nikunj Kapadia, and Dilip Madan. "Stock return characteristics, skew laws, and the

differential pricing of individual equity options." The Review of Financial Studies 16, no. 1 (2003): 101-

143.

Bali, Turan G., and Scott Murray. "Does risk-neutral skewness predict the cross-section of equity option

portfolio returns?." Journal of Financial and Quantitative Analysis 48, no. 4 (2013): 1145-1171.

Basu, Sudipta. "The conservatism principle and the asymmetric timeliness of earnings." Journal of

accounting and economics 24, no. 1 (1997): 3-37.

Carhart, Mark M. "On persistence in mutual fund performance." The Journal of finance 52, no. 1 (1997):

57-82.

Chen, Joseph, Harrison Hong, and Jeremy C. Stein. "Forecasting crashes: Trading volume, past returns,

and conditional skewness in stock prices." Journal of financial Economics 61, no. 3 (2001): 345-381.

Conrad, Jennifer, Robert F. Dittmar, and Eric Ghysels. "Ex ante skewness and expected stock returns." The

Journal of Finance 68, no. 1 (2013): 85-124.Drobetz et al

Fama, Eugene F., and Kenneth R. French. "Industry costs of equity." Journal of financial economics 43,

no. 2 (1997): 153-193.

Fama, Eugene F., and Kenneth R. French. "Common risk factors in the returns on stocks and

bonds." Journal of financial economics 33, no. 1 (1993): 3-56.

Glosten, Lawrence R., Ravi Jagannathan, and David E. Runkle. "On the relation between the expected value

and the volatility of the nominal excess return on stocks." The journal of finance 48, no. 5 (1993): 1779-

1801.

Gompers, Paul, Joy Ishii, and Andrew Metrick. "Corporate governance and equity prices." The quarterly

journal of economics118, no. 1 (2003): 107-156.

Hui, Kai Wai, Steve Matsunaga, and Dale Morse. "The impact of conservatism on management earnings

forecasts." Journal of Accounting and Economics 47, no. 3 (2009): 192-207.

Hui, Kai Wai, Sandy Klasa, and P. Eric Yeung. "Corporate suppliers and customers and accounting

conservatism." Journal of Accounting and Economics 53, no. 1 (2012): 115-135.

Khan, Mozaffar, and Ross L. Watts. "Estimation and empirical properties of a firm-year measure of

accounting conservatism." Journal of accounting and Economics 48, no. 2 (2009): 132-150.

Li, Ningzhong, Scott Richardson, and İrem Tuna. "Macro to micro: Country exposures, firm fundamentals

and stock returns." Journal of Accounting and Economics 58, no. 1 (2014): 1-20.

Mensah, Yaw M., Xiaofei Song, and Simon SM Ho. "The effect of conservatism on analysts' annual

earnings forecast accuracy and dispersion." Journal of Accounting, Auditing & Finance 19, no. 2 (2004):

159-183.

Penman, Stephen H., and Xiao-Jun Zhang. "Accounting conservatism, the quality of earnings, and stock

returns." The accounting review 77, no. 2 (2002): 237-264.

Penman, Stephen H., and Xiao-Jun Zhang. "Connecting book rate of return to risk: The information

conveyed by conservative accounting." Unpublished paper, Columbia University and University of

California, Berkeley (2014).

Watts, Ross L., and Jerold L. Zimmerman. "Towards a positive theory of the determination of accounting

standards." Accounting review (1978): 112-134.

Watts, Ross L. "Conservatism in accounting part I: Explanations and implications." Accounting

horizons 17, no. 3 (2003): 207-221.

Zhang, Jieying. "The contracting benefits of accounting conservatism to lenders and borrowers." Journal

of accounting and economics 45, no. 1 (2008): 27-54.