Innovation Output and Idiosyncratic Volatility: US Evidence

: Firms engaging in innovative practices have patents to prevent competitive forces from eroding the resulting economic rents; however, there is limited evidence regarding the impact of innovation on risk. We shed new light on how ﬁrms’ involvement in innovation activities impacts their volatility, particularly their idiosyncratic volatility. In this paper, we empirically examine the effect of innovation on idiosyncratic volatility. To do so, we empirically examine the impact of innovation, measured by patents weighted by citations and R&D expenditure, on the idiosyncratic volatility of ﬁrms. Using a large sample of 8256 US ﬁrms, we ﬁnd that more innovation is associated with lower idiosyncratic volatility. We also ﬁnd that information uncertainty is the channel through which innovation affects idiosyncratic risk. The results are robust for different measures of idiosyncratic volatility. These results have empirical implications for investors, managers, and ﬁrms engaging in innovation-related activities.


Introduction
The purpose of this paper is to investigate the impact of innovation output on idiosyncratic volatility (IVOL).Economic theory suggests that innovation contributes positively to firm value and economic growth (Jaffe 1986;Hall 1993;Solow 1957).On the other hand, innovation can also have a "creative destruction" impact on markets.Shiller (2000) suggests that excess volatility increases significantly in periods of rapid technological innovation.An analysis of trends in unsystematic risk shows that it has increased since the 1960s, and this might be attributed to new technologies and listing of riskier companies (Brown and Kapadia 2007).
Firms engage in innovative activities, at first, through investing in R&D projects that are inherently risky due to their low success rate, irreversibility, and high adjustment costs (Holmstrom 1989;Bloom 2007).These investments increase the uncertainty of future economic growth and lead to an increase in stock return volatility (Chan et al. 2001;Kung and Schmid 2015).If R&D projects produce valuable innovations, firms are more likely to apply for patents to secure the economic rent resulting from these projects.A patent provides legal protection for firms and reduces the uncertainty surrounding future cash flows (Balasubramanian and Sivadasan 2011;Hall et al. 2005;Kogan et al. 2017).In addition, applications provide significant details about the invention.Thus, obtaining patents is expected to help reduce the uncertainty associated with R&D projects.
Previous studies have investigated the impact of innovation on firms' risk levels.Several studies have shown that innovation increases firms' risk levels (Chan et al. 2001;Zhang 2015;Gu 2016).On the other hand, other studies show that firms' risk levels decrease 2. Hypothesis Development Schumpeter (1934) suggests that firms can achieve long-term success by continuous innovation that creates economic rents that establish a temporary monopoly.The process of capturing these economic rents includes spending on R&D projects and protecting fruitful projects through patenting.Empirical evidence suggests that firms that are more innovative, i.e., those that have patents with more citations, have higher market valuations (Hall et al. 2005).
The economic impact of R&D spending and patenting may differ due to the different nature of these activities.R&D spending is an example of Knightian uncertainty because its benefits are largely unknown (Knight 1921).Thus, as a firm increases its R&D expenditure, its risk level is expected to increase.Zhang (2015) shows that R&D investment increases distress risk.In addition, Bloom (2007) suggests that R&D investment is inflexible and has high adjustment costs.Xu (2006) investigates the reaction of stock price volatility to R&D progress.He shows that stock price volatility decreases proportionally with progress in the R&D process.Patents, on the other hand, work in the opposite direction from R&D spending.When a firm successfully patents its innovative activities, the risk associated with R&D spending and innovative activities is reduced, and this is expected to be reflected in the firm's stock price volatility.Based on this discussion, we formulate our first hypothesis: Hypothesis 1a.IVOL is negatively associated with patents, ceteris paribus.
Although patents decrease IVOL, firms with low information uncertainty would not gain much from patenting their activities because patents do not help market participants to learn more about the future profitability of the firm.In contrast, firms with high information uncertainty are expected to have a higher benefit from their patents because they disseminate information to the market about the future profitability of these firms.As a result, patents should have a higher impact, in absolute terms, on IVOL in firms with higher information uncertainty.This discussion leads us to our second hypothesis: Hypothesis 1b.The effect of patents on IVOL is stronger when firms have higher information uncertainty, ceteris paribus.

Sample Selection and Research Design
The sample in this study comprises US firms with available data in CompStat, Center of Research in Security Prices (CRSP), and CRSP/CompStat Merged database from 1982 to 2015.In addition, Fama and French 3-factor and Carhart 4-factor data were obtained from the Fama and French & Liquidity Factors database.The patents dataset is constructed from three databases from the United Patent Trademark Office (USPTO) data.The first database is the National Bureau of Economic Research (NBER)'s Patent Data Project database (PDP).This dataset is constructed by Hall et al. (2001).The second database was built by Kogan et al. (2017).The third database was created by Li et al. (2014), and it is used to update the first two databases.
The choice of 1982 as a starting date for the sample is due to the availability of the data needed to construct all the dependent variables.We exclude firms in the banking, utilities, insurance, and other industries (i.e., 31,45,and 48,respectively).Additionally, we exclude firms with negative net income.The final sample consists of 8256 firms, representing 79,923 firm years.The choice of 2015 as the end date for the sample was in order to account for the number of patent citations.
Table 1 shows the sample's frequency distribution based on the Frama and French 48-industry classification (Fama and French 1997).The table shows that the sampled firms are classified into 44 industries.The industries with the highest percentage of observations are Business Services (12.1%),Electronic Equipment (8.0%), and Pharmaceutical Products (6.3%).Table 2 shows the summary statistics of the dependent and control variables.To minimize the impact of outliers, all variables are winsorized at the 1st and 99th percentiles.The annualized standard deviation of the residuals of the market model using weekly data (IVOL_MM) is 0.53 over the sample period (the standard deviation of the residuals of the Fama and French three-factor model using weekly data (IVOL_FF3) and the standard deviation of the residuals of the Carhart four-factor model using weekly data (IVOL_C4) are also reported).The average firm in our sample has weighted patents (PAT) of 0.22 and an R&D expense as a percentage of sales (R&D) of 0.18.On average, the standard deviation of analysts' expectations of a firm's EPS scaled by price (DISP) is 0.18, the cash flow volatility (CFVOL) is 0.13, the firm size (SIZE) is 5.43, a natural log of age (AGE) of 2.74, a market to book ratio (M.B.) of 2.80, and a market leverage ratio (LEV) of 0.34.The average cash holding included in our sample (CASH) is 0.18.The average firm has an average dividend payout ratio (DPO) of 0.16, a bid-ask spread (BIDASK) of 0.03, and an ROA of 0.08.Additionally, the average concentration within an industry (HHI) and tangibility of assets (TANG) are 0.07 and 0.29, respectively.
To investigate the impact of innovation on IVOL, we estimate the following panel regression model: The dependent variable in the model is IVOL at time t.The primary variable of interest is PAT it−1 .The coefficient of the variable is expected to be negative and significant.Controls it−1 , as discussed previously, is a vector of firm characteristics that could affect the IVOL.Firm i and Year t are firm and year dummies that are available in the model to control for firm and time fixed effects.We acknowledge that a firm's innovative activities and other included financial variables are contemporaneously determined within the firm.Thus, we follow Mazzucato and Tancioni (2012) and use the lagged values of the control variables.This means that pre-determined values are used to estimate simultaneous relations.
To test H1b, we estimate the following panel regression model: In this model, we interact the PAT with DISP to investigate the marginal impact of innovation output on firms with different levels of information uncertainty.We expect the coefficient on the interaction variable to be negative and statistically significant.

Variables' Definitions
To estimate IVOL, we use the annualized standard deviation of the residuals of the market model.The model is estimated using the following regression equation: where r it is the excess return for stock i at time t, and R m,t is the value-weighted excess market return at time t.The model is estimated using weekly returns.We require at least 6 weeks to compute the IVOL.The IVOL that is calculated from the market model is denoted IVOL_MM.
Additionally, we employ the Fama and French (1993) three-factor model and the Carhart (1997) four-factor model.All the models are estimated using weekly returns.We require at least six observations to compute the IVOL.The Fama and French three-factor model is calculated using the following regression equation: where SMB i,t and HML i,t are the size premium (small minus big) and the value premium (high minus low).The Carhart four-factor model is estimated using the following regression model: where U MD i,t is the momentum premium (up minus down).The IVOL values that are computed from the Fama and French three-factor model and the Carhart four-factor model are denoted IVOL_FF3 and IVOL_C4, respectively.Two variables are used in the literature to measure a firm's innovation: R&D expenditure and number of patents.The former only captures an observable input of innovation rather than the quality of innovation.However, the latter measure captures the firm's utilization of observable and unobservable innovation inputs and turning them into outputs.For innovation, we use the natural log of the number of patents weighted by citations (PAT) to capture a firm's innovation output.Following He and Tian (2013) and Fang et al. (2014), we use the natural log of one plus.The number of patents weighted by citations as a measure of corporate innovation output is used to avoid losing observations from the sample.
To address truncation bias, we follow Squicciarini et al. (2013) and count citations over seven years after the publication date.Thus, most patents have the same window of time to be cited regardless of their application year.Moreover, we follow Atanassov (2013) and drop the last two years of the sample because they exhibit severe forms of bias.
We control for several variables that have been shown to affect IVOL.We control for operations risk using the standard deviation of the operating cash flow over the last three years (Zhang 2006).Cao et al. (2008) show that growth opportunities positively correlate to IVOL.Thus, we include the market-to-book ratio (MB) as a proxy for growth opportunities.Larger firms tend to have lower IVOL (Pástor and Pietro 2003).Therefore, we control for size (SIZE), which is measured by the natural log of the market value of equity.Brown and Kapadia (2007) suggest that the dividend payout ratio is negatively correlated to the IVOL.Therefore, we control our model's dividend payout ratio (DPO).Pástor and Pietro (2003) show a negative association between a firm's age and IVOL, so we include the natural log of a firm's age (AGE) as a control variable.Chan et al. (2001) show that firms with high R&D expenditure exhibit higher volatility.Therefore, we include R&D expenditure scaled by total assets to control for R&D spending.
In addition, we control for information uncertainty measured by the standard deviation of the analysts' forecasts of firms' EPS (DISP) and information asymmetry proxied by bid-ask spread (BIDASK).We follow Zhang (2015) and control for cash holdings (CASH) and profitability, which are measured by cash divided by total assets and ROA, respectively.These two variables are expected to be negatively correlated with firms' risk.Prior literature suggests that competition is an essential determinant of IVOL (Gaspar and Massa 2006;Irvine and Pontiff 2009).Therefore, we control market competition by including the Herfindahl-Hirschman Index (HHI).Additionally, we follow Zhang's (2015) control for asset tangibility.Furthermore, we add the lagged values of the IVOL to account for volatility persistence (Wei and Zhang 2006).Detailed variable descriptions are provided in Appendix A.

Univariate Analysis
This section conducts a univariate analysis to examine the relationship between IVOL and patents.To further explore our sample, we divide our sample into firms that invest in R&D projects and firms with no R&D expenditure (firms that report no R&D activities).Table 3, panel A compares the mean IVOL and other control variables for both groups.The analysis shows that firms investing in R&D projects have higher IVOL, size, market to book ratio, cash holdings, and cash flow volatility, indicating that such firms that engage in risky long-term projects are large firms with more growth opportunities and higher cash flow volatility.On the other hand, positive R&D firms have lower leverage, dividend payout ratio, bid-ask spread, profitability, and asset tangibility.These results are consistent with the finding of Phillips and Zhdanov (2013).
Similarly, we conduct the same analysis after classifying firms in our sample into patent and no-patent firms.As shown in Table 3, panel B, firms with patents have lower volatility, leverage, cash flow volatility, bid-ask spread, and ROA, indicating that firms producing patents have a healthy financial status, rely less on debt, and have lower volatility and bid-ask spread.These findings are consistent with the results of Balasubramanian and Sivadasan (2011).
Table 4 shows the Pearson correlation matrix for all the variables.The negative association between IVOL measures and PAT provides preliminary evidence that is consistent with our first hypothesis.However, this univariate analysis is only suggestive because it does not consider other variables.Thus, we rely on the subsequent analyses to make an inference about the proposed hypotheses.In addition, the bivariate correlations between the independent variables are low; hence, multicollinearity is not a problem in our analyses.5, panel A (a) shows the difference in the means and medians of the entire sample.The results indicate that IVOL is negatively correlated to PAT.The lowest patent quantile has an average (median) IVOL_MM of 0.545 (0.467) compared to 0.455 (0.391) in the highest quantile.The difference between the two averages is significant at the 1% level.Panel A (b) through panel A (g) show similar results across all R&D quantiles.An important observation is that the mean (median) IVOL monotonically declines as the number of patents increases across all R&D quintiles.These results provide preliminary evidence that IVOL is negatively correlated to patents after controlling for R&D spending, supporting our first hypothesis.Additionally, this shows that R&D and patents capture different dynamics of the innovation process.These results are consistent with those of previous studies (e.g., Czarnitzki and Toole 2011).
Table 5.Double sorting.Panel A reports the average (median) IVOL of firms grouped and sorted based on R&D and patent quantiles over the sample period.The reported t-statistic (chi-squared) is for the difference between the mean (median) of the average IVOL in the lowest and highest quantiles.Panel B reports the comparison means (median) test based on the variance of analyst forecasts and patent quantiles.The sample period is from 1982 to 2015.*** denotes that the difference between the highest and the lowest quantile is significant p-value at the 1% level.
Panel A: firms grouped and sorted on R&D and patents.highest PAT quantile.The difference is also significant at the 1% level.Interestingly, the difference between the average (median) IVOL in the lowest PAT quantile and the highest PAT quantile increases as we move up the DISP quantile.This indicates that the impact of patents is higher for firms with higher information uncertainty as measured by DISP, which is consistent with Hypothesis 1b.

Baseline Results
Table 6 shows the results of the regression model, Equation (1), where IVOL proxies are regressed on the control variables.We hypothesized that IVOL would be negatively correlated to a firm's innovation after we control for fixed effects.Consistent with our hypothesis, the results show that innovation output has a significant negative relationship with idiosyncratic volatility.In model ( 1), the coefficient for PAT (β 1 = −0.09) in the regression on IVOL is significant at the 1% level.The result is robust to alternative measures of IVOL.Table 6.Innovation and idiosyncratic volatility.This table shows the relationship between innovation, measured by the natural log of the number of patents weighted by citations (PAT it−1 ), and different proxies of idiosyncratic volatility (IVOL_X it ).The definitions of the variables are provided in Appendix A. Fixed effects are included.The standard errors are clustered by firm and year and are reported in parentheses.The sample period is from 1982 to 2015.***, **, and * denote significance at the 1, 5, and 10% level, respectively.
( In models (4), ( 5), and ( 6), we regress IVOL proxies on PAT it .Fixed effects are introduced to the model to mitigate the impact of endogeneity issues that might arise due to the omitted variables bias and the other control variables besides industry and year fixed effects.The results of the fixed effects regression are similar to the results presented in models (1), (2), and (3).This indicates that these results are not driven by time-variant or time-invariant unobserved heterogeneity.
The results in Table 6 show that the coefficients of most of the control variables are significant and have the predicted sign.Consistent with the previous literature, firms that are larger (SIZE), are older (AGE), have higher payout ratios (DPO), have higher cash holdings (CASH), and are more profitable (ROA) have a lower IVOL.On the other hand, firms with higher information uncertainty (DISP), growth opportunities (MB it ), leverage (LEV it ), and information asymmetry (BIDASK it ) have higher IVOL.
In an unreported previous robustness check, we repeat the analysis using the subsample of firms with positive R&D firms, positive patents, and firms with positive R&D AND positive patents.The results are similar to the reported results, suggesting that the negative association between IVOL and patents is not driven by the jump from no patents to having positive patents or by innovative firms that have lower IVOL in the first place.

Patents and Information Uncertainty
If patents help investors to predict future firm performance and reduce risk, we should expect this effect to be more pronounced for firms with higher information uncertainty.This is because patents disseminate positive information and reduce the information uncertainty in these firms.To test this hypothesis, we follow Diether et al. (2002) and Zhang (2006) and use DISP as a proxy for information uncertainty.We interact the variable with PAT and add the interaction term to the regression analysis.We expect the parameter estimate to be significant and negative.Table 7 shows the results.Consistent with hypothesis H1.b, the parameter estimate on the interaction term is negative and statistically significant at the 1% level in all specifications.The coefficient on PAT it continues to be negative and statistically significant.These results support the hypothesis that the impact of patents is higher for firms with higher information uncertainty.

Conclusions
In this paper, we examine the impact of innovation output on IVOL.Using alternative measures of IVOL for a large sample of US firms, we find that IVOL is negatively associated with innovation output after controlling for several firm under different model specifications.In addition, we show that the impact of innovation output on IVOL is more pronounced in firms with higher information uncertainty, as captured by dispersion in analysts' forecasts.This is consistent with our conjecture that patenting improves information dissemination.
The findings of this paper advance our knowledge of how innovation output affects a firm's risk and how innovative activities are evaluated by the capital market.Our results can help managers to better understand the impact of innovative projects on a firm's risk profile and its capital market implications.This will help them allocate capital effectively and efficiently to their available investment opportunity set.Additionally, our results contribute to our understanding of the behavior of IVOL, which affects portfolio diversification, options pricing, and market efficiency.
Similar to other studies, this study has the following limitations.There might be firm-specific or market variables that impact firms' IVOL but are not included in the model.Additionally, the paper does not address the impact of innovation characteristics (radical and incremental innovation) on firms' risk levels.Future research should investigate this issue as it may have importance to investors and corporate executives.

IVOL_C4 it
The standard deviation of the residuals of the Carhart four-factor model using weekly data.

PAT it
The natural log of one plus the number of patents weighted by citations in the seven years following the publication date.

R&D it
R&D expenditure scaled by sales.

DISP it
Standard deviation of analysts' forecasts from I/B/E/S database scaled by stock price.

SIZE it
The natural logarithm of the market value of equity.

Age it
The natural logarithm of the number of years the firm is covered in the CRSP or CompStat database, whichever is older.

MB it
Market value of firm's equity to the book value of firm's equity.

LEV it
The market leverage ratio.

CASH it
Cash holdings divided by total assets.

CFVOL it
The standard deviation of the operating cash flows.

DPO it
Dividend payout ratio.

BIDASK it
The absolute value of bid-ask divided by stock price.

ROA it
Operating income divided by total assets.

TANG it
Property, plant, and equipment divided by total assets.

Table 1 .
Sample distribution of the sample according to the Fama and French 48-industry classification code.

Table 2 .
Summary statistics of variables used in the analysis.Variables' definitions are provided in Appendix A.

Table 3 .
Comparison of means test.Panel A shows the comparison of means t-test after classifying the firms in our sample as No-R&D firms or R&D firms.Panel B shows the comparison of means t-test after classifying the firms in our sample into firms with no patents and firms with patents.The t-statistic is adjusted for unequal variance.The sample period is from 1982 to 2015.***, **, and * denote significant two-tailed p-values ≤ 1%, 5%, or 10%, respectively.

Table 4 .
Pearson correlations between the variables included in the analysis.The sample period was from 1982 to 2015.The correlations in bold are at least significant at the 1% level, and a and b denote correlations significant at the 10% and 5% level, respectively (the other measures of IVOL were removed due to space limitations; the full correlation matrix is available upon request).

Table 5 ,
panel A reports the differences in the means and medians of subsamples double-sorted based on R&D spending and PAT.Panel B reports double sorting based on PAT and DISP.Table

Table 7 .
The interaction between innovation, information uncertainty, and idiosyncratic volatility.This table shows the interaction between innovation and information uncertainty and their relationship's effect on idiosyncratic volatility.The definitions of the variables are provided in Appendix A. Fixed effects are included.Standard errors clustered by firm and year are reported in parentheses.The sample period is from 1982 to 2015.***, **, and * denote significance at the 1, 5, and 10% level, respectively.