Idiosyncratic Volatility and Cash Flow Volatility: New Evidence from S&P 500

Transcription

1 Idiosyncratic Volatility and Cash Flow Volatility: New Evidence from S&P 500 Yuntaek Pae a, Sung C. Bae b*, Namhoon Lee c January 2017 * Corresponding author; ) bae@bgsu.edu a Assistant Professor of Finance, College of Business, Central Washington University; Des Moines, WA 98198; Tel) ; ) paey@cwu.edu. b Professor of Finance, College of Business Administration, Bowling Green State University, Bowling Green, OH, USA; Tel) ; ) bae@bgsu.edu. c Assistant Professor of Finance, School of Business, Southern Wesleyan University, Central, SC, USA; Tel) ; ) nlee@swu.edu. The authors acknowledge helpful comments from Mingsheng Li on the earlier version of the paper. The usual disclaimer applies.

2 Idiosyncratic Volatility and Cash Flow Volatility: New Evidence from S&P 500 Abstract Employing firm-level data of S&P 500 constituent companies from 1990 to 2012, we find that idiosyncratic stock return volatility (Ivol) is positively related to the volatility of the three components of DuPont ROE used as measures of firms cash flows.. In particular, aggregate asset turnover volatility, representing uncertainty of asset management efficiency, alone explains 69% of the time series variation of aggregate Ivol, and all independent variables explain 93% of the aggregate Ivol during the sample period. These R-squared values are substantially higher than those in previous studies. Panel regression results support these findings. Furthermore, rolling window regressions uncover that while the significance of asset turnover volatility diminishes in the late 2000s, equity multiplier volatility turns highly significant surrounding the global financial crisis. Profit margin volatility remains as a significant explanatory variable of Ivol during both recessions in the early and late 2000s. Keywords: Idiosyncratic volatility, cash flow volatility, DuPont system, S&P 500 JEL Codes: G10, G12 2

3 1. Introduction Over the past decades, firms idiosyncratic stock return volatility (Ivol) has been subject to rigorous academic research. According to the Modern Portfolio Theory, a firm s stock return volatility consists of two components, market volatility and firm-specific idiosyncratic volatility. As Ivol can be diversified away by holding a large number of securities in a portfolio, the relevant risk is market volatility, measured by beta. Nevertheless, Ivol is found to be related to firm value 1, and researchers have questioned what contributes to this association. A group of researchers has investigated the association of Ivol with cash flow variables such as earnings, ROE, and sales with mixed evidence. The underlying rationale of these studies is intuitive because in a rational market, a firm s stock prices should reflect its expected future cash flows. While Ivol is reported to be positively related to earnings (Xu and Malkiel, 2003), volatility of ROE (Wei and Zhang, 2006), sales growth (Jiang et al., 2009), and idiosyncratic volatility of cash flows (Irvine and Pontiff, 2009), it is negatively related to ROE (Wei and Zhang, 2006). Chen et al. (2012) suggest that the variation of Ivol between 1978 and 2009 can be explained by accrual volatility. In this paper, we revisit the main research issue of whether and how Ivol is related to firms cash flow. Unlike existing studies in the literature, we take a different approach to offer new empirical insights into the key functional areas in a business system that directly affect firms cash flow levels. We employ DuPont components of ROE profit margin, asset turnover, and equity 1 Several studies have examined whether Ivol is related to stock returns with inconclusive evidence. On the one hand, Goyal and Santa-Clara (2003), Guo and Savickas (2008), Fu (2009), Vozlyublennaia (2012), Mateus and Konsilp (2014) and Garcia et al. (2014) find a positive relationship between stock returns and Ivol. On the other hand, Ang et al. (2006), Chen and Petkova (2012), Peterson and Smedema (2013), and Babenko et al. (2016) report a negative association of Ivol with stock returns. Umutlu (2015) finds no link between global Ivol and global portfolio returns. 3

4 multiplier as cash flow measures and show that the three components of cash flow measures explain Ivol better than ROE alone with significant associations with Ivol. ROE is widely used in valuation and financial statement analysis. For example, ROE combined with a firm s retention ratio is used in the sustainable growth model and the justified price to earnings ratio. Furthermore, Pastor and Veronesi (2006) and Xu and Malkiel (2003) report meaningful relationships between ROE and Ivol. Compared to ROE, however, three components of the DuPont system provide detailed information about the underlying factors contributing to firm performance in the firm s operational (profit margin), asset management (asset turnover) and financing (equity multiplier) activities. Hence, the DuPont system would help one understand if a firm s Ivol reflects the uncertainty in its three main activities and how the volatilities of cash flows (which we denote CFvol) generated from these activities are associated with firm specific risk or Ivol. Furthermore, relative to the widely used raw cash flow measures such as sales, earnings, and dividends, DuPont components are scale free, and thus, normalization that may harm robustness of analysis is not necessary. We contribute three major findings to the literature of Ivol. First, employing extensive firmlevel data of S&P 500 constituent stocks from 1990 to 2012, we report that the aggregate volatility of the three components of DuPont ROE, together with illiquidity and firm size, explain aggregate Ivol with higher r-squared values than previous studies. Second, time series analysis reveals that all independent variables of CFvols, illiquidity, and firm size have significant positive relationships with aggregate Ivol. The panel regression results confirm these relationships and further show that Ivol is interestingly lower during the recent global financial crisis than during the dot.com bubble period. Third, cross-sectional regression with four-year rolling windows finds that the Ivol-CFvol relationships have changed over the sample period and vary by period of 4

5 economic condition. It also discovers that cash flow variables are more robust explanatory variables than liquidity and firm size throughout the sample period. 2. Data and Measurement of Variables 2.1. Data Our sample consists of S&P 500 constituent companies during Financial data and stock price data of sample firms are collected from CRSP and Compustat. Risk factors are extracted from Ken-French data library. We screen stocks that have at least 16 quarters of financial data in order to ensure enough time series data to compute standard deviations of cash flows. In addition, profit margin, asset turnover, and equity multiplier are winsorized at top and bottom 2.5% in order to mitigate the impact of outliers Measurement of Ivol We use the direct composition method in Xu and Malkiel (2003) to estimate Ivol. Ivol is defined as standard deviation of excess returns of individual security during the four-year period assuming the Fama-French three-factor model. Accordingly, individual stock s Ivol is calculated as 3 Ivol i = STDEV [r i α i θ k i R k ] (1) where r i denotes daily return of stock i, α i represents intercept of three factor model, θ k i is regression coefficients of three factors, and R k represents risk factors such as market, size, and value from Ken- French data library. k=1 5

6 We first regress stock returns of each company against three risk factors and calculate the standard deviation of residuals each quarter in order to allow changes in θ k i, the regression coefficient of each risk factor. Because we use 16 quarters of estimation period, the average of quarterly Ivol is used as Ivol for the corresponding period 2. After having each company s Ivol for a specific estimation period t, we take cross-sectional averages to compute aggregate Ivol, used in time series analysis, as follows: Ivol(t) = 1 n Ivol i(t) n i=1 (2) 2.3. Measurement of cash flow volatility (CFvol) We employ DuPont components of ROE as cash flow proxies; profit margin (PM), asset turnover (AT), and equity multiplier (EM). ROE can be decomposed as ROE = Net Income Sales Sales Assets Assets Equity. (3) CFvol of stock i is defined as time-series standard deviation of each cash flow measure during each of four-year estimation periods between 1990 and Choosing the right number of quarterly data to compute CFvol is a subjective decision, and using more quarterly data to compute CFvol means less number of observations during the sample period. We determine to use four years of quarterly data in order to secure enough number of observations and at the same time to have robustness in computing standard deviations of cash flows. 3 Aggregate CFvol is the crosssectional average of individual companies CFvol in each estimation period. 2 We obtain similar results when Ivol is estimated using entire 16 quarters of stock return data. 3 We perform our analyses using five and six years of estimation period but find little difference in the empirical results. 6

7 CFvol(t) = 1 n CFvol i(t) n i=1 (4) 2.4. Measurement of illiquidity and firm size Illiquidity and firm size serve as control factors as firm specific volatility is widely believed to be negatively associated with firm size and liquidity. For instance, Xu and Malkiel (2003) report a negative relationship of Ivol with firm size, and Han and Lesmond (2011) show that Ivol loses predictive power on future returns when liquidity is controlled. Bali et al. (2005) also report that the relationship between stock return and Ivol is driven by small stocks and liquidity premium. Following Huang (2009), we measure illiquidity (ILL) of each individual stock as the monthly average of absolute daily return over daily volume divided by the cross-sectional average of the values such as ILL i (t) = previous within month mean of daily returni daily volume i Cross secional average of the numerator. (5) Firm size is measured as the quarterly time-series average of market capitalization of stock i, and aggregate firm size, SIZE, is the cross sectional average of individual SIZE i in quarter t. SIZE t = 1 n SIZE i(t) n i=1 (6) Table I presents the summary statistics of key variables in our sample of S&P 500 constituent companies during All variables except for ROE and profit margin ratio exhibit right-skewed distributions with mean values being substantially larger than median values. Looking at the median values, a typical firm in our sample has approximately $6 billion in total assets, $1.9 billion in equity, $59 million in net income, $994 million in sales, and $4.1 billion in market capitalization. It is also shown that a typical sample firm has the (monthly) illiquidity ratio 7

8 of 0.01, ROE of 0.04, profit margin ratio of 0.07, asset turnover ratio of 0.20, and equity multiplier ratio of Empirical Analysis and Results 3.1. Aggregate Ivol, CFvols, illiquidity, and firm size Table II presents aggregate values of Ivol, three measures of cash flow volatility (profit margin volatility (PMV), asset turnover volatility (ATV), equity multiplier volatility (EMV)), volatility of ROE (ROEV), illiquidity (ILL), and natural logarithm of firm size (SIZE) over fouryear rolling windows during our sample period of Figure 1 presents these variables graphically. Looking at the movement of Ivol over time, Ivol does not show a deterministic trend whose evidence is consistent with Ferreira and Gama (2005), Cao et al. (2008), Brandt et al. (2010) and Bekaert et al. (2012). Ivol increased before and during the economic crises; for example, Ivol peaked before the recession in 2002 and peaked again during the global financial crisis in the late 2000s. Interestingly, the Ivol level was lower during the financial crisis than during the dot.com bubble period, implying that firm specific risk contributed more during the dot.com bubble than during the financial crisis. It is also shown in Figure 1 that CFvols tend to move together with Ivol, peaking during the economic crises. Looking into three components of CFvols, PMV peaked during and after the dot.com bubble period in the early 2000s and during the global financial crisis, indicating that firms profit margin was highly volatile during the two recession periods. PMV was higher in 2007 than in 2002, implying that firms profitability was more uncertain and volatile during the global financial crisis than during the previous recession. After the dot.com bubble period, PMV remained high for the following three years until 2005, and showed a similar pattern during and 8

9 after the global financial crisis, though the period of uncertainty lasted shorter than the earlier recession. EMV increased to the highest level between 2008 and 2012, implying continued uncertainty and problems related to firms financial risk. Unlike PMV and EMV, ATV is relatively smooth during the last two decades; it increased before the dot.com bubble but followed a downward trend until the global financial crisis. Similar to Ivol, ATV is lower during the recent recession than during the previous recession. Firms asset management efficiency was more uncertain during the IT bubble than the financial crisis. Firm-level financial risk increased during the financial crisis, but IT bubble did not appear to have a strong impact on firm level financial risk as observed from EMV in Figure 1. ILL shows a decreasing trend after mid-1990s, while SIZE increased until the global financial crisis Time-series analysis of aggregate Ivol In order to investigate time-series relationships of aggregate Ivol with each and all three CFvol variables of PMV, ATV, and EMV, we estimate the following time-series regression model of aggregate Ivol as dependent variable with aggregate CFvols as key test variables and ILL and SIZE as control variables. Ivol is estimated from daily stock returns, and cash flow variables are estimated from quarterly data. Following Xu and Malkiel (2003), we take natural log on all regression variables to improve normality of variables: 4 Log(Ivol(t)) = α + β 1 Log(PMV(t)) + β 2 Log(ATV(t)) + β 3 Log(EMV(t)) +β 4 Log(ILL(t)) + β 5 Log(SIZE(t)) + e(t) (7) 4 Logarithmic transformations make skewed distributions of our non-negative independent variables including volatility measures (Ivol and CFvols) less skewed and more approximately normal. 9

10 Table III reports the results from time-series regressions. Looking first at the regression results of two control variables of illiquidity (ILL) and firm size (SIZE), both variables carry significant regression coefficients in models (4), (6) and (7). These results also justify our usage of ILL and SIZE as control variables in our regressions of Ivol as these two variables improve explanatory power of our regression models as shown in Table III. Turning to main results on key test variables, profit margin volatility (PMV) is significantly (at the 1% level) related to Ivol when ILL and SIZE are controlled with an adjusted R-squared of 59.7%, though PMV alone does not carry a significant regression coefficient. These results are in line with those in Xu and Malkiel (2003) who show a significant relationship between Ivol and future earnings growth when firm size is controlled, and are also indirectly supportive of Jiang et al. (2009) that Ivol loses predictive power of future returns when earnings are controlled. Uncertain profitability is associated with investors free cash flow and dividends, therefore, the relationship is economically meaningful. The regression coefficient of asset turnover volatility (ATV) is positive and significant at the 1% level. Hence, its coefficient of indicates that a 1% increase in ATV leads to an increase of 1.046% in Ivol. Surprisingly, ATV alone explains 68.6% of the variation of Ivol, whose evidence is new and undocumented in the current literature. Combined with illiquidity (ILL) and firm size (SIZE), ATV yields the explanatory power of 69.6%. Hence, when firms are uncertain about how much capacity to utilize for their production, the overall market level of firm specific risk increases. Similarly, uncertainty in firms debt management would cause volatile interest expenses and returns on investment, and thus affect Ivol. Equity multiplier volatility (EMV), representing uncertainty of a firm s usage of debt capital, also yields a significant (at the 1% level) regression 10

11 coefficient with and without ILL and SIZE. While EMV alone explains a mere 8.9% of variation of Ivol, it captures a whopping 82% of the Ivol variation when combined with ILL and SIZE. When all three CFvol variables are regressed together with ILL and SIZE, they all carry positive and significant (at the 1% level) regression coefficients and are capable of explaining 93.1% of variation in Ivol. These results show that the decomposition has stronger explanatory power than using ROE only. The r-squared value of 93.1% in Table III is substantially higher than those reported in the existing studies on aggregate Ivol. For example, Wei and Zhang (2006) report an adjusted r-squared of 61% in their time series regression of Ivol with ROE and volatility of ROE. Bekeart et al. (2012) show 80% of aggregate Ivol to be explained by multiple market variables. Time series relationships between aggregate CFvols and aggregate Ivol suggest that the changes of Ivol in the market (of S&P 500 companies) is relevant to overall trend of unstable operation and management. As implied in the sustainable growth model, all three components of cash flows measures have positive associations with firms future growth rates and thus with stock returns. Therefore, any changes in DuPont component should contribute to firm risk considering that none of the DuPont components of ROE is considered as a systematic risk factor in the three factor model used to compute Ivol. The results are especially helpful when forecasting future Ivol of the market because this provides a way of predicting Ivol from various aspects of firms activities. For example, expected stable management and operation would predict a lower level of Ivol in the market Cross-sectional analysis of Ivol We examine the cross-sectional relationships of Ivol with each and all three of CFvols using the following regression equation (8). Again, ILL and SIZE enter the regressions as control 11

12 variables. As with the time-series regressions, we take natural log on all regression variables to improve the normality of variables. Ivol is estimated from daily stock returns and CFvols are estimated from quarterly data. Log(Ivol i ) = α + β 1 Log(PMV i ) + β 2 Log(ATV i ) + β 3 Log(EMV i ) + β 4 Log(ILL i ) + β 5 Log(SIZE i ) + e i (8) Table IV presents results from cross-sectional regressions using 27,983 observations that have four years of data on cash flows and stock prices between 1990 and Similarly to Table III, the two control variables of ILL and SIZE carry significant (at the 1% level) regression coefficients in all regressions except for ILL in Model (7). The negative coefficients for ILL and SIZE indicate that lower illiquidity (or higher liquidity) and/or a smaller firm size are associated with greater Ivol or firm-specific risk. Hence, at the firm level, the negative regression coefficient of ILL indicates that less illiquid (or more liquid) stock has higher firm specific stock return volatility. It is worth noting that this negative regression coefficient of ILL is contrary to the positive one for ILL in the time series regression as reported in Table III. However, time-wise, the positive sign of ILL in the time series regression is consistent with the decreasing trend of ILL or improved liquidity of sample company stocks during the sample period as shown in Fig 1 as Ivol also declined during the sample period. All three CFvol variables have positive and significant (at the 1% level) regression coefficients with and without other control variables. Among the three CFvols, ATV carries the largest regression estimates with and without control variables; hence, the volatility in a firm s asset management efficiency contributes to firm specific risk most among the three CFvols. Following ATV, PMV has the second largest regression coefficient, whose result indicates that the uncertainty of a firm s profitability contributes to firm specific risk less than that of the asset 12

13 management efficiency but more than financial risk represented by EMV. In all cross-sectional regressions, the adjusted r-squared values are at the acceptable level, but are substantially lower than those in time-series regressions as reported in Table III. Again, CFvols show stronger explanatory power than ROEV alone, suggesting that the decomposition of ROE into three cash flow components is beneficial in investigating Ivol at the firm level as well as at the aggregate level. Our findings offer meaningful and practical implications for portfolio managers as well as retail investors. When selecting a candidate stock for a portfolio, firm specific risk plays as hidden risk that impact the Sharpe ratio or information ratio of a resulting portfolio. Our analysis suggests that investors consider various aspects of a candidate stock or a risky asset such as profitability, asset management efficiency, and financial leverage in addition to previously documented factors such as liquidity, firm size, and ROE in order to avoid an unexpected increase in portfolio risk Panel regression of Ivol While the cross-sectional regression detects how Ivol is related to CFvols across all sample firms at a single point in time, it does not capture the time series effect or firm specific contribution. In contrast, panel regression offers more robust results because it uses entire observations and further allows one to include dummy variables to control for firm and each period. The panel regression is especially suitable to analyze the characteristics of Ivol because our sample data contain both time series and cross sectional data together. We estimate the following panel regression: Log(Ivol i,t ) = α + β 1 Log(PMV i,t ) + β 2 Log(ATV i,t ) + β 3 Log(EMV i,t ) +β 4 Log(ILL i,t ) + β 5 Log(SIZE i,t ) + i=1 d i + t=1 d t + e i,t (9) n 1 T 1 13

14 where d i and d t are dummy variables for firm and time in quarter, respectively. Table V shows panel regression results. All independent variables carry significant regression coefficients at the 1% level. Similarly to the results of cross-sectional regressions, panel regression results indicate that all three CFvols are meaningful explanatory variables of Ivol with an adjusted r-squared of 56% with the presence of ILL and SIZE as control variables. Hence, an increase in the volatility of a firm s profit margin, asset turnover, and/or equity multiplier will lead to an increase in the firm s idiosyncratic return volatility. It is also shown that the decomposition of ROE has slightly better explanatory power than using ROEV alone. We also present Ivol in time from panel regression in Figure 2. Consistent with Figure 1, excluding the effects of CFvols, ILL, SIZE and firm specific factors, Ivol is lower during the recent global financial crisis than during the dot.com bubble period, indicating that firm specific risk is lower even if we account for the individual firm contribution to Ivol. Therefore, we suspect that lower Ivol during the global financial crisis is not because there was a less number of volatile firms during the recent crisis than during the dot.com bubble period, but because overall firm specific risk has declined Cross-sectional analysis of Ivol with four-year rolling windows A cross-sectional analysis with a rolling window allows one to examine whether and how individual independent variable s contribution has changed over time. In this section, we perform cross-sectional regressions with four-year rolling windows. Both Ivol and CFvol are calculated over the rolling windows of four years between 1990 and 2013 in order to detect possible changes in the cross-sectional relationship between Ivol and CFvol over the past two decades. ILL and SIZE are measured as the averages of ILL and SIZE values during each four-year rolling window. 14

15 In each rolling period, we estimate cross-sectional regression of Ivol with CFvols, ILL, and SIZE as follows: Log(Ivol i ) = α i + β i 1 Log(PMV i ) + β i 2 Log(ATV i ) + β i 3 Log(EMV i ) +β i 4 Log(ILL i ) + β i 5 Log(SIZE i ) + ei (10) Table VI reports cross-sectional regression results with 4-year rolling windows. We find time varying relationships between Ivol and independent variables. For example, PMV starts showing a significant relationship with Ivol from 1998, whereas ATV exhibits a significant relationship with Ivol during most of our sample period but loses its significance in late 2000s, implying that firm specific risk is less related with firm level asset management efficiency but more associated with profitability than the past. EMV becomes a significant explanatory variable only during and after the global financial crisis, being consistent with the serious debt management problems that U.S. firms faced surrounding the financial crisis. The results also show that ILL and SIZE have significant regression coefficients mostly during the recession periods, indicating that the contribution of U.S. firms illiquidity and size to their idiosyncratic return volatility became more significant during the recession times, and cash flow variables are more robust explanatory variables than the two control variables over the sample period. It is also interesting to observe that while the maximum r-squared is 42.1% over the rolling window of , r-squared values stay high during the two recession periods of early and late 2000s. This evidence strongly implies that firm-specific attributes such as cash flow volatility, illiquidity, and firm size are capable of explaining the variation of the firm s idiosyncratic volatility to a greater extent when the economy is in trouble. The results further indicate that the DuPont 15

16 system is particularly effective in firm valuation during the recession period when a systematic measure such as beta loses its meaning. In sum, our regression results provide strong evidence that a firm s CFvols, along with the firm s illiquidity and size, explains a significant portion of the firm s Ivol. In other words, uncertainty in a firm s operation and asset management is associated the firm s high Ivol. When choosing a stock for a portfolio, stable asset management of the corresponding firm played as a key factor in reducing Ivol before the financial crisis, whereas a firm s foreseeable operation represented by low PMV contributed to lower Ivol after the millennium. 4. Robustness Check In order to ensure the robustness of our empirical results, we perform two robustness tests The effect of measurement of variables without rolling windows We test whether our results are sensitive to the way that the variables are measured over 4- year rolling windows. While this method provides more reliable measures because of extended period of measurement, it has a potential problem of autocorrelation in the time series data. Hence, in order to reduce the effect of autocorrelation, we compute our variables with four quarters of data but without any overlap between time series data. The results are reported in Table VII. The overall regression results are similar to those in Table III but offer lower adjusted R-squared values in most regression models. In addition, EMV in Model (7) carries a positive but insignificant (at the 10% level) regression coefficient. Still, the three CFvol variables together explain 70.8% of the variation of Ivol when regressed along with ILL and SIZE, whereas ROEV has R-squared of 52.3%. These results confirm our earlier findings that the decomposition of ROE brings more explanatory power. 16

17 4.2. The effect of no logarithmic transformation of variables We have so far used logarithmic-transformed values of variables in all regression models. While the log transformation transform skewed distributions into one close to a normal distribution, this method may alter the underlying true distributions of the variables. Accordingly, we estimate regressions of Ivol using the variables without log transformation and report the results in Table VIII. It is worth noting that for brevity s sake we report the regression estimates of Models (4) through (7) for both time-series and cross-sectional regressions, which can be directly compared to those of Models (4) through (7) in Tables III and IV. First, compared to the time-series regression results in Table III, the estimation results in Table VIII are similar except that EMV is not significant in Model (7). When all variables are regressed, PMV, ATV, ILL and SIZE have significant relationships with Ivol and explain 84.6% of the variation of Ivol. Second, compared to the cross-sectional regression results in Table IV, the regression results in Table VIII exhibit similar estimates in terms of significance levels and adjusted R-squared values; all independent variables carry significant regression coefficients in Models (4) through (7). The only noticeable difference is the positive and small magnitudes of the regression estimates of ILL and SIZE. Lastly, compared to the results in Table V, the estimates of panel regression in Table VIII are qualitatively the same with respect to the signs and significance levels; all regression coefficients are positive and significant at the 1% level. Given that the panel regression offers more reliable regression estimates, our robustness test on the effect of log transformation confirms that the log transformation does not alter our main results. In sum, the volatilities of all three cash flow measures have significant relationships with Ivol and, together with ILL and SIZE, explain more than 57% of the variation of Ivol. 17

18 5. Summary and Conclusion We investigate the relationships between idiosyncratic return volatility and the volatilities of cash flows (CFvols). Distinguished from existing studies in the literature, we employ three components of DuPont system of ROE, profit margin, asset turnover, and equity multiplier, as cash flow measures. This approach allows us to offer additional insights into whether and how a firm s idiosyncratic volatility or firm-specific risk is related to the variation in the firm s three main activities of operation, investment, and financing. Employing firm-level data of S&P 500 companies during , we find that there are meaningful time series and cross-sectional relationships between Ivol and CFvols even after controlling for illiquidity and firm size, and that such relationships vary by period of economic condition. The time series analyses show that CFvols explain aggregate Ivol with high statistical significance during our sample period. In particular, the volatilities of profit margin, asset turnover, and equity multiplier are all significantly related to Ivol and, together with control variables of illiquidity and firm size, explain more than 93% of the time series variation of aggregate Ivol, which is noticeably higher than the R-squared of 85% with the volatility of ROE alone. Asset turnover volatility alone explains 69% of the variation in Ivol during the sample period, whose evidence suggests that the volatility in asset management efficiency is closely related to the firmspecific risk. Our results suggest that the decomposition of ROE using the DuPont system would be particularly helpful in estimating future Ivol of the market because predicting cash flows would be less difficult than predicting stock return volatility. For example, under favorable and normal economic environments, DuPont components of ROE would be stable, which in turn would lead 18

19 to the predication of a low level of Ivol in the market. This is consistent with the trend of Ivol shown in Fig 1 that Ivol peaked during recession periods and stabilized in other periods. The cross sectional regressions with 4-year rolling windows reveal that asset turnover volatility explains Ivol until mid-2000s, and profit margin volatility exhibits a strong association with Ivol from 1997 to These findings indicate that firm specific risk of S&P 500 companies is more related to profit margin volatility than asset management volatility in a recent period. In contrast, equity multiplier volatility exhibits its significant association with Ivol only after 2006, whose evidence is consistent with the serious debt problems that Corporate America faced during the global financial crisis. The results from panel regressions confirm these findings. These results further strengthen the importance of the DuPont system that firms operation and management are relevant to Ivol. Therefore, for a firm with great uncertainty in its operation and management, portfolio managers should expect a higher level of risk than the one predicted by beta or other systematic risk measures. Our findings provide strong evidence on the practical importance of the DuPont system in portfolio risk management and firm valuation. Any uncertainty in the components of the DuPont system that is associated with firm specific risk would lead to an underestimation of the portfolio risk and thus its risk-adjusted return as well if such idiosyncratic volatility is ignored. In addition, the three components of the DuPont system are found to have stronger explanatory power on Ivol during the two recessions, suggesting that the volatilities of the three cash flow measures in the DuPont system complement systematic risk measures when the systematic risk measures converge to one value and lose their explanatory power. 19

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23 Figure 1. Aggregate Ivol, CFvols, illiquidity, and firm size The sample consists of S&P 500 constituent companies during Ivol is measured as the standard deviation of excess returns of individual stock over the four year period assuming the three-factor Fama-French model. CFvol (PMV, ATV, EMV, ROEV) is measured as the crosssectional average of time-series standard deviations of quarterly cash flow measure over four-year rolling windows. Illiquidity (ILL) is measured as the monthly average of absolute return over volume divided by the cross-sectional average of the numerator value. Firm size (SIZE) is measured as market capitalization value. Illiquidity, profit margin, asset turnover, and equity multiplier are winsorized at bottom and top 2.5% level. 23

24 Figure 2. Time series variation of Ivol from panel regression 24

25 Table I. Summary statistics of key variables The sample consists of S&P 500 constituent companies during Illiquidity is measured as the monthly average of absolute return over volume divided by the cross-sectional average of the numerator value. Firm size is measured as market capitalization value. Illiquidity, profit margin, asset turnover, and equity multiplier are winsorized at bottom and top 2.5% level. Variables Mean Median Min Max No. of obs. Total assets ($ million) 30,047 5, ,363,878 53,395 Equity ($ million) 5,092 1, ,838 53,395 Net income ($ million) , ,140 53,395 Sales ($ million) 2, ,872 53,395 Firm size ($ million) 11,780 4, ,458 50,816 Illiquidity ,788 ROE Profit margin ratio , ,395 Asset turnover ratio ,395 Equity multiplier ratio , ,395 25

26 Table II. Aggregate Ivol, CFvols, illiquidity, and firm size The sample consists of S&P 500 constituent companies during Ivol is measured as the standard deviation of excess returns of individual stock over the four year period assuming the three-factor Fama-French model. CFvol (PMV, ATV, EMV, ROEV) is measured as the crosssectional average of time-series standard deviations of quarterly cash flow measure over four-year rolling windows. Illiquidity (ILL) is measured as the monthly average of absolute return over volume divided by the cross-sectional average of the numerator value. Firm size (SIZE) is measured as market capitalization value. Illiquidity, profit margin, asset turnover, and equity multiplier are winsorized at bottom and top 2.5% level. Period No. of firms Idiosyncratic volatility (Ivol) ROE Volatility (ROEV) Profit margin volatility (PMV) Asset turnover volatility (ATV) Equity multiplier volatility (EMV) Illiquidity (ILL) Log(firm size) (SIZE)

27 Table III. Time series regressions of aggregate Ivol This table reports time series relationships of aggregate Ivol with three measures of cash flow volatility (CFvol), return on equity (ROE), profit margin volatility (PMV), asset turnover volatility (ATV), and equity multiplier volatility (EMV) together with volatility of ROE (ROEV). Illiquidity (ILL) and firm size (SIZE) are used as control variables. Aggregate Ivol is measured as the cross-sectional average of the time-series standard deviation of excess returns of individual stock over the four year period assuming the three-factor Fama-French model. Aggregate CFvol is measured as the cross-sectional average of time-series standard deviations of each cash flow measure over four-year rolling windows. ILL is measured as the monthly average of absolute return over volume divided by the cross-sectional average of the numerator value. SIZE is measured as market capitalization value. All independent variables except for firm size are winsorized at bottom and top 2.5% level. The sample consists of S&P 500 constituent companies during All regression variables are log-transformed to improve normality of variables and standard errors are adjusted following Newey- West (1987). ***, **, * denote significance at the 1%, 5%, and 10% level, respectively, in two sided t-test. Log(Ivol(t)) = α + β 1 Log(PMV(t)) + β 2 Log(ATV(t)) + β 3 Log(EMV(t)) + β 4 Log(ILL(t)) + β 5 Log(SIZE(t)) Independent variables Model (1) Model (2) Model (3) Model (4) Model (5) Model (6) Model (7) Benchmark Constant *** *** *** 2.892*** *** Log(ROEV) *** Log(PMV) *** 0.429*** Log(ATV) 1.044*** 1.046*** 0.631*** Log(EMV) 0.538*** 1.952*** 0.661*** Log(ILL) 0.283*** *** 0.155*** 0.414*** Log(SIZE) *** ** Adj. R 2-1.1% 68.6% 8.9% 59.7% 69.6% 82.2% 93.1% 85.0% 27

28 Table IV. Cross sectional regressions of Ivol This table reports cross-sectional relationships of Ivol with three measures of cash flow volatility (CFvol), return on equity (ROE), profit margin volatility (PMV), asset turnover volatility (ATV), and equity multiplier volatility (EMV) together with volatility of ROE (ROEV). Illiquidity (ILL) and firm size (SIZE) are used as control variables. Ivol is measured as the standard deviation of excess returns of individual stock over the four year period assuming the three-factor Fama-French model. CFvol is measured as the timeseries standard deviations of each cash flow measure over four-year rolling windows. ILL is measured as the monthly average of absolute return over volume divided by the cross-sectional average of the numerator value. SIZE is measured as market capitalization value. All independent variables except for firm size are winsorized at bottom and top 2.5% level. The sample consists of 27,983 firm-year observations of S&P 500 constituent companies during All regression variables are log-transformed to improve normality of variables. ***, **, * denote significance at the 1%, 5%, and 10% level, respectively, in two sided t-test. Log(Ivol i ) = α + β 1 Log(PMV i ) + β 2 Log(ATV i ) + β 3 Log(EMV i ) + β 4 Log(ILL i ) + β 5 Log(SIZE i ) Independent Model (1) Model (2) Model (3) Model (4) Model (5) Model (6) Model (7) Benchmark variables Constant *** *** *** *** *** *** *** *** Log(ROEV) 3.118*** Log(PMV) 0.078*** 0.073*** 0.079*** Log(ATV) 0.105*** 0.090*** 0.102*** Log(EMV) 0.015*** 0.019*** 0.023*** Log(ILL) *** *** *** Log(SIZE) *** *** *** *** *** Adj. R 2 2.9% 6.7% 0.1% 8.0% 10.3% 5.8% 13.9% 10.8% 28

29 Table V. Panel regression of Ivol This table reports results of panel regression of Ivol with three measures of cash flow volatility (CFvol), profit margin volatility (PMV), asset turnover volatility (ATV), and equity multiplier volatility (EMV) together with volatility of ROE (ROEV). Illiquidity (ILL) and firm size (SIZE) are used as control variables. The panel regression also includes firm specific dummy variables (di) and time dummy variables for each quarter (dt). Ivol is measured as the standard deviation of excess returns of individual stock over the four year period assuming the three-factor Fama-French model. CFvol is measured as the time-series standard deviations of each cash flow measure over four-year rolling windows. ILL is measured as the monthly average of absolute return over volume divided by the cross-sectional average of the numerator value. SIZE is measured as market capitalization value. All independent variables except for firm size are winsorized at bottom and top 2.5% level. The sample consists of S&P 500 constituent companies during All regression variables are log-transformed to improve normality of variables. ***, **, * denote significance at the 1%, 5%, and 10% level, respectively, in two sided t-test. Log(Ivol i,t ) = α + β 1 Log(PMV i,t ) + β 2 Log(ATV i,t ) + β 3 Log(EMV i,t ) n 1 + β 4 Log(ILL i,t ) + β 5 Log(SIZE i,t ) + d i + d t Independent variables Model (1) Benchmark Constant *** *** Log(ROEV) 2.868*** Log(PMV) 0.073*** Log(ATV) 0.060*** Log(EMV) 0.038*** Log(ILL) 0.075*** 0.078*** Log(SIZE) 0.041*** 0.043*** No. of observations No. of variables Adjusted R % 55.68% i=1 T 1 t=1 29

30 Table VI. Cross-sectional regressions with 4-year rolling windows This table reports cross-sectional relationships of aggregate Ivol with three measures of cash flow volatility (CFvol), profit margin volatility (PMV), asset turnover volatility (ATV), and equity multiplier volatility (EMV) with 4-year rolling windows. Illiquidity (ILL) and firm size (SIZE) are used as control variables. Ivol is measured as the standard deviation of excess returns of individual stock over the four year period assuming the three-factor Fama-French model. CFvol is measured as the time-series standard deviations of each cash flow measure over four-year rolling windows. ILL is measured as the monthly average of absolute return over volume divided by the crosssectional average of the numerator value. SIZE is measured as market capitalization value. All independent variables except for firm size are winsorized at bottom and top 2.5% level. The sample consists of S&P 500 constituent companies during All regression variables are logtransformed to improve normality of variables and standard errors are adjusted following Newey and West (1987). ***, **, * denote significance at the 1%, 5%, and 10% level, respectively, in two sided t-test. Log(Ivol i ) = α + β 1 Log(PMV i ) + β 2 Log(ATV i ) + β 3 Log(EMV i ) +β 4 Log(ILL i ) + β 5 Log(SIZ i ) Period No. of Adj. obs. R 2 α β 1 β 2 β 3 β 4 β % *** *** 0.041* ** % *** *** *** % *** *** *** % *** *** ** *** % *** * 0.112*** % *** *** % *** *** % *** *** % *** 0.054** 0.096*** % *** 0.065*** 0.139*** % *** 0.072*** 0.135*** *** *** % *** 0.058*** 0.115*** *** *** % *** 0.062*** 0.134*** *** *** % *** 0.100*** 0.152*** *** % *** 0.078*** 0.150*** % *** 0.121*** 0.072*** ** % *** 0.135*** 0.030* 0.053*** *** % *** 0.117*** 0.028* 0.074*** ** *** % *** 0.132*** *** *** *** % *** 0.112*** *** *** *** 30