Turnover: Liquidity or Uncertainty?

Transcription

1 Turnover: Liquidity or Uncertainty? Alexander Barinov Terry College of Business University of Georgia This version: July 2009 Abstract The paper shows that turnover proxies for firm-specific uncertainty, not liquidity. I provide a new explanation of why high turnover firms have low expected returns. The explanation is aggregate volatility risk: high uncertainty firms, which usually have high turnover, beat the CAPM when aggregate volatility increases. Firmspecific uncertainty reduces risk through real options. Real options become less sensitive to the underlying asset value as firm-specific uncertainty goes up. Hence, real options betas decrease more and the value of real options decreases less in volatile times, which are typically recessions. I find empirically that the aggregate volatility risk factor can explain why high analyst disagreement firms and high turnover firms have low future returns. Consistent with the story that firm-specific uncertainty works through real options, the negative relation between turnover and future returns is stronger for firms with high leverage or high market-to-book. All results about turnover are also true for turnover variability. The paper therefore explains the puzzling negative relation between turnover variability and future returns. I also find that the turnover factor helps to resolve the new issues puzzle because the turnover factor picks up aggregate volatility risk. The turnover factor betas of small growth firms and small growth new issues tend to be extremely negative, which is inconsistent with the liquidity story, but consistent with the aggregate volatility risk story. JEL Classification: G12, G13, G32 Keywords: liquidity, idiosyncratic volatility, uncertainty, turnover, aggregate volatility risk, real options

2 1 Introduction The asset-pricing literature has long treated turnover (trading volume over shares outstanding) as a proxy for liquidity 1. The well-established negative cross-sectional relation between turnover and future returns is then interpreted as the evidence of liquidity premium (high turnover stocks are more liquid and therefore have low expected returns). The microstructure literature, on the other hand, uses turnover as a proxy for firmspecific uncertainty (see, e.g., Blume, Easley, and O Hara, 1994). Turnover is found to be high if prices fluctuate a lot, if traders disagree about the firm value, or if they receive a lot of information about the firm (see, e.g., Karpoff, 1987, and references therein). In assetpricing applications, the proponents of this view use turnover as a measure of uncertainty and show, for example, that several anomalies are stronger for high turnover firms (see Lee and Swaminathan, 2000, Jiang, Lee, and Zhang, 2005). However, if turnover measures uncertainty, the negative relation between turnover and future returns is puzzling. In this paper I show that turnover measures firm-specific uncertainty and reconcile it with the lower expected returns of high turnover firms. The mechanism is similar to the one in Johnson (2004) and Barinov (2009a). More uncertainty about the assets behind a valuable real option (e.g., growth options, the call option created by leverage) reduces the risk of the real option by making its value less responsive to the changes in the underlying asset value. The beta of a real option is, by Ito s lemma, the product of the underlying asset beta and the option value elasticity with respect to the underlying asset value. While changes in the uncertainty about the underlying asset do not influence its beta, they do make the elasticity and, hence, the real option s beta smaller. Both aggregate volatility and firm-specific uncertainty are high during recessions (see the results in Barinov, 2009c, and references therein). According to the previous paragraph, when firm-specific uncertainty increases, the risk exposure of real options declines. Hence, during volatile periods real options lose less value than what the CAPM predicts. Also, holding everything else equal, real options increase in value when the uncertainty about the underlying asset increases 2. These two effects of uncertainty on growth options are stronger for high uncertainty firms (see Appendix A for the formal proof). Hence, high 1 See, e.g., Datar, Naik, and Radcliffe (1998), Rouwenhorst (1999), Eckbo and Norli (2002, 2005), and Avramov and Chordia (2006). 2 A recent analysis by Grullon, Lyandres, and Zhdanov (2008) suggest that changes in volatility have a substantial effect on the value of real options. 1

3 uncertainty firms with valuable real options should outperform the CAPM during volatile times. Campbell (1993) and Chen (2002) show that investors would require a lower risk premium from the stocks, the value of which correlates least negatively with aggregate volatility news, because these stocks provide additional consumption precisely when investors have to cut their current consumption for consumption-smoothing and precautionary savings motives. Ang, Hodrick, Xing, and Zhang (2006) confirm this prediction empirically and coin the notion of aggregate volatility risk. They show that the stocks with the least negative sensitivity to aggregate volatility increases have abnormally low expected returns and that the portfolio tracking surprise changes in expected aggregate volatility earns a significant risk premium. This paper builds on this literature and shows that high turnover firms have low expected returns because they are a hedge against aggregate volatility risk. Because in my story firm-specific uncertainty impacts the firm s aggregate volatility risk through real options, I predict that, if turnover measures uncertainty, the effect of turnover on future returns will be greater for the firms with valuable real options. For example, the negative effect of turnover on future returns should be stronger for highly levered firms (the equity of a levered firm is a call option on its assets) and the firms with high market-to-book (abundant growth options). I also predict that the difference in aggregate volatility risk between high and low turnover firms will increase with leverage and market-to-book, thus explaining why the return differential between high and low turnover firms increases with leverage and market-to-book. An important feature of my aggregate volatility risk story is that the story is conditional on the market risk. Because the market return is strongly negatively correlated with aggregate volatility (the correlation between the market factor and the change in the VIX index is ), any stock with a positive beta, including high turnover stocks, will react negatively to increases in expected aggregate volatility. My prediction is that high turnover firms beat the CAPM when aggregate volatility increases, which means that high turnover firms have low aggregate volatility risk. This is the reason why these firms have negative CAPM alphas. I do not predict, however, that high turnover firms will go up in value when aggregate volatility increases. The main empirical result of the paper is that high turnover firms have negative aggregate volatility risk exposure, and low turnover firms have positive aggregate volatility 2

4 risk exposure. The difference in aggregate volatility risk can completely explain the return differential between low and high turnover firms. I also find, consistent with the aggregate volatility risk story that works through real options, that the negative relation between turnover and future returns strengthens as either leverage or market-to-book increase, and the difference in exposure to aggregate volatility risk between low and high turnover firms increases with both leverage and market-to-book. Moreover, I show empirically that the firms in the highest turnover quintile have more than 50% higher idiosyncratic volatility and analyst forecast dispersion than the firms in the lowest turnover quintile. However, I observe little to no dependence of price impact and exposure to changes in aggregate liquidity on turnover. These three pieces of evidence lead me to the conclusion that the return differential between low and high turnover firms reflects the compensation for aggregate volatility risk, not liquidity risk. All these conclusions also carry over to turnover variability, resolving the apparent puzzle in Chordia, Subrahmanyam, and Anshuman (2001), who find that turnover variability, which they interpret as the measure of variations in liquidity, is negatively related to future returns. I do not find any evidence that the variability in turnover is positively associated to variability in other liquidity measures, such as price impact and exposure to changes in aggregate liquidity. What I do find is that high turnover variability is synonymous to high firm-specific uncertainty and low aggregate volatility risk. Firms with high turnover variability beat the CAPM when aggregate volatility increases unexpectedly, and this fact can explain why high turnover variability is associated with lower expected returns in cross-section. The main conclusion of the paper is that turnover is not a good measure of liquidity. Using a turnover-based factor in asset-pricing tests can result in misleading conclusions about the role of liquidity risk. A case in point is the liquidity explanation of the new issues puzzle in Eckbo and Norli (2005). Eckbo and Norli (2005) show that a turnoverbased factor, short in high turnover firms and long in low turnover firms, can explain the low returns to IPOs and SEOs. Eckbo and Norli (2005) interpret the negative loadings of new issues on this factor as the evidence that new issues have lower liquidity risk. I revisit their findings and find that the smallest growth firms, which is the group 50% of IPOs and 25% of SEOs come from, have large and negative loadings on the turnover factor. I also find that the smallest IPOs and SEOs have the most negative turnover 3

5 factor betas. These results are hard to interpret as the evidence of hedging ability of small growth firms and small IPOs against liquidity risk, since this conclusion would not be supported by any other liquidity measure. However, the negative turnover factor betas of small growth firms and small IPOs make perfect sense if one assumes that turnover proxies for uncertainty, because the uncertainty about firm value usually decreases with size. Therefore, I conclude that the turnover factor of Eckbo and Norli (2005) picks up aggregate volatility risk, not liquidity risk. The paper proceeds as follows: Section 2 describes the data sources, and Section 3 tests my main empirical hypotheses that the negative relation between turnover and future returns is explained by aggregate volatility risk, not liquidity. Section 4 illustrates that the liquidity explanation of the new issues puzzle in Eckbo and Norli (2005) is in fact aggregate volatility risk explanation. Section 5 shows that my results on turnover generalize to turnover variability, thus providing an explanation for the negative relation between turnover variability and future returns in Chordia, Subrahmanyam, and Anshuman (2001). In Section 6, I use the changes in the VIX index directly to show that the firms with high turnover and the firms high variability of turnover beat the CAPM when aggregate volatility increases. Section 7 summarizes the findings and concludes. The formal real options model behind my predictions is in Appendix A. Appendix B collects the proofs of the propositions in Appendix A. 2 Data The data in the paper come from CRSP, Compustat, SDC Platinum, IBES, and the CBOE indexes databases. The sample period is from January 1964 to December I define turnover as trading volume divided by shares outstanding (both from CRSP). NASDAQ turnover is divided by two. A firm is classified as a NASDAQ firm if its CRSP events file listing indicator - exchcd - is equal to 3. In the paper, I use an annual measure of turnover, which is the average monthly turnover in the previous calendar year (at least 5 valid observations are required). I measure turnover variability with the coefficient of variation, computed in the past 36 months (at least 12 months with non-missing turnover are required). The coefficient of variation is the standard deviation of turnover over the turnover mean during the same 4

6 period. Firm size is also from CRSP and is shares outstanding times price. I compute market-to-book and leverage from Compustat data. Market-to-book is market value of equity (item #25 times item #199) over the sum of book equity (item #60) and deferred taxes (item #74). Leverage is long-term debt (Compustat item #9) plus short-term debt (Compustat item #34) divided by equity value (Compustat item #25 times Compustat item #199). When I sort firms on market-to-book or leverage at the end of the year, I use their value from the fiscal year ending no later than June of the sorting year. I use two proxies for firm-specific uncertainty - idiosyncratic volatility and analyst forecast dispersion. I define idiosyncratic volatility as the standard deviation of the Fama- French model residuals. The Fama-French model is fitted to daily data for each firm-month with at least 15 non-missing observations. The data on Fama-French factors are from Kenneth French s website 3. Analyst forecast dispersion is the standard deviation of all outstanding earnings-per-share forecasts for the current fiscal year scaled by the absolute value of the outstanding earnings forecast (zero-mean forecasts and forecasts by only one analyst excluded). The data on analyst forecasts are from IBES. My proxy for expected aggregate volatility is the old VIX index. It is calculated by CBOE and measures the implied volatility of one-month options on S&P 100, available from January 1986 to December I get the values of the VIX index from CBOE data on WRDS. Using the old version of the VIX gives me a longer data series compared to newer CBOE indices. I define FVIX, my aggregate volatility risk factor, as a factor-mimicking portfolio that tracks the daily changes in the VIX index. I regress the daily changes in VIX on the daily excess returns to the six size and book-to-market portfolios (sorted in two groups on size and three groups on book-to-market). The fitted part of this regression less the constant is the FVIX factor. I cumulate returns to the monthly level to get the monthly return to FVIX. All results in the paper are robust to changing the base assets from the six size and book-to-market portfolio to the ten industry portfolios (Fama and French, 1997) or the five portfolios sorted on past sensitivity to VIX changes (Ang, Hodrick, Xing, and Zhang, 2006). The daily returns to the six size and book-to-market portfolios and the ten industry portfolios come from Kenneth French website. 3 /ken.french/ 5

7 In Section 4, I use the SDC Platinum database to extract the dates of new issues and the identities of the issuing firms. I match the new issues with the CRSP returns data by the six-digit CUSIP, requiring at least one valid return observation in the three years after the issue. My IPO and SEO portfolios are rebalanced monthly and include the IPOs and SEOs performed from 2 to 37 months ago. The first month is excluded because of the well-known IPO underpricing and the price support of the underwriters in the month after the issue. The results are robust to keeping the first month in the sample. I include only the IPOs and SEOs listed on NYSE/AMEX/NASDAQ after the issue (the exchcd listing indicator from the CRSP events file is used). I keep utilities in my sample, as well as mixed SEOs, but discard units issues (both IPOs and SEOs) and SEOs with no new shares issued. Excluding utilities and mixed SEOs, or including units issues does not change my results. My sample includes 5969 IPOs and 6974 SEOs performed between December 1982 and October 2006 (new issues in 1983 enter the new issues portfolio in 1986 as two to three year old issues). When I look at the new issues puzzle in different size portfolios, I measure size using the after-issue market capitalization from SDC. In Section 4, I also look at the cumulative issuance puzzle documented in Daniel and Titman (2006). I follow the definition of the cumulative issuance variable from their paper. The cumulative issuance is the growth of the market value unexplained by returns to the pre-existing assets and is measured as the log market value growth minus the log cumulative returns in the past five years. The turnover-based liquidity factor in Section 4 is from Eckbo and Norli (2005). At the end of each year firms are sorted independently into two equal groups on size and three groups - top 30%, middle 40%, and bottom 30% - on turnover. The liquidity factor is the value-weighted return differential between the lowest and highest turnover groups averaged across the two size groups. 3 Turnover and Aggregate Volatility Risk 3.1 Descriptive Statistics Returns and Firm Characteristics In Table 1 I report the descriptive statistics across the turnover quintiles. The turnover quintiles are formed using NYSE (exchcd=1) breakpoints and are rebalanced annually. The 6

8 first two rows of Panel A show the CAPM and the Fama-French (1993) equal-weighted alphas. I confirm the previous findings starting with Datar, Naik, and Radcliffe (1998) that high turnover stocks earn much lower returns than low turnover stocks. In my sample period the low minus high differential is 1.14% per month for the CAPM alphas and 0.83% per month for the Fama-French alphas, both highly significant. Using value-weighted returns (results not reported to save space) makes the differential smaller by about a half, but still leaves it significant. I also notice that while the CAPM alphas attribute approximately equal weight to the long and short part of the differential, the Fama-French alphas suggest that about 70% of the differential comes from the short side (high turnover firms). In the next three rows of Panel A I report the Fama-French betas of the turnover quintile portfolios. I find that high turnover firms have higher market betas, higher size betas and lower HML betas than low turnover firms. The last fact is consistent with the evidence in Panel B, where I find that low turnover firms have lower median market-to-book at the portfolio formation date. However, the patterns in the market beta and the size beta seem at odds with the fact from the second row of Panel B that the median capitalization of high turnover firms is almost three times higher than the median capitalization of low turnover firms. If high turnover firms are normally larger than low turnover firms, they should have lower size betas and lower market betas. The potential resolution of this contradiction is in the middle rows of Panel B, where I find that the idiosyncratic volatility and analyst forecast dispersion of high turnover firms is more than 50% higher than that of low turnover firms. The idiosyncratic volatility can drive the pattern in the market and size betas, because both betas are known to be positively correlated with idiosyncratic volatility in cross-section (see, e.g., Ang, Hodrick, Xing, and Zhang, 2006, and Barinov, 2009a). The higher idiosyncratic volatility and higher analyst disagreement about high turnover firms confirms the view in the behavioral literature that high turnover usually means high uncertainty (Lee and Swaminathan, 2000, Jiang, Lee, and Zhang, 2004). It also provides the first piece of evidence that high turnover can mean lower aggregate volatility risk because of the hedges created by firm-specific uncertainty. 7

9 3.1.2 Turnover and Liquidity In the last two rows of Panel B I look at relation between turnover and price impact. The first measure is the Amihud (2002) illiquidity measure, which is the average ratio of absolute return to dollar volume. The second measure is the Pastor and Stambaugh (2003) gamma, which is the slope from the firm-level regression of returns on yesterday s signed volume. Large positive values of the Amihud (2002) illiquidity measure and large negative values of the Pastor and Stambaugh (2003) gamma mean large price impact and low liquidity. I do not find any relation between the price impact measures and turnover except for the large upward spike in the lowest turnover quintile. While the spike is consistent with the view that the lowest turnover firms are less liquid, because they have higher price impact, there are two other possible views on this evidence. First, the negative relation between turnover and the Amihud (2002) illiquidity measure is partly mechanical (and it is therefore surprising we do not see it in the other quintiles), because dollar volume is in the numerator of turnover and in the denominator of the illiquidity measure. Second, as Amihud (2002) and Harris and Raviv (1993) point out, price impact measures are also inverse measures of disagreement. If all investors agree on the interpretation of the arriving information (which is more likely to happen for high uncertainty firms), prices will move with little volume, which will mean low turnover and high price impact measures. In Panel C, I look at the exposure of the turnover quintile portfolios to aggregate liquidity risk. I use three non-traded factors from Amihud (2002), Sadka (2006), and Pastor and Stambaugh (2003). The Amihud factor is the innovation to the market-wide average of the Amihud illiquidity measure. The Sadka factor is the innovation to the market-wide average of a price impact measure, calculated from intraday transaction data. The Pastor- Stambaugh non-traded factor is the innovation to the market-wide average of the Pastor and Stambaugh (2003) gamma. I multiply the Amihud factor by -1 to bring it in line with the Sadka factor and the Pastor-Stambaugh factor, which measure liquidity. I also use the Pastor-Stambaugh traded factor, which is the equal-weighted return differential between the top and bottom decile in the sorts on the return sensitivity to unexpected changes in the Pastor-Stambaugh traded factor. The data on all liquidity factors except for the Amihud factor are from CRSP. To compute the Amihud factor, I take the average daily ratio of the return-to-volume ratio 8

10 for each firm-month (at least 15 observations are required) and then for each month take the average of the monthly averages across all firms. The innovation is from the AR(1) model fitted to the latter average. The negative loadings on the liquidity factors mean the hedging ability against liquidity risk. For the non-traded factors, the negative loading means positive returns when aggregate liquidity declines. For the traded factor, the negative loading means that the return to the portfolio is positive when the stocks with positive sensitivity to liquidity innovations decrease in value, which implies the same desirable negative correlation between returns and aggregate liquidity. The loadings on the liquidity factors are measured by regressing portfolio returns on the three Fama-French (1993) factors and the liquidity factor. In Panel C, I see only weak evidence that higher turnover means better hedging ability against aggregate liquidity risk. In fact, the only liquidity factor, for which I observe significant difference in the hedging ability of high and low turnover firms, is the Sadka factor. I also observe weak pattern in the Pastor-Stambaugh non-traded factor, the loadings on which decline monotonically with turnover, but the decline is significant only at the 10% level. For the other two factors, the loadings are essentially flat. Overall, Panel C extends the results of Lee and Swaminathan (2000) that turnover is only weakly related to other liquidity measures. While Lee and Swaminathan (2000) focus on firm characteristics, such as price level and bid-ask spread, I look at the sensitivity to aggregate liquidity movements and conclude that high turnover firms do not hedge against them either. I also find in Panel B strong evidence that turnover is positively related to firm-specific uncertainty, manifested through idiosyncratic volatility and analyst disagreement, and that turnover is mostly unrelated to price impact. The bottom line from Table 1 is that turnover is more likely to pick up firm-specific uncertainty than liquidity or liquidity risk. 3.2 Characteristic-Based Tests Turnover, Real Options, and Future Returns My hypothesis that in cross-section high turnover predicts low future returns because high turnover means high firm-specific uncertainty. Relative to the assets with the same market betas, the real options of high uncertainty firms increase in value and have low risk during volatile periods, which means that these firms have low aggregate volatility 9

11 risk. Because firm-specific uncertainty is transformed into lower aggregate volatility risk by real options, I also hypothesize that the effect of turnover on future returns is stronger for the firms with abundant real options: highly levered firms and firms with high marketto-book. In cross-sectional regressions of returns on lagged firm characteristics I should see a significant negative coefficient for the product of market-to-book and turnover and the product of leverage and turnover. The negative relation between turnover and returns should disappear when either of the products is present. The empirical problem with testing these hypotheses is that there are many confounding effects in the data. First, leverage and market-to-book are strongly negatively correlated (distressed firms are usually highly levered, firms with few growth options take on a lot of debt to mitigate the free cash flow problem, etc.). Therefore, if the product of either market-to-book and turnover or leverage and turnover is used alone in the cross-sectional regressions, it will pick up both conflicting effects and the coefficient will be biased towards zero. Second, turnover is positively associated with size, and the dependence of returns on the interaction of turnover and market-to-book can run against the well-known dependence of the value effect on size (see, e.g., Loughran, 1997). My prediction is that the effect of turnover on future returns is more negative if market-to-book is high, that is, the product of turnover and market-to-book is negatively associated with future returns. The value effect, i.e. the negative relation between market-to-book and future returns, is stronger for small firms (Loughran, 1997), so the product of market-to-book and size should be positively related to returns. If there is no relation between market-to-book and the turnover effect on returns, I would expect that the product of market-to-book and turnover is positively related to future returns, because turnover would just substitute for size. If there is no relation between leverage and the turnover effect on future returns, I would expect to find that the product of turnover and leverage is negatively related to future returns, just as my hypothesis predicts, but only because turnover is positively related to size, and leverage is negatively related to market-to-book. Therefore, not controlling for the product of size and market-to-book would artificially make the product of market-to-book and turnover too weak and the product of leverage and turnover too strong. All these confounding effects make me choose the multiple regression framework to test whether the effect of turnover on future returns depends on market-to-book and leverage. 10

12 In Table 2, I run Fama-MacBeth (1973) regressions using monthly data. The risk controls I use in all regressions are the current month market beta, the previous year size, and the previous year market-to-book. All firm characteristics, except for the market beta, are percentage ranks. Using percentage ranks mitigates the impact of outliers and allows to interpret the coefficients as the difference in returns between extreme quintile in the sorts on the variable. In the case of Table 2, one has to multiply the coefficient by 80 to get such estimate in percentage points. In Panel A I test whether the effect of turnover on future returns depends on marketto-book and leverage. I first confirm that the previous year turnover does predict current returns. The first column estimates the return differential between the lowest and the highest turnover quintiles at = 0.605% per month, reasonably close to what it actually is in Table 1. The turnover coefficient is highly significant. Contrary to my hypothesis, in the second column I find that the product of marketto-book and turnover is insignificant and turnover retains significance in its presence. As discussed above, the lack of apparent relation between future returns and the product of turnover and market-to-book can be because the product runs against the well-known relation of size and the value premium. In the third column, I add the product of size and market-to-book that should capture this relation. Once the relation between size and the value premium is controlled for, the product of turnover and market-to-book becomes significant, and the turnover coefficient drops by two thirds compared to the first column and becomes insignificant. The coefficient on the product of market-to-book and turnover implies that, holding everything else constant, the return differential between the lowest and the highest turnover quintile varies from = 0.31% per month in the lowest market-to-book quintile to = 0.88% per month in the highest market-to-book quintile. In unreported results, I also try omitting the product of turnover and market-to-book and keeping the product of size and market-to-book only. I find that the product of size and market-to-book does not eliminate the significance of turnover, so, as hypothesized, it is the interaction of turnover and market-to-book that explains the link between turnover and future returns. In the fourth column, I test whether there is an interaction between the effect of turnover on future returns and leverage. The coefficient on the product of leverage and turnover is negative and significant, and turnover itself loses significance in the presence 11

13 of the product. The coefficient on the product implies that the return differential between the lowest and the highest leverage quintiles varies from = 0.41% per month in the lowest leverage quintile to = 0.78% per month in the highest leverage quintile, consistent with my model. As I mentioned earlier, the product of turnover and leverage can proxy for the wellknown relation between size and the value premium. In the fifth column I show that it is partially true, because the coefficient on the product drops by 14% and becomes marginally significant when I add the product of size and market-to-book. Because market-to-book and leverage are negatively related, and the products of both with turnover are negatively related to future returns, having both products in one regression should reinforce their significance. This is what I find in column six, where the products of market-to-book and leverage with turnover are both highly significant and larger than in the previous columns. It does not change in column seven, where I add the product of size and market-to-book, which additionally strengthens the product of market-to-book and turnover and has no impact on the product of leverage and turnover. Summing up the results in Panel A of Table 2, I conclude that, consistent with my model, the effect of turnover on future returns is significantly stronger for the firms with valuable real options (highly levered firms and growth firms). It appears that the interaction of turnover and real options can produce the variation in the turnover effect on returns of at least bp per month and leave insignificant the remaining part of the turnover effect Turnover or Idiosyncratic Volatility? It is interesting to test whether the effect of turnover on future returns and its dependence on market-to-book is different from the similar effect idiosyncratic volatility and its product with market-to-book has on future returns (see Ali, Hwang, and Trombley, 2003, Barinov, 2009a). On the one hand, I hypothesize that turnover and idiosyncratic volatility pick up essentially the same thing - the hedging power against aggregate volatility risk, created through real options. If this is the case, one of them should subsume the other. On the other hand, they can pick up different aspects of the same concept of uncertainty, and therefore they can overlap only partially. In Panel B, I start by putting turnover and idiosyncratic volatility in one regression. I 12

14 observe that the turnover coefficient drops by about 30%, but remains significant, which means that while idiosyncratic volatility and turnover have some overlap, their effects on future returns seem distinct from each other. In the second column of Panel B, I add the product of idiosyncratic volatility and market-to-book, and see that while it can perfectly explain the effect of idiosyncratic volatility on future returns, it cannot explain the effect of turnover. However, in the third column, I find that the product of market-to-book and turnover is insignificant in the presence of the product of market-to-book and idiosyncratic volatility, and it is even smaller than it was in Panel A. In column four, I use the product of leverage and idiosyncratic volatility instead, and find that it comes out significantly negative, leaves idiosyncratic volatility marginally significant and has little impact on turnover. A more decisive evidence is in column five, where the product of leverage and idiosyncratic volatility subsumes the product of leverage and turnover. Overall, columns two to five suggest that the interaction of turnover and real options is totally subsumed by the interaction of idiosyncratic volatility and real options. It means that as a proxy for uncertainty turnover contains little to no additional information compared to idiosyncratic volatility. This is further confirmed in the sixth column, where I add all four products in one regression. I find that the products of idiosyncratic volatility with market-to-book and leverage have sizeable coefficients and are significant, and the products of turnover with market-to-book and leverage are minuscule and insignificant in their presence. In the last column, I add the product of size and market-to-book and see that nothing changes compared to the sixth column. It happens because, quite expectedly, the interaction of size and market-to-book is totally subsumed by the interaction of idiosyncratic volatility and market-to-book. 3.3 Covariance-Based Tests Turnover and Aggregate Volatility Risk The main prediction of my paper is that high turnover firms have low aggregate volatility risk, because they are high uncertainty firms. The firm-specific uncertainty is transformed into lower aggregate volatility risk by real options, so the best hedges should be the firms with high levels of both. While the previous subsections brought some evidence in favor 13

15 of the last prediction, a more direct test of the model is to verify that, first, the pattern in the abnormal returns across turnover quintiles in Table 1 is aligned with a similar pattern in the aggregate volatility risk factor betas, and second, that the interactions between real options and turnover in Table 2 can also be traced back to aggregate volatility risk. In Panel A of Table 3, I look at the turnover quintiles from Table 1 and consider the CAPM, the Fama-French model, the ICAPM with the market factor and the aggregate volatility risk factor (the FVIX factor), and the Fama-French model augmented with FVIX. The sample period is from January 1986 to December 2006 because of the availability of the VIX index, which is my proxy for expected aggregate volatility. The first row of Panel A reports the value-weighted CAPM alphas for the new sample period and confirms that in the last 21 years of data going long in low turnover stocks and short in high turnover stocks yields a sizeable abnormal return (58 bp per month, t-statistic 2.15). The low minus high return differential even stronger in equal-weighted returns (results not reported to save space). In the next row, I show that controlling for aggregate volatility risk changes the return differential to -15 bp per month, t-statistic The key to the success is the FVIX beta of the highest turnover quintile (0.797, t-statistic 8.82). By construction, the FVIX factor is the combination of the base assets with the most positive correlation with VIX changes (VIX is my proxy for expected aggregate volatility). Therefore, the positive FVIX beta of high turnover firms means that these firms beat the CAPM when aggregate volatility increases, i.e. buying them and short-selling the firms with the same market beta would create a hedge against aggregate volatility risk. I also observe a significant aggregate volatility risk exposure for low turnover firms (FVIX beta , t-statistic -7.2), which brings the low minus high differential in FVIX betas to , t-statistic In the Fama-French model with FVIX, the FVIX betas remain of the same magnitude with somewhat smaller, yet still highly significant, t-statistics. To sum up, the strong and monotonic decrease in FVIX betas from highest to lowest turnover firms and the considerable differential in the FVIX betas between the extreme portfolios shows that turnover is strongly associated with aggregate volatility risk, and this association can completely explain the relation between turnover and future returns without appealing to the doubtful (see Table 1) higher liquidity of high turnover firms. 14

16 This is the main point of the paper: high turnover does not mean high liquidity, but rather means higher firm-specific uncertainty, and it is possible to reconcile this interpretation of turnover with the negative relation between turnover and expected returns by showing that high turnover (high uncertainty) means low aggregate volatility risk Turnover, Real Options, and Aggregate Volatility Risk In Panel B, I look at the returns to the turnover arbitrage portfolio across market-to-book deciles. The turnover arbitrage portfolio buys the firms in the lowest turnover quintile and shorts the firms in the highest turnover quintile. This strategy is followed separately in each market-to-book quintile. I make the sorting into turnover quintiles conditional on size to mitigate the confounding effects described in Section However, the confounding effects are too numerous and complex, so the power of my test is likely to be low. It means that it would be very hard to come up with the evidence showing that the abnormal return to the turnover arbitrage portfolio increases with market-to-book, as my model predicts, and that this pattern maps into a similar increase in the aggregate volatility risk factor betas. Indeed, in Panel B I cannot come up with any evidence that the difference in the valueweighted CAPM alphas between the lowest and the highest turnover firms increases with market-to-book. I do, however, find strong evidence that going long in low turnover and short in high turnover firms means no exposure to aggregate volatility risk for value firms (no important hedges foregone by shorting high turnover firms with no growth options), but this exposure increases strongly across market-to-book quintiles. For the firms in the top market-to-book quintile, the turnover arbitrage portfolio has the FVIX beta of , t-statistic The large FVIX beta of the turnover arbitrage portfolio comes primarily from shorting high turnover growth firms, which would give good hedge against aggregate volatility risk. The strong increase in the FVIX betas of the turnover arbitrage portfolio means that, as predicted by the model, the negative dependence of future returns on the product of turnover and market-to-book I observed in Table 2 can be explained by aggregate volatility risk. In Panel C, I repeat the analysis in Panel B using leverage sorts instead of market-tobook sorts. To control for the negative relation between leverage and market-to-book, I make the leverage sorts conditional on market-to-book. However, I do not find any pattern 15

17 in either the CAPM alphas or the Fama-French alphas of the turnover arbitrage portfolio. Even worse, in the ICAPM the FVIX betas of the turnover arbitrage portfolio go strongly against my hypothesis: they start at , t-statistic -9.73, in the lowest leverage quintile and decline monotonically to , t-statistic -2.36, in the highest leverage quintile, meaning that it is less risky to buy low turnover firms and sell high turnover firms in the subsample of highly levered firms. In Section 2 and in the model in Appendix A I make the opposite prediction. However, it turns out that the conditional sorting does not really destroy the negative relation between leverage and market-to-book. The lowest leverage quintile still has average market-to-book of 5.07, versus the average market-to-book of 3.50 for the highest leverage quintile. I attempt to control for the difference in the market-to-book by looking at the FVIX betas of the turnover arbitrage portfolio in the augmented Fama-French model, where the HML factor can help in isolating the market-to-book effects. In the augmented Fama-French model in Panel C the FVIX betas of the turnover arbitrage portfolio do line up with my predictions, starting at -0.15, t-statistic -1.33, in the lowest leverage quintile, and increasing to , t-statistic -7.15, in the highest leverage quintiles. It means that short-selling high turnover firms exposes the investor to larger-than-expected losses during aggregate volatility increases only if leverage is high and the real option created by leverage is valuable, exactly as my story predicts. 4 The Turnover Factor and the New Issues Puzzle: An Application 4.1 Motivation In the previous section, I show that turnover picks up firm-specific uncertainty rather than liquidity. Consequentially, sorting on turnover implies inverse sorting on aggregate volatility risk. I find that high turnover firms have much lower exposure to aggregate volatility risk than low turnover firms, and this difference in aggregate volatility risk can completely explain the return differential between high and low turnover firms. Eckbo and Norli (2005) form a turnover-based liquidity factor and show that this factor can explain the new issues underperformance. Their liquidity factor goes long in the bottom 30% and short in top 30% of firms sorted on turnover. Eckbo and Norli (2005) 16

18 look at this return differential separately for the firms below and above NYSE median size. Their liquidity factor is the simple average between the two return differentials. The main result in Eckbo and Norli (2005) is that the underperformance of IPOs and SEOs is completely eliminated once one controls for the turnover factor. IPOs and SEOs have large negative turnover factor betas, which, according to Eckbo and Norli (2005), reveal the ability of new issues to hedge against liquidity risk. Eckbo and Norli (2005) corroborate this conclusion by showing that issuing equity increases turnover for several years after the issue. Brav, Geczy, and Gompers (2000) document that 50% of IPOs and 25% of SEOs come from only one bin in the five-by-five sorts on size and market-to-book - smallest growth stocks. They show that the performance of the smallest growth firms and new issues is likely to be driven by a common factor and conclude that new issues underperform only because the existing asset-pricing models cannot explain the low returns to small growth firms. Barinov (2009b) proposes an asset-pricing factor that explains both puzzles - the FVIX factor. Small growth firms tend to have high idiosyncratic volatility and operate in uncertain environment, which should make their growth options good hedges against aggregate volatility risk. Barinov (2009b) shows that the negative alphas of the smallest growth firms and new issues completely disappear after one controls for aggregate volatility risk. Smallest growth firms and new issues have large negative FVIX betas, which shows their ability to hedge against aggregate volatility risk. The preliminary analysis (not tabulated) shows that in my sample period (January December 2006) the CAPM alpha of the liquidity factor is 74 bp per month, t- statistic If I augment the CAPM with FVIX, the alpha drops to 8 bp, t-statistic The FVIX beta of the liquidity factor is , t-statistic Similarly, the CAPM alpha of the FVIX factor is -56 bp per month, t-statistic -3.0, and drops to -24 bp, t-statistic in the CAPM augmented with the liquidity factor. The liquidity beta of the FVIX factor is -0.44, t-statistic It seems that empirically the FVIX factor and the turnover factor have a high ability to proxy for each other, with the FVIX factor being able to explain the returns to the turnover factor, but not vice versa. This is surprising, because Barinov (2009a) shows that FVIX is positively correlated with returns to high idiosyncratic volatility firms, which tend to be small and illiquid. Hence, both high volatility firms and the FVIX portfolio should have 17

19 high liquidity risk and positive liquidity betas. So, if the turnover factor picks up liquidity risk, FVIX should be positively correlated with the turnover factor. If, as I argue in this paper, turnover is more of an uncertainty measure than a liquidity measure, the strong negative relation between the turnover factor and the FVIX factor (see the FVIX beta of the liquidity factor) is not surprising. FVIX is constructed to have strong positive correlation with aggregate volatility changes, hence it is a hedge aggregate volatility risk. The turnover factor buys low turnover firms (which have high aggregate volatility risk, see Table 3) and shorts high turnover firms (which have low aggregate volatility risk, see Table 3). Therefore, if turnover is uncertainty rather than liquidity, the turnover factor should have high aggregate volatility risk and negative FVIX beta. 4.2 New Issues Puzzle, Turnover Factor, and Aggregate Volatility Risk In Table 4, I look at three related puzzles - the small growth anomaly, the new issues puzzle, and the cumulative issuance puzzle from Daniel and Titman (2006). The small growth anomaly is represented by two portfolios - the smallest and the second smallest quintile within the top market-to-book quintile. The new issues puzzle is represented by the IPO and SEO portfolios, which include the IPOs and SEOs made in the past three years. The cumulative issuance puzzle is represented by the arbitrage portfolio long in the 30% least issuing firms and long in the 30% of the most issuing firms. The cumulative issuance is the log market value growth minus the cumulative log return in the past five years. I look at each puzzle where it is the strongest, so the returns to the two smallest growth portfolios are value-weighted, and the returns to the other three portfolios are equal-weighted. The first row of Table 4 shows that all puzzles are strong in my sample period (from January 1986 to December 2006 because of the FVIX availability). All CAPM alphas are significant and range from -51 bp per month (SEOs) to -99 bp per month (the smallest growth portfolio). In the next pair of rows I reproduce the results of Barinov (2009b) and show that all alphas drop to almost zero and become insignificant when I add FVIX to the CAPM. All five portfolios have large, positive and highly significant FVIX betas, which imply that small growth firms, new issues and routine issuers tend to beat the CAPM when expected aggregate volatility unexpectedly increases and therefore are good hedges 18

20 against aggregate volatility risk. In the next pair of rows I augment the CAPM with the turnover factor from Eckbo and Norli (2005) and find that it also brings the alphas very close to zero. The additional float from issuance story in Eckbo and Norli (2005) can potentially explain why the turnover factor works for IPOs, SEOs, and the cumulative issuance portfolio and why these firms have negative liquidity betas. However, it is very hard to explain why the smallest growth firms have negative exposure to liquidity risk of the same magnitude. According to all other liquidity measures, these firms have one of the lowest liquidity levels in the double sorts on size and market-to-book. In the last three rows of Table 4, I run the horse race between the turnover factor and the FVIX factor. Surprisingly, the turnover factor almost completely subsumes the FVIX factor, which means that they measure the same thing. However, the negative turnover factor beta of small growth firms and the negative correlation between FVIX and the turnover factor suggest that it is the turnover factor that proxies for aggregate volatility risk, not the FVIX factor that proxies for liquidity risk, even if econometrically the turnover factor wins. 4.3 New Issues Puzzle in Cross-Section In Table 5, I look at the underperformance of IPOs, SEOs, and routine issuers across the size groups - top 30%, bottom 40%, and low 30%. I determine the size breakpoints using NYSE (exchcd=1) only firms and distribute the new issues into the size groups by comparing their after-issue market value from SDC to the breakpoints. The aggregate volatility risk story suggests that the underperformance of new issues and routine issuers is driven by the smallest firms, which have the highest firm-specific uncertainty, and, therefore, the lowest aggregate volatility risk. If the aggregate volatility story is true, I expect the underperformance of new issues and routine issuers to decline with size, and their FVIX betas should behave the same way. The liquidity story suggests the opposite, because large new issuers and large routine issuers are clearly more liquid than small issuers and should provide the greatest hedge against liquidity risk. In the first row I observe that the CAPM alpha of the smallest IPOs (-77 bp per month, t-statistic -2.29) is significantly more negative than the CAPM alpha of the largest IPOs (26 bp, t-statistic 0.92). The difference is statistically significant with t-statistic