Price delay premium and liquidity risk

Available online at www.sciencedirect.com

Journal of Financial Markets 17 (2014) 150–173 www.elsevier.com/locate/finmar

Price delay premium and liquidity risk$ Ji-Chai Lina,n, Ajai K. Singhb, Ping-Wen (Steven) Sunc, Wen Yud a

Department of Finance, E.J. Ourso College of Business Administration, Louisiana State University, Baton Rouge, LA 70803-6308, USA b Lehigh University, USA c Jiangxi University of Finance and Economics, China d University of St. Thomas, USA Received 12 February 2012; received in revised form 3 December 2012; accepted 3 December 2012 Available online 13 December 2012

Abstract Hou and Moskowitz (2005) document that common stocks with more price delay in reflecting information yield higher returns and that the delay premium cannot be explained by the CAPM, Fama-French three-factor model, or Carhart’s four-factor model. It cannot be explained by conventional liquidity measures either. They contend that the premium is attributable to inadequate risk sharing arising from lack of investor recognition, as Merton (1987) suggests. Using a parsimonious and powerful asset pricing model developed by Liu (2006), we re-examine the issue and find that firms with greater price delay have more difficulty attracting traders (higher incidents of non-trading) and their investors face higher liquidity risk, which accounts for their anomalous returns. Our findings suggest that the price delay premium is due to systematic liquidity risk, not inadequate risk sharing. & 2012 Elsevier B.V. All rights reserved. JEL classifications: G12 Keywords: Liquidity risk; Price delay premium; Investor recognition

$ We thank Viral Acharya, Robin Chou, Kathryn Clark, Amit Goyal, Adam Lei, Wei Li, Weimin Liu, Avanidhar Subrahmanyam, an anonymous referee, and seminar participants at Louisiana State University, National Central University, University of St. Thomas, the 2009 Taiwan Finance Association Annual Meeting, and 2010 Financial Management Association Annual Meeting for comments and suggestions. We are responsible for any remaining errors. n Corresponding author. Tel.: þ1 225 578 6252; fax: þ1 225 578 6366. E-mail address: fi[email protected] (J.-C. Lin).

1386-4181/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.finmar.2012.12.001

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1. Introduction Does the speed at which information gets reflected in prices affect expected returns on common stocks? Hou and Moskowitz (2005) contend that the delay in price response to market-wide information can capture the essence of market frictions. Intriguingly, they find that firms with higher price delay yield significantly higher stock returns, and that the delay premium cannot be explained by the capital asset pricing model (CAPM), the FamaFrench (1993) three-factor model, or Carhart’s (1997) four-factor model. Hou and Moskowitz argue that the delay effect on stock returns is largely attributable to market frictions associated with investor recognition. Their argument supports Merton’s (1987) hypothesis that investors faced with incomplete information require a higher premium to hold less recognized stocks,1 and the delay premium is due to inadequate risk sharing arising from lack of investor recognition. In this study, we offer and test an alternative view, based on systematic liquidity risk, to explain why firms whose stock prices respond slower to information (more ‘‘delayed’’ firms) earn higher returns. Specifically, we argue that while facing the investor recognition problem, more delayed firms generally have lower liquidity, lower levels of monitoring from institutional investors, and less analyst coverage. These factors make the stock prices of such firms less informative with a longer price delay in reflecting information. Consequently, more delayed firms would be more sensitive to shocks to market liquidity because their intrinsic values have greater uncertainty and thus fewer traders would step up to absorb the shocks. Further, when shocks to market liquidity occur, market makers of more delayed stocks face more order imbalance because such stocks attract fewer traders to absorb the shocks. It also causes market makers to face higher inventory holding risk, as well as higher adverse selection risk, which force them to impose wider spreads and lower depths on more delayed stocks. This effectively raises the transaction costs, resulting in a greater incidence of non-trading and more price delay in reflecting information. In sum, we hypothesize that firms with more price delay tend to attract fewer traders to absorb shocks to market liquidity,2 causing their shareholders to face higher liquidity risk and to accept a lower price if they need to sell in a bad market.3 Accordingly, to hold stocks with more price delay, investors require higher returns to compensate them for the greater liquidity risk they face.4 1 In Merton’s (1987) model, investors of less recognized firms hold undiversified positions in the stocks, and thus require higher expected returns to compensate them for the increased idiosyncratic risk associated with their positions. However, recently, Bali and Cakici (2008) show that there is no robustly significant relation between idiosyncratic volatility and expected returns. 2 According to Chien and Lustig (2009), if a large fraction of agents encounter binding solvency constraints, the economy is said to be hit by a negative liquidity shock. More generally, as Chordia, Roll, and Subrahmanyam (2000) point out, there is strong commonality in liquidity among individual stocks. And, shocks to market liquidity are manifested in unexpected changes in aggregate liquidity. Amihud (2002) and Liu (2006) demonstrate that large negative shocks to market liquidity tend to occur when the market experiences substantial declines [see also Pastor and Stambaugh (2003) and Acharya and Pedersen (2005)]. 3 Eisfeldt (2004) argues that, in a bad market characterized by low productivity and adverse selection, agents are more likely to sell claims to low quality projects, resulting in lower claim price and lower liquidity. 4 Our hypothesis is in line with Pastor and Stambaugh (2003) and Acharya and Pedersen (2005), who argue that investors will require higher expected returns for holding assets that are difficult to sell when aggregate liquidity is low.

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Using a parsimonious and powerful asset pricing model developed by Liu (2006), we test the liquidity risk hypothesis in explaining the price delay premium of Hou and Moskowitz (2005). Consistent with our hypothesis, we find that firms with greater price delay have higher liquidity risk, which can account for their anomalous returns. Our findings imply that it is not the speed of information dissemination per se that is essential in explaining stock returns; instead, what matters is the magnitude of liquidity risk investors face. Hou and Moskowitz (2005, p. 963) recognize that price delay may also result from lack of liquidity. Accordingly, they examine the efficacy of their price-delay measure controlling for size, microstructure, and liquidity effects using traditional liquidity proxies: ‘‘Traditional liquidity proxies, such as volume, turnover, price, number of trading days, bid-ask spread, and the price impact and trading cost measures of Amihud (2002) and Chordia, Subrahmanyam, and Anshuman (2001), do not subsume the delay effect y There is also little relation between the delay premium and the aggregate liquidity risk factor of Pastor and Stambaugh (2003).’’ However, Liu (2006) argues that conventional liquidity measures have three limitations: (1) they fail to capture the multi-dimensional properties of liquidity,5 (2) they do not reflect the illiquidity of non-trading,6 and (3) they fail to take into consideration the endogeneity of the trading decision as a function of trading costs.7 To overcome these problems, Liu proposes a new measure of liquidity, LM12, which is the standardized turnoveradjusted number of days with zero-trading volume over the prior 12 months. Liu demonstrates that LM12 is highly correlated with traditional measures of liquidity (that are controlled for by Hou and Moskowitz) and yet has significant incremental explanatory power on asset pricing.8 Based on LM12, Liu (2006) develops a liquidity-augmented CAPM (LCAPM). He shows that the LCAPM can explain the anomalies associated with firm size, bookto-market, cash-flow-to-price, earnings-to-price, dividend yield, and long-run price reversals. His study illustrates that the liquidity premium associated with non-trading plays a very important role in asset pricing. Therefore, we use Liu’s LCAPM in this study to check whether it can also explain Hou and Moskowitz’s (2005) price delay premium. Specifically, using Liu’s (2006) LCAPM, we ask and find positive answers to the following related questions: Are firms with greater price delay less liquid, as measured by LM12? Are they more sensitive to shocks to market liquidity? Do they offer higher returns because investors demand higher liquidity premium? Ultimately, can Liu’s LCAPM explain the price delay premium? To summarize, we find that the market and liquidity 5

Liquidity can be defined as the ability to buy or sell large quantities of an asset quickly and at low cost. Adverse selection could cause an asset to be illiquid. In the extreme case of Akerlof (1970), the market breaks down and liquidity disappears. This illiquidity of non-trading could be temporary, but the frequency of its occurrence could be important. 7 As Lesmond, Ogden, and Trzcinka (1999) and Lin, Singh, and Yu (2009) point out, liquidity traders may refrain from trading if trading costs outweigh the improvement in portfolio allocation; similarly, informed investors would trade only if the value of information exceeds trading costs [see also Lesmond (2005) and Bekaert, Harvey, and Lundbald (2007)]. Thus, ceteris paribus, greater incidence of no trading should reflect higher latent trading costs and lower liquidity. 8 Similarly, Lin, Singh, and Yu (2009) argue that ‘‘while the bid-ask spread is conventionally used to measure trading costs, it has a limitation—the bid and ask quotes are often for small-size trades whereas a larger transaction size may need to be negotiated,’’ and ‘‘because of the endogeneity of the trading decision, standard measures such as Amihud’s (2002) illiquidity measure and Kyle’s (1985) lambda, which focus on price impacts of trades, may not be able to fully capture the illiquidity of non-trading.’’ 6

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factors subsume the price delay effect. That is, once we control for market risk and Liu’s liquidity risk, there is no evidence of a price delay premium. The rest of the paper is organized as follows. Section 2 describes the data, and discusses the correlation between Liu’s (2006) liquidity measure and Hou and Moskowitz’s (2005) price delay measure. Section 3 uses Liu’s (2006) LCAPM to test our liquidity risk hypothesis for explaining the price delay premium. Section 4 reports cross-sectional analysis of liquidity risk. Section 5 contains our concluding remarks.

2. Data The premise in this study is that firms with more price delay tend to attract fewer traders to absorb shocks to market liquidity, thus subjecting them to greater liquidity risk. Further, higher returns required by investors to compensate them for the greater liquidity risk underlie the price delay premium documented by Hou and Moskowitz (2005). To test this hypothesis, we use a sample of NYSE/AMEX/NASDAQ common stocks listed in the Center for Research in Security Prices (CRSP) files with share codes of 10 or 11 from 1973 through 2009.9 We obtain firm characteristics, including size, book equity, number of shareholders, and number of employees, from the Compustat and CRSP files; the number of analysts from I/B/E/S; and institutional ownership from Thomson Financial.10 Also, we obtain Liu’s (2006) liquidity factor, LIQ, from Weimin Liu, and the conventional asset pricing factors, including risk-free rate (rf), excess return on the market (Rmrf), Small minus Big (SMB), High minus Low (HML), and Winner minus Loser (WML), from Kenneth French’s website. To include in our analysis, we require each sample firm to have (1) one-year daily trading volume data available in the prior year for computing Liu’s (2006) liquidity measure, LM12, and (2) prior two years of weekly returns for estimating Hou and Moskowitz’s (2005) first-stage and second-stage price delay measures,11 which will be explained below. The data requirements allow us to conduct asset pricing tests from 1974 through 2009.

2.1. Measuring price delay To measure price delay, we follow Hou and Moskowitz (2005) by regressing each sample firm’s weekly returns on the contemporaneous and four weeks of lagged returns of the 9

The reason our sample period starts in 1973 is that to compute Liu’s (2006) liquidity measure, we need daily trading volume, which is available for most firms in the CRSP files starting from 1973. Also, due to trading volume data availability, NASDAQ stocks are included in analysis from 1983 onwards. 10 Note that institutional ownership data is available in the database since 1980. While the I/B/E/S has data on the number of analysts since 1976, not many firms were covered in the early years. Hence, our data of institutional ownership and analyst coverage start in 1980. In addition, during the time period from 1980 to 2009, we assume that a firm that is not covered in the I/B/E/S has no analyst following. Similarly, we assume no institutional holding if a firm is not included in the Thomson Financial database. 11 We estimate Hou and Moskowitz’s (2005) first-stage price delay measure for our sample stocks, starting in 1972; and infer their second-stage price delay measure and Liu’s (2006) liquidity measure, starting in 1973.

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market portfolio over the prior year (i.e., from July year t1 to June year t):12 Rj,t ¼ aj þ bj Rm,t þ

4 X

dðj nÞ Rm,tn þ ej,t ,

ð1Þ

n¼1

where Rj,t and Rm,t, respectively, are stock j’s and the market’s (i.e., CRSP value-weighted market portfolio) returns in week t, and Rm,tn are the market returns in prior n weeks. For each firm-year, we require at least 24 weekly returns to ensure that the coefficients are estimated with sufficient observations. As Hou and Moskowitz (2005) point out, the more quickly a stock’s price responds to market news, the more the variation of its returns is captured by contemporaneous market returns. Conversely, if the stock price delays in incorporating market news, then more of its return variation is explained by lagged market returns. Thus, Hou and Moskowitz propose to measure price delay by: D1 ¼ 1

R2dðnÞ ¼ 0,8n2½1,4 j

R2

where R2 and R2ðnÞ dj

¼ 0,8n2½1,4

, are the R-squared values based on the above unrestricted and

restricted (i.e., restricting the coefficients of lagged market returns to be zero) regressions in Eq. (1), respectively.13 According to Hou and Moskowitz, this individual stock’s first-stage D1 can capture a firm’s severity of market frictions—the more severe are its frictions, the higher is the D1 measure and the greater is the delay in its price response to information. Nevertheless, Hou and Moskowitz (2005, p. 987) contend that ‘‘due to the volatility of weekly individual stock returns, the coefficients from eq. (1) are estimated imprecisely. To mitigate an errors-in-variables problem, we also sort firms into portfolios based on their market capitalization and individual delay measure, compute delay measures for the portfolio, and assign the portfolio delay measure to each firm in the portfolio.’’ They find that using this second-stage portfolio delay measure to assign stocks into portfolios produces stronger results than those directly employing D1 (the first-stage individual stock delay measure). We examine both Hou and Moskowitz’s first-stage and second-stage D1 measures, and agree with their assessment. We present and discuss the results based on their second-stage D1 in analyzing the price delay premium. Specifically, following Hou and Moskowitz (2005), we obtain the second-stage D1 for each stock as follows. First, at the end of June of calendar year t, we sort stocks into deciles based on their market capitalization. Second, within each size decile, we then sort stocks into deciles based on their first-stage D1, estimated using weekly return data from July of year t1to June of year t. Third, the equal-weighted weekly returns of the 100 size-delay portfolios are computed over the following year from July of year tto June of year tþ1. Then, we re-run Eq. (1) using the weekly portfolio returns and obtain the second-stage D1 for each of the 100 portfolios. The computed-delay measure for each portfolio is then 12

Following Hou and Moskowitz (2005), the weekly returns are computed between adjacent Wednesdays. To further distinguish the explanatory power of recent versus earlier lags, Hou and Moskowtiz (2005) also       4 4 P P ndðj nÞ  ndðj nÞ =se dðj nÞ n¼1 n ¼1  P  as alternative price delay measures [for detail, see suggest D2 ¼  and D3 ¼  4  4  P jbjþ dðnÞ  jbj=se bÞþ dðnÞ =seðdðnÞ 13

j

n¼1

j

j

n¼1

Hou and Moskowitz (2005)]. The untabulated results show correlations of 0.98 between D1 and D2, and between D1 and D3 across the price delay-sorted portfolios. For brevity, we report results of price delay measure, D1. Results are robust using D2 or D3 delay measure.

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assigned to the stocks in the portfolio at the end of June in year tþ1. As Hou and Moskowitz note, this procedure essentially shrinks each stock’s individual delay measure to the average for stocks of similar size and individual first-stage delay. Table 1 reports average firm characteristics for firms in each of the ten second-stage D1-sorted decile portfolios. Specifically, by the end of each June, we sort stocks based on their second-stage D1 into ten decile portfolios. The average second-stage D1 ranges from 0.007 for decile 1 (the least delayed) portfolio to 0.544 for decile 10 (the most delayed) portfolio. Consistent with Hou and Moskowitz (2005), firms with higher D1 tend to be smaller and have higher book-to-market ratio. Also, they tend to have less investor recognition, with lower institutional ownership, less analyst coverage, and fewer shareholders and employees. The evidence supports Hou and Moskowitz’s contention that investor recognition plays an important role in the speed of information diffusion and the price formation process.

2.2. Measuring stock liquidity Hou and Moskowitz (2005) indicate that conventional liquidity measures, such as the volume, turnover, price, number of trading days, bid-ask spread, and the price impact and Table 1 Sample characteristics. This table reports average firm characteristics by price delay-sorted portfolio. We use Hou and Moskowitz’s (2005) second-stage price delay measure (D1) to sort firms into ten decile portfolios (from low to high) at the end of each June from 1974 to 2008. Turnover is in 103 as the average ratio of monthly trading volume to the number of rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  shares outstanding. Roll’s Spread is in percentage as cov ri,t ,ri,t1 Þ , using monthly returns. Amihud’s illiquidity i,t j , where ri,t is the monthly return, pi,t is the closing measure (Amihud’s IM) is in 107 as the monthly average pi,tjrvol i,t

price or bid/ask average, and voli,t is the monthly volume. Size is the market value in millions, and B/M is the ratio of book equity value (Compustat item 60þitem 74) to market value of equity by the end of each June. Employee is the number of employees in 1000s (Compustat item 29), and Investor is the number of shareholders in 1000s (Compustat item 100) available by the end of each June. Instpct, is the quarterly average 13f institutions’ share ownership in percentage from Thomson Financial in the year ending each June. Analyst, is the monthly average number of analysts that issue EPS forecasts for fiscal year 1 from I/B/E/S in the year ending each June. Instpct and Analyst are obtained from 1980 to 2008 (see footnote 10).

1

2

3

Price delay-sorted portfolio 4 5 6 7

8

9

10

D1 0.007 0.020 0.039 0.062 0.092 0.131 0.180 0.248 0.349 0.544 LM12 0.426 1.907 3.821 7.228 10.468 16.915 23.724 32.780 45.215 63.446 97.926 99.860 97.398 93.590 87.893 76.799 67.598 58.208 56.518 55.160 Turnover (103) Roll’s Spread (%) 2.810 3.066 3.406 3.604 3.882 4.231 4.468 4.746 5.409 6.361 Amihud’s IM 0.064 0.549 0.796 0.954 1.698 4.593 5.000 9.168 18.893 47.800 (107) Size(106) 6528.05 2964.42 1127.59 542.779 420.242 470.921 105.143 54.347 137.509 19.363 B/M 0.676 0.745 0.799 0.856 0.901 0.979 1.064 1.128 1.200 1.342 Employee (103) 31.074 16.824 8.061 5.221 4.383 3.237 2.012 1.336 1.119 0.571 54.881 27.360 13.914 9.322 10.181 7.826 3.393 3.617 10.898 2.090 Investor (103) Instpct (%) 53.432 48.569 43.216 38.093 33.819 26.781 21.442 15.610 11.529 7.558 Analyst 14.968 9.731 6.653 4.569 3.911 2.634 1.755 1.029 0.693 0.282 Average # of firms 452.057 424.943 429.286 430.200 429.257 423.000 430.657 428.371 425.000 411.229

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trading cost measures of Chordia, Subrahmanyam, and Anshuman (2001), Amihud (2002), and Pastor and Stambaugh (2003), cannot explain the price delay premium. However, Liu (2006) argues that the conventional liquidity measures cannot fully capture the illiquidity of non-trading. He proposes a new liquidity measure, LM12, the standardized turnover-adjusted number of days with zero trading volume over prior 12 months. Specifically, he formulates his liquidity measure as: LMx ¼ ½Number of zero daily volumes in prior x months  1=ðxmonth turnoverÞ 21  x þ ,  Deflator NoTD where ‘‘x-month turnover’’ is the stock’s turnover in the prior x months, calculated as the sum of daily turnover over the prior x months; daily turnover is the ratio of the number of shares traded on a day to the number of shares outstanding at the end of the day,14 NoTD is the total number of the trading days in the market over the prior x months, and Deflator turnoverÞ is chosen such that 0o 1=ðxmonth o1 for all sample stocks (e.g., Liu chooses a Deflator deflator of 11,000 in constructing his LM12). At the end of each June, we measure each stock’s level of liquidity by LM12 over the prior 12 months. Liu (2006) notes that ‘‘LMx uses the pure number of zero daily trading volumes over the prior x months to identify the least liquid stocks, but it relies on turnover to distinguish the most liquid among frequently traded stocks as classified by the pure number of zero trading volumes.’’ As Lin, Singh, and Yu (2009) indicate, LMx captures the intuition that greater incidence of no trading implies higher latent costs of trading and that non-trading reflects illiquidity. Liu (2006) demonstrates that LM12 is strongly correlated with conventional liquidity measures, such as bid-ask spread, trading volume, and Amihud’s (2002) price impact measure, and yet it exhibits significant incremental explanatory power on asset pricing. In particular, Liu shows that there is a significant and robust liquidity premium associated with firms with high LM12, relative to firms with low LM12. We use Liu’s LM12 to measure stock liquidity in our re-examination of the price delay premium. 2.3. Correlations between price delay and liquidity To the extent that trading facilitates information incorporation into stock prices, price delay [i.e., Hou and Moskowitz’s (2005) D1] and the illiquidity of non-trading [i.e., Liu’s (2006) LM12] should be closely related. Intuitively, one expects that the stocks of firms with more non-trading days would have longer delays in reflecting information; and, conversely, for more liquid stocks with active trading, stock prices would respond to information in a more timely fashion. This subsection examines the D1-LM12 relation, which paves the way for us to explore the extent to which the liquidity premium may account for the price delay premium. 14

Trading volume for NASDAQ stocks includes inter-dealer trades, which makes it incomparable to the NYSE/ AMEX trading volume. To correct for possible bias in LM12 as a liquidity measure due to the way NASDAQ reports trading volume, we have also experimented in LM12 calculation to divide the NASDAQ trading volume by a factor of two. We find that the correlation between the adjusted LM12 and the LM12 based on Liu’s formula is essentially equal to one in our sample. This suggests that the number of non-trading days in the first part of LM12 dominate LM12 and the turnover part only plays a minor role. Consequently, we find that the empirical results of our study are robust and not affected by the way to adjust NASDAQ trading volume. For brevity, we report results of LM12 as described by Liu (2006).

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Table 2 Correlation matrix. This table reports Pearson correlations for main variables used in Table 3. D1 is the second-stage price delay measure obtained by the end of each June. The variables, LM12, Turnover, Roll’s Spread, Amihud’s IM, Employee, Investor, Instpct, and Analyst are defined in Table 1. lnLM12 ¼ lnð1 þ LM12Þ, ln employee ¼ lnð1 þ EmployeeÞ, lninvestor ¼ lnð1þ InvestorÞ, lninstpct ¼ lnð1 þ InstpctÞ, and lnanalyst ¼ lnð1 þ AnalystÞ. The p-values are given below the correlation estimates. lnLM12

D1 lnLM12 Turnover (103) Roll’s Spread (%) Amihud’s IM (107) lnemployee lninvestor lninslpct

Turnover (103)

0.572 0.126 (o0.0001) (o0.0001) 0.332 (o0.0001)

Roll’s Spread (%) 0.199 (o0.0001) 0.058 (o0.0001) 0.105 (o0.0001)

Amihud’s lnemployee lninvestor IM (107) 0.151 (o0.0001) 0.166 (o0.0001) 0.049 (o0.0001) 0.085 (o0.0001)

0.452 (o0.0001) 0.415 (o0.0001) 0.005 (0.107) 0.184 (o0.0001) 0.065 (o0.0001)

0.344 (o0.0001) 0.378 (o0.0001) 0.057 (o0.0001) 0.144 (o0.0001) 0.044 (o0.0001) 0.635 (o0.0001)

lninslpct

lnanalyst

0.510 (o0.0001) 0.561 (o0.0001) 0.313 (o0.0001) 0.167 (o0.0001) 0.092 (o0.0001) 0.511 (o0.0001) 0.247 (o0.0001)

0.574 (o0.0001) 0.640 (o0.0001) 0.239 (o0.0001) 0.167 (o0.0001) 0.090 (o0.0001) 0.663 (o0.0001) 0.527 (o0.0001) 0.691 (o0.0001)

Table 1 shows that D1 and LM12 are strongly correlated, as expected. The average LM12 of the least delayed portfolio is 0.43 turnover-adjusted no-trade days; it increases monotonically to 1.91 no-trade days and to 3.82 no-trade days for portfolios 2 and 3, respectively, and reaches 63.45 no-trade days for the most delayed portfolio15. The pattern of the average LM12 suggests that firms with higher Hou and Moskowitz’s (2005) pricedelay measure exhibit a greater incidence of non-trading, implying that they are less liquid and their investors face higher latent trading costs. Table 2 reports the correlations between D1 and several conventional liquidity measures, including turnover, Roll’s (1984) effective spread, Amihud’s (2002) illiquidity measure, and Liu’s (2006) LM12. Consistent with Hou and Moskowitz (2005), less liquid stocks tend to have greater price delay. Interestingly, among the liquidity measures, LM12 has the highest correlation with D1. Furthermore, according to Table 3, LM12 can explain 38.4% of the cross-sectional variation in D1. In contrast, the explanatory powers of turnover, Roll’s effective spread, and Amihud’s illiquidity measure are 3.8%, 4.6%, and 11.7%, respectively. The finding that LM12 has the highest correlation with D1 has an implication for the quality of LM12 being a liquidity measure. As Stoll (2000) suggests, trading cost or illiquidity is an

15

Liu (2006) reports that, on average, ‘‘over 50% (30%) of NYSE/AMEX (NASDAQ) stocks trade every day throughout the prior 12 months.’’

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Table 3 Cross-sectional analysis of price delay. This table reports time-series average of the coefficient estimates from Fama-Macbeth (1973) cross-sectional regressions of Hou and Moskowitz’s price delay measure (D1) on firm characteristics, including liquidity variables lnLM12, Turnover, Roll’s Spread and Amihud’s Illiquidity measures, and investor recognition variables lnemployee, lninvestor, lninslpct and lnanalyst. The dummy variable, exchdummy, is an indicator variable equal to one if the sample stock is listed on the NASDAQ, and zero otherwise The variables are defined as in Tables 1 and 2. The t-values for the coefficient estimates are in parentheses. nnn, nn, n Significant at 1%, 5%, and 10% level, respectively, for the t-tests.

(1) Intercept lnLM12

0.075nnn (10.37) 0.061nnn (16.78)

Turnover (103)

(2) 0.193nnn (12.43)

Model (3) 0.135nnn (11.30)

(4) 0.155nnn (11.12)

(5) 0.330nnn (12.77)

0.235nnn (12.00) 0.039nnn (18.66)

0.006nnn (5.98) 0.005nnn (5.88) 0.264nnn (11.57) 0.066nnn (12.03)

0.011nnn (7.49) 0.005nnn (3.34) 0.226nnn (14.18) 0.042nnn (10.76) 0.020nnn (10.14) 0.523

0.0006nnn (5.90) 0.007nnn (10.71)

Roll’s Spread (%) Amihud’s IM (107)

0.004nnn (4.07)

lnemployee lninvestor lninslpct lnanalyst exchdummy Adjusted R2

(6)

0.384

0.038

0.046

0.117

0.443

(7) 0.208nnn (11.12) 0.041nnn (15.76) 0.0002nnn (5.23) 0.002nnn (10.21) 0.001n (1.78) 0.008nnn (6.75) 0.007nnn (4.06) 0.221nnn (13.42) 0.043nnn (11.20) 0.011nnn (5.37) 0.539

important source of market friction. Among the liquidity measures, LM12 seems to have the best capacity to capture the illiquidity effect associated with price delay. Table 2 also shows that both D1 and LM12 are strongly correlated to institutional ownership, number of employees, number of shareholders, and analyst coverage, in the direction of less known firms having lower liquidity and more price delay. While Hou and Moskowitz (2005) suggest that investors require a higher premium to hold more delayed stocks due to their inadequate risk sharing arising from lack of investor recognition, Liu (2006) shows that high LM12 firms command a significant liquidity premium. The high correlations between LM12 and D1 and between LM12 and the proxies for the degree of investor recognition provide a basis for us to ask: To what extent may liquidity premium account for Hou and Moskowitz’s (2005) price delay premium? Table 4 reports the regression results in an attempt to answer which firm characteristic, price delay or illiquidity of non-trading, is more related to individual stock returns. Models (1) and (2) show that individual stocks’ monthly returns are positively related to LM12 and D1, respectively. This suggests that either variable alone has explanatory power for stock returns. However, in Model (5), where both LM12 and D1 are included, along with a set of controlling

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Table 4 Fama-MacBeth (1973) cross-sectional regressions of stock returns on liquidity (LM12) and price delay (D1). This table reports the averages of monthly coefficient estimates (and their t-values in parentheses) of Fama-MacBeth (1973) cross-sectional regressions of individual stocks’ monthly returns in excess of one-month T-bill rate on Liu’s (2006) liquidity measure, LM12, and Hou and Moskowitz’s (2005) second-stage D1. Both LM12 and D1 are obtained at the end of each June from 1974 to 2008. Individual stock returns used in regressions are over the subsequent year. The test period is from July 1974 to June 2009. Control variables include Size, B/M, stock price level, past stock returns and four investor recognition variables Employee, Investor, Instpct, and Analyst as defined in Table 1. The variable, lnprice is the log of the stock price at the end of each June; past_ return is the previous year’s cumulative monthly returns (from month t-12 to t-2), and the exchdummy variable, is an indicator variable equal to one if the sample stock is listed on the NASDAQ, and zero otherwise. lnLM12¼ ln(1þLM12), lnsize¼ln(Size), lnbm¼ln(B/M), lnemployee¼ln(1þEmployee), lninvestor¼ln(1þInvestor), lninstpct¼ln(1þInstpct), lnanalyst¼ ln(1þAnalyst). nnn, nn, n Significant at the 1%, 5%, and 10% level, respectively, for the t-tests. Model

Intercept lnLM12 D1 lnsize lnbm lnprice past_ return lnemployee lninvestor lninstpct lnanalyst exchdummy

(1)

(2)

(3)

(4)

(5)

0.007nn (2.30) 0.002nnn (3.60)

0.006nn (2.25)

0.016nnn (3.40)

0.012n (1.89) 0.001nn (2.01)

0.002nnn (3.12) 0.002nnn (3.11) 0.003nn (1.98) 0.005nn (2.19) 0.001 (1.34) 0.0007 (1.40) 0.008nn (2.32) 0.003nnn (4.81) 0.001 (1.27)

0.001nn (2.32) 0.002nnn (3.00) 0.003nnn (2.63) 0.005nn (2.13) 0.0008 (0.96) 0.0009 (1.54) 0.009nnn (2.77) 0.003nnn (5.78) 0.001 (1.21)

0.012n (1.94) 0.001nn (2.08) 0.003 (0.85) 0.001nn (2.35) 0.002nnn (3.03) 0.004nnn (2.67) 0.005nn (2.18) 0.0008 (0.96) 0.0009 (1.58) 0.009nnn (2.79) 0.003nnn (5.84) 0.001 (1.23)

0.020nnn (3.00)

variables.16 LM12 remains statistically significant while D1 becomes insignificant. Thus, the evidence shows that the price delay premium can be subsumed by the liquidity premium, which implies that the illiquidity of nontrading is a more important factor than price delay in affecting stock returns. We next incorporate liquidity risk into the analysis to see whether more delayed firms face higher liquidity risk, and whether it is higher liquidity risk or inadequate risk sharing that leads to more delayed firms earning higher returns. 16

The control variables include firm size, B/M, stock price level, past stock returns, and four investor recognition variables.

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2.4. Measuring liquidity risk Based on LM12, Liu (2006) develops a Liquidity-augmented Capital Asset Pricing Model (LCAPM) in which expected returns on risky assets are determined by their market and liquidity risks. To capture liquidity risk, Liu (2006) constructs a liquidity factor, LIQ, as the return difference between a low-liquidity portfolio (containing stocks with high LM12) and a high-liquidity portfolio (containing stocks with low LM12). The construction is similar to Fama and French’s (1993) size factor, SMB, and B/M factor, HML. According to Liu’s (2006) LCAPM, the risk premium on stock i can be expressed as:     E Ri,t rf ,t ¼ bm,i ½E Rm,t rf ,t  þ bliq,i E ðLIQt Þ, ð2Þ where E(Rm,t) is the expected return of the market portfolio, E(LIQt)is the expected value of the mimicking liquidity factor, LIQ, and bm,i and bliq,i are firm i’s market beta and liquidity beta, respectively. Liu (2006) demonstrates that this two-factor LCAPM performs better than Fama and French (1993) three-factor model and Pastor and Stambaughs’ (2003) liquidity risk model in explaining the cross-section of stock returns.17 Thus, we use Liu’s LCAPM to estimate liquidity risk and test our liquidity risk hypothesis in explaining Hou and Moskowitz’s (2005) price delay premium. 3. Asset pricing tests In this section we test our liquidity risk hypothesis for explaining Hou and Moskowitz’s (2005) price delay premium. Our hypothesis is based on the notion that when facing shocks to market-wide liquidity, more delayed firms would attract fewer traders to step up and absorb the shocks. Under the circumstances, market makers for more delayed firms would face higher price uncertainty, maintain smaller inventories, and demand greater price concessions from traders. This causes investors to face lower depth and higher trading costs, and forces them to accept a lower (higher) price if they want to sell (buy) in a bad (good) market. Accordingly, to hold more delayed stocks, investors require higher returns to compensate them for the greater liquidity risk they face. 3.1. The price delay premium revisited Following Hou and Moskowitz (2005), by the end of each June, we sort firms into ten price-delay decile portfolios, from the least to the most delayed firms. To measure liquidity risk for each portfolio, we implement Liu’s (2006) LCAPM by running the following timeseries regression: Ri,t rf ,t ¼ ai þ bm,i ½Rm,t rf ,t  þ bliq,i LIQt þ ei,t ,

ð3Þ

where Ri,trf,tis the excess return on portfolio i in month t, Rm,trf,t is the excess return on the market portfolio (i.e., CRSP value-weighted market index), LIQt is Liu’s (2006) mimicking liquidity factor, ai is the abnormal return measure of portfolio i, and ei,t is the 17 Pastor and Stambaugh (2003) suggest that liquidity risk can be measured by return sensitivity to market liquidity. However, their measure does not capture the liquidity risk stemming from trading discontinuity; instead, it captures the illiquidity related to the price impacts of trades.

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error term assumed to have zero mean and constant variance. We also run the regression for a hedge portfolio, which has a long position in the most delayed portfolio and a short position in the least delayed portfolio. Table 5 reports the estimation results. In the LCAPM estimations, we are interested in three things. First, our liquidity risk hypothesis predicts that more delayed firms should have higher liquidity betas. Consistent with our hypothesis, as shown in Panel E of Table 5, the liquidity beta increases monotonically with the delay measures of the portfolios. The least delayed portfolio has a liquidity beta of 0.12 (t-value ¼ 4.15), and it increases to 0.79 (t-value ¼ 8.89) for the most delayed portfolio. The hedge portfolio’s liquidity beta of 0.90 (t-value ¼ 10.38) shows that the difference in liquidity beta between the two extreme portfolios is highly significant. The difference in risk premium is 0.98% per month between the most delayed and the least delayed portfolios (see Table 5, Panel A). We estimate the contribution of the liquidity risk difference (of 0.90) to the price delay premium as follows. The monthly average of LIQt over the sample period 1973-2009 is 0.65%. We use the monthly average of LIQt as a measure of E(LIQt) and obtain Dbliq E ðLIQt Þ ¼ 0:90  0:65% ¼ 0:585%: Thus, the difference in liquidity risk between the most delayed and the least delayed portfolios accounts for about 60% of the price delay premium of 0.98%. Second, when we compare the LCAPM estimation results to those of the CAPM, as reported in Panel B of Table 5, one can see that adding the liquidity factor LIQ to the asset pricing model significantly increases the market beta estimations for more delayed portfolios. Specifically, under the CAPM, the most delayed portfolio has a market beta of 0.97, which is significantly lower than the market beta of 1.11 for the least delayed portfolio. On the other hand, under the LCAPM (see Panel E of Table 5), the market beta of the most delayed portfolio increases to 1.39, while the market beta of the least delayed portfolio shows a slight decrease to 1.05. Thus, under Liu’s (2006) LCAPM, the portfolios with more price delay also have higher market betas, consistent with the notion that firms with more price delay are riskier. Again, to see how much the difference of 0.34 in market risk contributes to the price delay premium, we use the average of monthly market excess returns over the sample period 1973–2009, which is 0.49%, as a measure of E(Rm,trf,t) and obtain  Dbm E Rm,t rf ,t ¼ 0:34  0:49% ¼ 0:167%: Thus, about 17% of the price delay premium of 0.98% is attributable to the difference in market risk between the most delayed and the least delayed portfolios. Third, if the LCAPM is well specified for the delay-sorted portfolios, their abnormal return measures should be insignificantly different from zero. Indeed, the estimate of ai is insignificantly different from zero for each of the ten portfolios and for the hedged portfolio as well. These results suggest that, after accounting for the liquidity risk premium and the market risk premium, there is no price delay premium. Consistent with Hou and Moskowitz (2005), Table 5 also shows that the CAPM, FamaFrench (1993) three-factor model, and Carhart’s (1997) four-factor model cannot explain the price delay premium. The abnormal return of the hedge portfolio is 1.05% (t-value ¼ 3.69), 0.77% (t-value¼ 2.97), and 0.55% (t-value ¼ 2.12) per month under the CAPM, Fama-French three-factor model, and Carhart’s four-factor model, respectively. Our findings that Liu’s (2006) two-factor model can explain the price delay premium, while the other three models cannot, imply that Liu’s LCAPM can better capture the pricing effects of market frictions that cause price delay.

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Table 5 Average monthly returns of price delay-sorted portfolios. This table reports the average monthly returns of the price delay-sorted portfolios. We sort firms into 10 deciles by Hou and Moskowitz’s (2005) second-stage price delay measure (D1) at the end of each June from 1974 to 2008. Portfolio returns are obtained over the year subsequent to the portfolio formation from July 1974 to June 2009. Panel A reports portfolio raw and excess returns (i.e., excess of T-bill rate). Panels B through E, respectively, report the coefficient estimates of the time-series regressions of excess portfolio returns based on the CAPM, Fama-French (1993) three-factor model, Carhart’s (1997) four-factor model, and Liu’s two-factor model. While Portfolio 1 includes the least delayed firms, portfolio 10 consists of the most delayed firms. The results for the hedged portfolio which is long portfolio10 and short portfolio 1 are reported in the last column. The t-values are in parentheses.

1

2

3

4

Price delay-sorted decile 5 6 7

8

9

10

10-1

Panel A: Raw and excess returns Raw 1.07 1.15 1.23 return (%) (4.00) (4.16) (4.22) Excess 0.60 0.68 0.76 return (%) (2.24) (2.46) (2.61)

1.30 (4.34) 0.83 (2.76)

1.32 (4.29) 0.85 (2.75)

1.42 (4.52) 0.95 (3.02)

1.51 (4.73) 1.04 (3.25)

1.54 (4.70) 1.07 (3.20)

1.69 (5.15) 1.22 (3.71)

2.05 (5.75) 1.58 (4.42)

0.98 (3.46) 0.98 (3.46)

Panel B: The CAPM a^ (%) 0.05 (0.64) 1.11 b^ m (63.14)

0.26 (1.82) 1.14 (37.04)

0.29 (1.74) 1.12 (31.36)

0.40 (2.17) 1.11 (28.27)

0.50 (2.50) 1.09 (25.56)

0.51 (2.37) 1.01 (22.03)

0.73 (3.06) 1.00 (19.81)

1.10 (3.92) 0.97 (16.34)

1.05 (3.69) 0.13 (2.23)

Panel C: Fama-French three-factor model a^ (%) 0.04 0.06 0.08 0.01 (0.56) (0.76) (0.98) (0.11) 1.12 1.12 1.13 1.12 b^ m (62.55) (59.91) (59.67) (54.44) 0.15 0.41 0.65 0.75 b^ smb (5.82) (15.45) (23.92) (25.40) 0.15 0.28 0.40 0.37 b^ hml (5.53) (9.88) (13.95) (11.84)

0.01 (0.06) 1.09 (42.85) 0.83 (22.74) 0.40 (10.37)

0.07 (0.59) 1.08 (38.00) 0.90 (22.15) 0.44 (10.18)

0.17 (1.13) 1.06 (32.25) 0.92 (19.66) 0.45 (9.10)

0.19 (1.14) 0.97 (25.34) 0.90 (16.33) 0.42 (7.25)

0.37 (1.96) 0.97 (22.52) 0.94 (15.15) 0.50 (7.57)

0.72 (3.01) 0.94 (17.45) 1.00 (12.92) 0.52 (6.26)

0.77 (2.97) 0.18 (3.07) 0.85 (10.18) 0.36 (4.10)

Panel D: Carhart’s four-factor model a^ (%) 0.17 0.13 0.07 (2.76) (1.94) (0.93) 1.09 1.09 1.10 b^ m (78.81) (70.18) (64.16) 0.12 0.39 0.63 b^ smb (6.33) (17.74) (25.80) 0.09 0.23 0.36 b^ hml (4.39) (9.63) (13.73) 0.23 0.21 0.16 b^ wml (17.50) (14.33) (10.02)

0.13 (1.45) 1.09 (56.48) 0.73 (26.54) 0.33 (11.26) 0.15 (7.91)

0.10 (0.91) 1.07 (42.78) 0.81 (22.92) 0.37 (9.73) 0.12 (4.88)

0.20 (1.61) 1.06 (37.93) 0.88 (22.36) 0.41 (9.53) 0.14 (5.13)

0.22 (1.47) 1.05 (31.70) 0.92 (19.52) 0.44 (8.72) 0.06 (1.77)

0.23 (1.29) 0.97 (24.92) 0.89 (16.21) 0.42 (7.01) 0.03 (0.89)

0.41 (2.10) 0.97 (22.10) 0.93 (15.03) 0.49 (7.28) 0.05 (1.18)

0.72 (2.94) 0.94 (17.24) 1.00 (12.87) 0.52 (6.18) 0.003 (0.05)

0.55 (2.12) 0.14 (2.46) 0.88 (10.68) 0.42 (4.80) 0.23 (4.22)

0.13 (1.24) 1.12 (49.85)

0.20 (1.52) 1.13 (40.39)

Panel E: Liu’s two-factor model a^ (%) b^ m b^ liq

0.16 (1.86) 1.05 (46.24) 0.12

0.18 (1.60) 1.09 (37.04) 0.05

0.18 (1.30) 1.15 (31.02) 0.02

0.21 (1.38) 1.17 (28.94) 0.06

0.17 (0.95) 1.19 (25.55) 0.14

0.14 (0.74) 1.26 (25.03) 0.29

0.14 (0.67) 1.30 (24.22) 0.40

0.04 (0.19) 1.28 (22.64) 0.52

0.12 (0.53) 1.35 (22.23) 0.67

0.39 (1.43) 1.39 (19.30) 0.79

0.23 (0.86) 0.34 (4.84) 0.90

(4.15)

(1.40)

(0.52)

(1.18)

(2.41)

(4.64)

(6.10)

(7.45)

(8.94)

(8.89)

(10.38)

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Fig. 1 illustrates the differences of the four models in explaining the risk premiums of the ten delay-sorted portfolios. Specifically, we regress the portfolios’ predicted risk premiums (under each asset pricing model) on their realized average monthly excess returns. If the excess return of each portfolio can be perfectly explained by a model, then the ten portfolios would be on a line with a slope of one. Thus, based on the slope of the regression line, we can see how well a model fits the data. Consistent with Table 5, Fig. 1 shows that Liu’s LCAPM is more capable of explaining the excess returns of the delay-sorted

Fig. 1. Price delay-sorted portfolio returns and risk factors. This figure plots the excess returns (i.e., excess of riskfree rate) of ten decile portfolios sorted by Hou and Moskowitz’s (2005) second-stage price delay measure. Each scatter point represents one of the 10 portfolios, with the realized average return on the X-axis and the fitted expected return on the Y-axis. The realized average return is the time-series average excess return of each portfolio. The fitted expected return is calculated as the fitted value from the time-series regression Ri,trf,t ¼ gbi,t, where Ri,t is the return of portfolio i and rf,t is the T-bill rate in month t, bi,t is a vector of factor loadings in each specified model, and g is a vector of the estimated risk factor premiums in each period. The risk factors include the Fama and French three factors, (Rm rf), SMB, and HML, and the fourth Carhart factor, WML, and Liu’s (2006) liquidity factor LIQ.

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Fig. 2. Price delay-sorted portfolio returns and liquidity betas. This figure plots the average excess returns of ten decile portfolios sorted by Hou and Moskowitz’s (2005) second-stage price delay (D1) measure and their liquidity betas as reported in Table 4. Each scatter point represents one of the 10 portfolios. Portfolio 1 includes the least delayed firms, and portfolio 10 includes the most delayed firms. Liquidity beta of each portfolio is the coefficient estimate bliq,i from the time-series regression: Ri,trf,t ¼aiþbm,i[Rm,trf]þbliq,iLIQtþei,t.

portfolios, which provides a better fit than the CAPM, Fama-French three-factor model and Carhart’s four-factor model. Fig. 2 plots the delay-sorted portfolios’ excess returns versus their liquidity betas. It demonstrates that as the excess return increases from the least to the most delayed portfolio, the increase in liquidity risk is almost parallel to the excess returns. It clearly illustrates that the higher returns earned by more delayed firms are largely attributable to their higher liquidity risk. One may still be concerned with the issue that liquidity risk’s predictability on stock returns could simply stem from the fact that liquidity beta is mechanically related to price delay and illiquidity of non-trading, both of which have been shown to be related to stock returns. To address this issue, we focus on the liquidity-beta residual, which is the part of liquidity risk uncorrelated to D1 and LM12. First, we estimate liquidity beta for each firm in June of each year, using prior five-year monthly returns,18 and then run a cross-sectional regression of liquidity beta on the price delay (D1) and liquidity (LM12) measures by the end of each June. From the regressions, we obtain the liquidity-beta residual for each firm in each year. Next, we form ten decile liquidity- beta residuals sorted portfolios and hold them for one year; and repeat the process each year from 1974 through 2008. Consequently, we collect monthly returns for the ten decile liquidity-beta residual-sorted portfolios from July 1974 through June 2009, and report the average monthly return for each portfolio in Table 6. The results show that (1) the average portfolio raw returns tend to increase with the liquidity-beta residuals. In particular, Portfolio 1, which includes firms with the smallest liquidity-beta residuals, has an average monthly return of 1.11% (t¼ 2.87), while portfolio 10, 18 For example, we use a firm’s monthly returns from July 1969 to June 1974 to estimate its liquidity beta for June 1974. To be included in the Fama-Macbeth (1973) cross-sectional regression analysis, a firm must have at least 24 non-missing monthly return observations during the five year period.

1

2

3

4

5

6

7

8

9

10

10-1

1.28 (4.01)

1.28 (4.60)

1.33 (5.28)

1.36 (5.54)

1.35 (5.58)

1.38 (5.55)

1.45 (5.58)

1.48 (5.16)

1.49 (4.33)

0.38 (1.98)

Panel B: Fama-French three-factor a^ (%) 0.44 (2.57) 1.09 b^ m (28.19) 0.72 b^ smb (13.11) 0.15 b^ hml (2.55)

model 0.08 (0.65) 1.01 (37.28) 0.62 (15.99) 0.02 (0.50)

0.02 (0.24) 0.97 (46.47) 0.55 (18.53) 0.21 (6.54)

0.10 (1.24) 0.90 (49.37) 0.53 (20.39) 0.26 (9.35)

0.14 (1.70) 0.89 (48.97) 0.51 (19.77) 0.30 (10.81)

0.11 (1.40) 0.88 (51.11) 0.51 (20.65) 0.36 (13.49)

0.11 (1.34) 0.90 (48.46) 0.54 (20.47) 0.38 (13.38)

0.13 (1.37) 0.92 (43.11) 0.57 (18.53) 0.41 (12.62)

0.07 (0.58) 0.96 (37.60) 0.64 (17.51) 0.39 (10.07)

0.12 (0.73) 0.97 (27.17) 0.83 (16.20) 0.27 (4.88)

0.56 (2.09) 0.11 (3.21) 0.11 (2.16) 0.42 (7.82)

Panel C: Liu’s two-factor model a^ (%) 0.14 (0.59) 1.26 b^ m (19.56) 0.19 b^ liq (2.36)

0.30 (1.65) 1.14 (23.72) 0.07

0.18 (1.26) 1.12 (28.94) 0.12

0.21 (1.65) 1.07 (32.56) 0.20

0.20 (1.66) 1.08 (33.82) 0.25

0.14 (1.21) 1.09 (34.77) 0.32

0.11 (0.92) 1.13 (34.81) 0.37

0.12 (0.90) 1.19 (33.83) 0.43

0.07 (0.42) 1.28 (30.29) 0.48

0.02 (0.11) 1.42 (23.45) 0.54

0.17 (1.04) 0.16 (3.62) 0.73

(1.26)

(2.48)

(4.84)

(6.49)

(8.22)

(9.30)

(9.92)

(9.30)

(7.25)

(13.78)

Panel A: Raw returns Raw return (%) 1.11 (2.87)

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Table 6 Average monthly returns of liquidity-beta residuals sorted portfolios. We first obtain liquidity betas for each firm in year t by running Liu’s (2006) two-factor model, in Eq. (3), using 5-year monthly returns from July of year t-5 to June of year t. We obtain price delay measure (D1) and liquidity measure (LM12) by the end of June of year t. We then run a cross-sectional regression of liquidity betas on D1 and LM12, and obtain the residuals of liquidity betas for each firm by the end of June of year t, based on which, we sort firms by their liquidity-beta residuals into ten portfolios. Panel A reports the average raw return of each portfolio. Panels B and C, respectively, report the coefficient estimates of the time-series regressions of excess portfolio returns based on the Fama-French three-factor model and Liu’s two-factor model. While Portfolio 1 includes firms with the smallest liquidity-beta residuals, portfolio 10 consists of firms with the largest liquidity-beta residuals. The results for the hedge portfolio, with a long position in portfolio10 and short in portfolio 1, are reported in the last column. The t-values are in parentheses.

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which consists of firms with the largest liquidity-beta residuals, has an average monthly return of 1.49% (t¼ 4.33). The difference of 0.38% in the average return between the two extreme portfolios is significant, with a t-value of 1.98 (see Table 6, Panel A). (2) The return differences between the two extreme portfolios cannot be explained by Fama-French (1993) three-factor model. Liu’s (2006) two-factor model, on the other hand, is able to explain such risk premium (see Table 6, Panels B and C). (3) The liquidity betas from Liu’s LCAPM preserve the ranking order of the liquidity-beta residuals. They increase monotonically with the liquidity-beta residuals. These findings suggest that the return predictability of the liquidity beta shown in Table 5 is not just a manifestation of the mechanical relation between liquidity betas and price delay/liquidity measures since the part of liquidity beta uncorrelated to the price delay and liquidity measures is still capable of predicting future returns. To further illustrate the notion that more delayed firms face higher liquidity risk, Fig. 3 plots the monthly averages of LM119 of the NYSE/AMEX firms in the most delayed decile portfolio (portfolio 10), along with those in decile 5 portfolio (the middle group) and in the least delayed decile portfolio (portfolio 1) before, during, and after the recessions. According to National Bureau of Economic Research, there were five recessions during our sample period from 1973 to 2009.20 We choose the time periods surrounding the recessions because liquidity shocks are more visible in these periods. Clearly, the figure shows that the most delayed firms’ liquidity is much more volatile and sensitive to liquidity shocks than those of the firms in the other two portfolios. The increases in illiquidity of the most delayed firms during the recessions suggest that while it is normally difficult to trade the most delayed firms’ stocks, it becomes even more difficult for investors to trade their stocks during recessions. Since we include NASDAQ firms in our sample starting in 1983, Fig. 4 plots the monthly averages of LM1 of NASDAQ firms in the three portfolios—the most delayed, the middle group, and the least delayed—in the periods surrounding the two recessions from 1990:07 to 1991:03 and from 2001:03 to 2001:11. Similar to the figure for NYSE/ AMEX firms, it shows that more delayed NASDAQ firms face higher liquidity risk. To cover the higher liquidity risk, as shown in Table 5 and Fig. 2, investors demand a premium.

3.2. Risk-adjusted returns The results discussed above are largely based on the analysis at the portfolio level. For robustness checks, in this subsection we run firm-level Fama-MacBeth (1973) crosssectional regression analyses on individual firms’ risk-adjusted returns. Specifically, we examine whether price delay still has any effect on risk-adjusted returns from h i turnoverÞ 211  NoTD, According to Liu (2006), LM1 ¼ Number of zero daily volumes in one month þ 1=ðonemonth Deflator where Number of zero daily volumes in one month is the number of days with no trading in the month; one-month turnover is the sum of daily turnover over the month; daily turnover is the ratio of the number of shares traded on a day to the number of shares outstanding at the end of the day; Deflator is set at 480,000 such that turnover Þ 0o 1=ðone-month o1 for each stock (Liu, 2006); and NoTD is the number of trading days in the market over Deflator the month. 20 The beginning and the ending of the five recessions are as follows: 1973:11–1975:03, 1980:01–1980:07, 1981:07–1982:11, 1990:07–1991:03, and 2001:03–2001:11. 19

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Fig. 3. Liquidity dynamics of delayed NYSE/AMEX firms surrounding recessions. This figure plots the monthly averages of LM1 of the price delay-sorted (D1 sorted) portfolios for NYSE/AMEX firms from month 24 to 1 before a recession, during the recession (with the longest recession lasting 17 months), and after the recession from month þ1 to þ24 in our sample period of 1973–2009. For each firm, we obtain its second-stage price delay measure (D1) (Hou and Moskowitz, 2005) at the end of month immediately before each recession. We sort firms into ten decile portfolios. Portfolio 1 is the least delayed decile portfolio, while portfolio 10 is the most delayed decile portfolio. LM1 is the standardized turnover-adjusted number of zero daily trading volumes over one month, as defined in footnote 19.

Liu’s LCAPM, using the following model: ri,t ðriskadjusted Þ ¼ b0 þ b1 D1i,t þ xi,t ,

ð4Þ

where ri,t(riskadjusted) is firm i’s risk-adjusted return at month t, which is equal to ai plus ei,t from the regression in Eq. (3) estimated over the sample period.21 Since the riskadjusted return is:     ai þ ei,t ¼ Ri,t rf ,t ½bm,i Rm,t rf ,t þ bliq,i LIQt , ð5Þ the model in Eq. (4) allows us to see whether Hou and Moskowitz’s (2005) D1 has any effect on returns not explained by market risk or liquidity risk. In other words, we test D1’s explanatory power on excess returns at the individual firm level after controlling for the market and liquidity risks. If Liu’s (2006) two factors can explain the price delay premium, D1 should be insignificant. Table 7 reports the time-series average of the Fama-MacBeth regression coefficients. Indeed, the average coefficient of D1 is insignificantly different from zero, suggesting that it 21

Our procedure to obtain each individual firm’s risk-adjusted returns is similar to Avramov and Chordia (2006).

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Fig. 4. Liquidity dynamics of delayed NASDAQ firms surrounding recessions. This figure plots the monthly averages of LM1 of the price delay-sorted (D1 sorted) portfolios for NASDAQ firms from month 24 to -1 before a recession, during the recession (with the longest recession lasting 9 months), and after the recession from month þ1 to þ24 in our sample period of 1983–2009. For each NASDAQ firm, we obtain its second-stage price delay measure (D1) (Hou and Moskowitz, 2005) at the end of month immediately before each recession. We sort NASDAQ firms into ten decile portfolios. Portfolio 1 is the least delayed decile portfolio, while portfolio 10 is the most delayed decile portfolio. LM1 is the standardized turnover-adjusted number of zero daily trading volumes over one month, as defined in footnote 19.

has no effect on the risk-adjusted returns.22 The finding confirms our earlier inference (from the analyses at the portfolio level) that once we control for market risk and liquidity risk, there is no price delay premium. As Hou and Moskowitz (2005) argue that the delay premium is largely attributable to market frictions associated with investor recognition, we also test whether investor recognition has any explanatory power over the risk-adjusted returns. We re-run the Fama-MacBeth (1973) regressions in Eq. (4) using the four proxies—institutional ownership, analyst coverage, investor base, and the number of employees—and report the results in Table 7. Their time-series averages of the Fama-MacBeth regression coefficients are all insignificant. The results suggest that, after controlling for market risk and liquidity risk, there is no premium associated with lack of investor recognition. 4. Cross-sectional analysis of liquidity risk Our review of the price delay premium suggests that firms with greater price delay face higher liquidity risk, and that it is the higher liquidity risk that accounts for their 22

The result on D1 is essentially the same when we add firm size, B/M, price level, and past returns into the Fama-MacBeth (1973) regression in Eq. (4).

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Table 7 Fama-Macbeth (1973) cross-sectional regressions of the market and liquidity risk-adjusted returns on price delay and investor recognition variables. This table reports Fama-Macbeth (1973) estimates of monthly cross-sectional regressions of individual stock’s market and liquidity risk-adjusted returns (i.e., ai plus ei,t from the regression in Eq. (3) using the stock’s monthly returns during the sample period) on Hou and Moskowitz’s second-stage D1 and proxies for investor recognition, respectively. The proxies for investor recognition include number of employees (lnemployee), investor base (lninvestor), institutional ownership (lninslpct), and analyst coverage (lnanalyst) as defined in Tables 1 and 2. The time-series average of the coefficient estimates and their associated t-values (in parentheses) are reported. nnn, nn, n Significant at the 1%, 5%, and 10% level, respectively, for the t-tests.

Intercept D1 lnemployee lninvestor lninslpct lnanalyst

(1)

(2)

0.0008 (0.71) 0.005 (1.02)

0.003 (1.58)

Model (3) 0.003 (1.41)

(4)

(5)

0.0002 (0.10)

0.0005 (0.23)

0.0005 (0.77) 0.0005 (0.98) 0.005 (1.18) 0.0009 (1.29)

anomalous higher returns. We next explore what factors may affect firms’ liquidity risk. We hypothesize that more delayed firms have greater difficulty attracting traders to absorb shocks to market liquidity. Hence, the questions we are interested in are: do more delayed firms have higher liquidity risk simply because their stocks have lower liquidity? Or, are delayed firms subject to additional liquidity risk due to a lack of investor recognition? Addressing these questions may enhance our understanding of the extent to which liquidity risk is a channel through which investor recognition variables affect asset pricing. We conduct our analysis as follows. First, at the end of June of year t (for t going from 1980 to 2009), we obtain explanatory variables, including LM12, D1, institutional ownership, number of analysts, number of shareholders, number of employees, size, B/M, and past returns from July of year t1 to May of year t. Next, we obtain liquidity beta and market beta for each sample firm by running Liu’s (2006) two-factor model in Eq. (3) using five-year monthly returns from July of year t through June of year tþ5.23 Then, we run a Fama-Macbeth (1973) crosssectional regression of liquidity beta on the explanatory variables each year. We report the variables’ correlations in Table 8; and the time-series average of the cross-sectional regression coefficients for each explanatory variable in Table 9. As expected, liquidity beta is positively related to LM12, suggesting that firms with lower liquidity tend to attract fewer traders to absorb shocks to market liquidity and thus face higher liquidity risk. Our results also show that more delayed firms (in terms of higher D1), value stocks (in terms of higher B/M), and riskier firms (in terms of higher market beta) face higher liquidity risk. 23

To include a firm in the Fama-Macbeth (1973) cross-sectional regression analysis, we require that a firm must have at least 24 non-missing monthly return observations during the five-year period.

lnLM12 lnemployee lninvestor lninslpct lnanalyst lnsize lnbm Past_ return Market_beta

lnemployee

lninvestor

lninslpct

lnanalyst

lnsize

lnbm

Past_ return

Market_ beta

Liquidity_beta

0.572 (o0.0001)

0.452 (o0.0001) 0.415 (o0.0001)

0.344 (o0.0001) 0.378 (o0.0001) 0.635 (o0.0001)

0.510 (o0.0001) 0.561 (o0.0001) 0.511 (o0.0001) 0.247 (o0.0001)

0.574 (o0.0001) 0.638 (o0.0001) 0.659 (o0.0001) 0.528 (o0.0001) 0.691 (o0.0001)

0.637 (o0.0001) 0.671 (o0.0001) 0.676 (o0.0001) 0.550 (o0.0001) 0.722 (o0.0001) 0.808 (o0.0001)

0.108 (o0.0001) 0.255 (o0.0001) 0.055 (o0.0001) 0.052 (o0.0001) 0.111 (o0.0001) 0.120 (o0.0001) 0.330 (o0.0001)

0.103 (o0.0001) 0.012 (o0.0001) 0.009 (0.0012) 0.006 (0.0594) 0.011 (o0.0001) 0.009 (0.0009) 0.141 (o0.0001) 0.353 (o0.0001)

0.016 (o0.0001) 0.013 (0.0002) 0.016 (o0.0001) 0.034 (o0.0001) 0.043 (o0.0001) 0.043 (o0.0001) 0.102 (o0.0001) 0.047 (o0.0001) 0.019 (o0.0001)

0.116 (o0.0001) 0.223 (o0.0001) 0.034 (o0.0001) 0.014 (o0.0001) 0.194 (o0.0001) 0.162 (o0.0001) 0.229 (o0.0001) 0.197 (o0.0001) 0.079 (o0.0001) 0.667 (o0.0001)

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D1

lnLM12

170

Table 8 Correlation matrix. This table reports Pearson correlations for main variables used in Table 9. D1 is the second-stage price delay measure obtained by the end of each June. The variables, LM12, Employee, Investor, Instpct, Analyst, Size, and B/M are defined in Table 1. The variable, past_ return is the cumulative monthly returns from prior July to the end of each May. The market beta and liquidity beta are estimated by running Liu’s (2006) two-factor model in Eq. (3) using 5-year monthly returns over five years after D1 is obtained. lnLM12 ¼ lnð1 þ LM12Þ, lnemployee ¼ lnð1 þ EmployeeÞ, lninvestor ¼ lnð1 þ InvestorÞ, lninstpct ¼ lnð1 þ InstpctÞ,   lnanalyst ¼ lnð1 þ AnalystÞ, ln size ¼ lnðSizeÞ, and ln bm ¼ ln B=M . The p-values are given below the correlation estimates.

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Table 9 Fama-Macbeth (1973) cross-sectional regressions of liquidity beta. This table reports the average of cross-sectional regression coefficients for each explanatory variable. We conduct our analysis as follows. First, at the end of June of year t, we obtain for each sample firm the explanatory variables, including LM12, D1, number of employees, number of shareholders, institutional ownership, number of analysts, size, B/M, past returns from July of year t-1 to May of year t, and the exchdummy variable, an indicator variable equal to one if the sample stock is listed on the NASDAQ, and zero otherwise. Next, we obtain liquidity beta and market beta for each firm by running Liu’s (2006) two-factor model in Eq. (3) using 5-year monthly returns from July of year t through June of year tþ5. Then, we run a Fama-Macbeth (1973) cross-sectional regression of liquidity beta on the explanatory variables. nnn, nn, n Significant at the 1%, 5%, and 10% level, respectively.

(1) Intercept lnLM12 D1 lnemployee lninvestor lninslpct lnanalyst lnsize lnbm Past_returns Market_beta exchdummy Adjusted R2

1.235nnn (15.24) 0.146nnn (18.85) 0.242nn (2.48) 0.014 (0.75) 0.126nnn (6.89) 0.480nnn (4.67) 0.100nnn (6.84) 0.061nnn (4.28) 0.084nnn (5.36) 0.092nn (2.75) 0.886nnn (16.16) 0.100nnn (2.92) 0.544

Model (2) 0.795nnn (18.56) 0.137nnn (17.25) 0.001 (0.02) 0.076nnn (6.14)

(3) 0.810nnn (8.32)

0.799nnn (6.14) 0.003 (0.14) 0.124nnn (7.43)

0.746nnn (6.73)

0.080nnn (4.38) 0.053 (1.45) 0.876nnn (16.34) 0.147nnn (4.83) 0.534

0.056nnn (3.65) 0.090nnn (4.60) 0.038 (0.91) 0.873nnn (16.25) 0.115nnn (3.05) 0.518

In the presence of other variables, as shown in Model 1 in Table 9, we find that liquidity beta is significantly negatively related to institutional ownership and analyst coverage. Given that institutional investors are subject to the prudent-man rule, higher institutional ownership may certify higher firm quality for investments. Institutional investors are also generally regarded as better informed investors, and they tend to closely monitor firm performance. Thus, firms with higher institutional ownership can attract more traders to absorb shocks to market liquidity and face lower liquidity risk. Analyst coverage can also reduce liquidity risk because when more analysts produce information on a firm, their coverage makes the firm more transparent. This allows more traders to observe the investment value of the firm when shocks to market liquidity occur. Conversely, firms that are neglected by institutional investors and by analysts would tend to have lower investment quality and higher uncertainty. Consequently, they would have more difficulty in attracting traders to absorb shocks to market liquidity. The findings

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suggest that the effects of the investor recognition proxies on liquidity risk are beyond its association with liquidity.24 5. Conclusion Merton (1987) states that ‘‘Perhaps the most-controversial conclusion of our model is that less well-known stocksytend to have relatively larger expected returns’’ (page 507). Hou and Moskowitz (2005) show that investor recognition, as modeled by Merton, along with other market frictions, has a significant effect on the delay with which stock price responds to information. Consistent with Merton’s hypothesis, they find that firms with greater price delay earn significantly higher returns, which cannot be explained by the CAPM, the Fama-French three-factor model, or Carhart’s four-factor model. Nor can the delay premium be explained by conventional liquidity measures. Using a parsimonious and powerful asset pricing model developed by Liu (2006), we re-examine Hou and Moskowitz’s (2005) price delay premium. Specifically, we posit that when they encounter shocks to market liquidity, firms with more price delay tend to attract fewer traders to absorb the shocks, causing their shareholders to face higher liquidity risk. Accordingly, to hold relatively more delayed stocks, investors require higher returns to compensate them for the greater liquidity risk they face. Consistent with our hypothesis, we find that more delayed firms have a greater incidence of non-trading and higher liquidity risk. Controlling for market risk and Liu’s (2006) liquidity risk, there is no evidence of a price delay premium. Thus, our findings suggest that the price delay premium is due to systematic liquidity risk, not inadequate risk sharing. Our findings illustrate that Liu’s (2006) LCAPM is useful in explaining the cross- section of stock returns. Furthermore, our findings imply that it is the magnitude of liquidity risk investors face that is essential in explaining stock returns, not the speed of information dissemination. We also find that institutional ownership and analyst coverage are important determinants of liquidity risk, which confirms that liquidity risk is an important channel through which the investor recognition proxies affect asset pricing.

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Surprisingly, our results also show that, holding other things constant, liquidity risk is positively related to firm size. This unexpected result could be due to the fact that firm size is highly correlated with the number of analysts, institutional ownership, and LM12, as shown in Table 8, and that they mitigate the (excess) effects on liquidity risk of investor recognition (as reflected by analyst coverage and institutional ownership) and liquidity (as reflected by LM12). As shown in Model 3 of Table 9, liquidity risk becomes significantly negatively related to firm size when we remove analyst coverage, institutional ownership, and LM12 from the regression analysis.

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