Electronic copy available at: http://ssrn.com/abstract=2266039

THE VOLATILITY OF BID-ASK SPREADS

By

Benjamin M. Blaua and Ryan J. Whitbyb

Abstract:

This paper provides evidence that supports the original hypothesis of Chordia, Subrahmanyam, and Ashuman (2001) that greater variability in liquidity should lead to higher expected returns. While prior research has often found a negative relation between the volatility of liquidity and expected stock returns, we find that the volatility of the bid-ask spread is positively related to future returns. The average risk-adjusted return for stocks in the highest spread volatility quintile is around 1.7 percent per month, with returns from High-Low quintiles as high as 2.7 percent per month. Furthermore, the spread volatility premium is robust to a variety of multivariate tests that control for the market risk factor, SMB, HML, momentum, and illiquidity risk. Our findings provide support for the hypothesis that variability in liquidity affects expected returns and is an important component of illiquidity.

aBlau is an Associate Professor in the Department of Economics and Finance at Utah State University. 3565 Old Main Hill, Logan, Utah 84322. Phone: 435-797-2340. Email: ben.blau@usu.edu. bWhitby is an Assistant Professor in the Department of Economics and Finance at Utah State University. 3565 Old Main Hill, Logan, Utah 84322. Phone: 435-797-0643. Email: ryan.whitby@usu.edu.

Electronic copy available at: http://ssrn.com/abstract=2266039

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1. INTRODUCTION

A variety of research has focused on the relation between liquidity and asset returns. For

example, Amihud and Mendelson (1986) model expected returns as a function of bid-ask spreads

and show both theoretically and empirically that stocks with larger spreads outperform stocks

with smaller spreads. This relation, which is often characterized as an illiquidity premium, has

also been documented in Brennan and Subrahmanyam (1996), Datar, Naik, and Radcliffe (1998),

Liu (2006), and Han and Lesmond (2011). Given the presence of a large illiquidity premium,

Chordia, Subrahmanyam, Anshuman (2001) hypothesize that the second moment of liquidity

should also be positively related to asset returns. They assume that risk-averse agents dislike

variability in liquidity and therefore require higher expected returns. Contrary to their hypothesis

however, they document a significant negative relation between expected returns and the

variability of trading volume and share turnover, which they use as proxies for liquidity. In fact,

this finding is so surprising that Hasbrouck (2006) questions the use of turnover volatility as a

proxy for liquidity risk.

In this paper, we revisit the original hypothesis in Chordia, Subrahmanyam, and

Anshuman (2001) that stocks with greater liquidity volatility command a return premium.

Instead of examining the relation between expected returns and the variability of trading activity,

we examine the volatility of bid-ask spreads.1 Liquidity, or the ability of market participants to

trade, is a vital component of well-functioning markets, but has many dimensions. The quantity

or depth of the market; trading costs, which include commissions, spreads, and the market

impact of trades; and the speed of trade execution are all important facets of liquidity. Persuad

(2003) states that there is also broad belief among practitioners and regulators (i.e. traders,

1 Chordia, Subrahmanyam, and Anshuman (2001) state that they use dollar trading volume and share turnover because they did not have data on bid-ask spreads for a length of time sufficient to run asset pricing tests.

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investors, and central bankers) that the principal concern about liquidity in financial markets is

not the average level of liquidity, which has improved over time, but variability and uncertainty

of liquidity. In our tests, we attempt to hold average levels of liquidity constant and focus on the

relation between expected returns and the variability of liquidity. Specifically, we examine the

volatility of the bid-ask spread, which we denote as spread volatility for brevity. While prior

research has used the term liquidity risk to describe measures of both liquidity and the volatility

of liquidity (see Pastor and Stambaugh (2003), Acharya and Pedersen (2005), Johnson (2008),

and Sadka (2010)), for clarity, we do not denote spread volatility as liquidity risk, but instead we

try to refer to more specific empirical proxies whenever possible. Further, prior research that

tests the hypothesis in Chordia, Subrahmanyam, and Anshuman (2001) focuses on the variability

in volume, share turnover, and price impact. We return to Amihud and Mendelson’s (1986)

original proxy for liquidity, the bid-ask spread, and test for a return premium associated with

spread volatility.

Consistent with the hypothesis in Chordia, Subrahmanyam, and Anshuman (2001), we

find strong evidence that stocks with higher levels of spread volatility outperform stocks with

lower levels of spread volatility. The return premium associated with spread volatility is not

only statistically significant, but the premium is also economically meaningful. For instance,

stocks in the highest spread volatility quintile have next-month excess returns ranging from

1.34% to 1.89% during the entire sample. The outperformance of stocks in the highest spread

volatility quintile, relative to stocks in the lowest spread volatility quintile, ranges from 2.29% to

2.67%.

In additional tests, the spread volatility premium is robust to a variety of factors that have

been shown to explain the cross section of returns, such as the market risk factor, SMB, HML,

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the momentum factor, and the Pastor and Stambaugh (1986) illiquidity factor. This return

premium is robust to controls for different tick-size regimes (e.g. pre- and post-decimalization).

Further, the spread volatility premium is largest in stocks with the highest mean spreads, the

smallest market capitalization, and the highest idiosyncratic volatility. We also find that the

spread volatility premium is unrelated to the level of trading volume.

We also examine the relation between the spread volatility premium and the proxies for

the variability of liquidity used in Chordia, Subrahmanyam, and Anshuman (2001) and Pereira

and Zhang (2010) and find mixed results. While we find some evidence of a positive relation

between the volatility of trading activity and expected returns, this positive relation only exists in

the highest spread volatility quintiles. In fact, in the lowest spread volatility quintiles, we find

that stocks with the highest volatility of trading activity have significantly lower expected returns

than stocks with the least volatility of trading activity. However, across each quintile that is

sorted on the volatility of trading activity, we find a robust return premium associated with

spread volatility. Furthermore, we find that the spread volatility premium is generally

increasing across quintiles based on trading volume volatility and share turnover volatility.

Combined with our initial tests, these findings support the hypothesis in Chordia,

Subrahmanyam, and Anshuman (2001) and indicate that spread volatility is indeed an important

determinant of asset prices.

The remainder of this paper is organized as follows. Section 2 discusses the related

literature. Section 3 describes the data used in the analysis. In Section 4, we present our

empirical tests and results with some concluding remarks in Section 5.

2. RELATED LITERATURE

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Liquidity in financial markets has been widely explored in the academic literature. The

empirical research relating the liquidity of securities to stock returns tends to follow one of two

paths. The first path examines liquidity at the firm level. As mentioned above, Amihud and

Mendelson (1986) study the effect of the bid-ask spread on asset prices at the firm level and find

evidence of an illiquidity premium. Brennan and Subrahmanyam (1996) find a significant

relation between monthly stock returns and daily illiquidity measures. Datar, Naik, and

Radcliffe (1998) conclude that liquidity plays a significant role in explaining the cross-sectional

variation of expected stock returns.2 Avramov, Chordia, and Goyal (2006) document a relation

between short-run reversals in stocks and illiquidity while Liu (2006) develops a new measure of

liquidity that incorporates the impact of zero trading days and finds that liquidity is an important

source of priced risk. In an additional study that determines whether liquidity affects asset prices,

Sadka (2006) decomposes firm level liquidity into a variable and fixed component and finds that

the variable component of liquidity risk is priced within the context of momentum and post-

earnings announcement drift. Fang, Noe, and Tice (2009) examine the relation between stock

market liquidity and firm value and find that liquidity increases the information content of

market prices and of performance-sensitive managerial compensation, which drives the positive

relation between liquidity and firm value. Recently, Han and Lesmond (2011) examine the

relation between liquidity and idiosyncratic volatility. They find that any return premium

associated with idiosyncratic volatility can be partially explained by zero returns and bid-ask

spreads.

The second path of research that relates liquidity to stock returns examines the

commonality in liquidity or whether a marketwide liquidity factor is priced in stocks. Chordia,

2 Given the evidence of a large premium associated with illiquidity, Lynch and Tan (2011) examine the role of transaction costs in liquidity premia and find that incorporating the predictability of returns and wealth shocks can cause transactions costs to produce a very large premia.

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Roll, and Subrahmanyam (2000) examine the common determinants of liquidity. They find that

after controlling for well known individual liquidity determinants, such as volatility, volume, and

price, common influences such as spread and depth remain significant. Pastor and Stambaugh

(2003) further explore the pricing of marketwide liquidity. They find that expected stock returns

are related to aggregate changes in market liquidity and find a premium of 7.5 percent annually

after controlling for other known risk factors. Acharya and Pedersen (2005) develop a simple

model that incorporates liquidity risk both at the firm and market level and document that, in

equilibrium, firms with high average illiquidity also tend to have high commonality of liquidity

with the market. Kamara, Lou, and Sadka (2008) show that the cross-sectional variation of

liquidity commonality has increased through time, which has resulted in a decreased ability to

diversify liquidity risk and has made the market more susceptible to unanticipated events.

Karolyi, Lee, and van Dijk (2012) find that the commonality in liquidity is greater in countries

with high market volatility, a greater presence of international investors, and more correlated

trading activity.

While the two streams of research that motivate our tests examine the relation between

liquidity and asset prices, other studies have investigated the variation of liquidity more

generally. Johnson (2008), for example, carefully examines the variance of liquidity to reconcile

the empirical result that volume and liquidity have been unrelated historically. Volume and

liquidity remain unrelated in his model, but volume is positively related to the variance of

liquidity. He empirically confirms the relation between volume and the variance of liquidity in

both bond and stock markets, but does not, however, examine the relation between the variance

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of liquidity and returns.3 Comerton-Forde, Hendershott, Jones, Moulton, and Seasholes (2010)

also examine the variation of liquidity through time. They analyze the inventory of specialists on

the NYSE and find that spreads widen when specialists have large positions or lose money.

They also note that this effect is more prominent in high volatility stocks.

This paper is closer to research that examines liquidity at the firm level rather than

research that explores the commonality of liquidity. However, the commonality research

emphasizes the importance of including controls for common liquidity, which we include in our

empirical tests. However, this study is different from much of the research that tests for an

illiquidity premium because we focus our analysis on the variability of liquidity instead of

average levels of liquidity. Of the studies that have examined the variability of liquidity, this

paper is most closely related to Chordia, Subrahmanyam, and Ashuman (2001). They

hypothesize that the second moment of liquidity should be positively related to asset returns if

investors care about the risk associated with liquidity fluctuations. Surprisingly, they actually

find a negative relation between expected returns and the volatility of their proxies for liquidity –

trading volume and share turnover. They posit that this unexpected relation could result from a

clientele effect but also state that their preferred proxy for liquidity, the bid-ask spread, was not

available for a sufficient length of time to run asset pricing tests. Using the standard deviation of

bid-ask spreads, we revisit the hypothesis in Chordia, Subrahmanyam, and Ashuman (2001). We

are not, however, the first study to revisit this hypothesis. Pereira and Zhang (2010) develop a

model to help explain the negative relation found in Chordia, Subrahmanyam, and Anshuman

(2001). They argue that higher liquidity volatility provides more opportunity for investors to

time their trades, which would lead to a lower required illiquidity premium. Pereira and Zhang

3 While Johnson (2008) refers to the variance of liquidity as liquidity risk, we prefer the term spread volatility since the term liquidity risk has been defined a variety of ways in a number of papers (see Pastor and Stambaugh (2003), Acharya and Pedersen (2005), and Sadka (2010) as examples).

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(2010) use price impact from Amihud (2002) as their proxy for liquidity, as well as the

variability of trading volume and share turnover, and find additional evidence of a negative

relation between expected returns and the volatility of liquidity.4

3. DATA DESCRIPTION

In this section, we describe the data used throughout the analysis. To measure bid-ask spreads,

we follow Roll and Subrahmanyam (2010) and obtain daily closing bid-ask spreads for the

universe of stocks available at the Center for Research on Security Prices (CRSP).5 For each

stock-month observation, we estimate the mean and the standard deviation of closing spreads,

where spreads are calculated as the difference between the ask price and the bid price scaled by

the midpoint of the closing ask and bid prices. From CRSP, we also gather daily and monthly

returns, volume, market capitalization, and prices. Using CRSP daily returns, we estimate

idiosyncratic volatility or the standard deviation of daily residual returns, where residual returns

are daily errors from a standard market model. We also estimate monthly CAPM betas (Beta)

using daily stock returns, market returns, and risk-free rates. From Compustat, we obtain

quarterly book-to-market ratios. The final sample used throughout the analysis consists of 11,334

unique stocks and 1,057,741 stock-month observations from 1990 to 2011.

Table 1 reports statistics that describe the sample. Spread is the mean of daily spreads and

σ(spread) is the standard deviation of daily spreads during a particular month. Price is the

closing monthly price according to CRSP while Size is the market capitalization or the product of

the CRSP price and shares outstanding. Volume is the monthly trading volume according to

4 In an additional study that examine the general effect of liquidity risk on asset prices, Akbas, Armstrong, and Petkova (2011) decompose liquidity into systematic and idiosyncratic components and find that the volatility of idiosyncratic liquidity risk is priced. 5 Chung and Zhang (2013) show that the use of CRSP closing bid-ask spreads is a very close approximation to using high frequency data when calculating bid-ask spreads. Roll and Subrahmanyam (2010) also find that closing bid-ask spreads in CRSP properly approximate intraday bid-ask spreads.

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CRSP while IdioVolt is our measure of idiosyncratic volatility. Beta is our estimate of CAPM

betas using daily returns and B/M is the book-to-market ratio obtained from Compustat. We note

several important regulatory changes that are present during our sample time period. On June

24th, 1997, the New York Stock Exchange (NYSE) reduced the minimum price variation for

trading stocks from 1/8ths of dollars to 1/16ths of dollars. Again, on January 29th 2001, the

NYSE reduced the minimum tick size from 1/16ths of dollars to pennies. Shortly after, the

Nasdaq stock market also introduced decimalization or the trading and quoting of stocks on

decimals instead of fractions of dollars. Because these tick size reductions affected liquidity (see

Goldstein and Kavajecz (2000) and Bessembinder(2003)), our tests for a return premium

associated with spread volatility might need to control for these different tick size environments.

Therefore, Panel A of Table 1 reports the results for the entire sample time period while Panels B

through D present mean spreads and standard deviations of spreads during these three different

tick-size regimes.

Panel A of Table 1 shows that the mean spread for the average stock during the entire

time period is 0.0348 or 3.48 percent. The average stock has σ(spread) of 0.0134 or 1.34

percent. We also report the summary statistics for other variables in Panel A. For instance, the

average stock has a price of $16.44, a market cap of $1.35 billion, monthly volume of 89,000,

and idiosyncratic volatility of 3.89 percent, and a book-to-market ratio of 0.3609.

In Table 1, we also find that the mean spreads for the average stock were highest during

the 1/8th tick-size environment as the average stock had a mean spread of 0.0567. Panels C and

D show that the mean spread for the average stock decreased across time aS the mean spread was

0.0381 during the 1/16th environment and 0.0191 during decimalization. While mean spreads

have appeared to decrease across time, the standard deviation of spreads have not. In particular,

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we find that the σ(spread) increased during the 1/16th environment from 0.0144 to 0.0156 and

then decreased during decimalization to 0.0115. Figure 1 provides a graphical representation of

the both mean spreads and spread volatility across each year of our sample time period. The

figure shows that mean spreads are generally decreasing across time although not monotonically.

For instance, mean spreads in 1992 were higher than in 1991 and spreads during the recent

financial crisis were twice as large as spreads during the years preceding the crisis. Spread

volatility, on the other hand, remained relatively constant from 1990 to 2002 and then

subsequently decreased until the 2008 financial crisis.

4. EMPIRICAL RESULTS

4.1 Determinants of Spread Volatility

We begin by examining factors that influence both mean spreads and spread volatility by

estimating the following equation using pooled stock-month observations in Table 2.

Spreadi,t or σ(spreadi,t) = β0 + β1Pricei,t + β2ln(sizei,t) + β3B/Mi,t + β4ln(volumei,t) + β5Betai,t +

β6Idiovolti,t + εi,t (1)

The dependent variable is either the average daily closing spread for each stock i during month t

(Spreadi,t) or the standard deviation of the daily closing spreads for each stock i during month t

(σ(spreadi,t)). The independent variables include the following: Price is the CRSP closing price

at the end of each month; ln(sizei,t) is the natural log of market capitalization using shares

outstanding and closing prices at the end of each month; ln(volumei,t) is the natural log of

monthly volume obtained from the CRSP; Beta is obtained from estimating a Capital Asset

Pricing Model using daily returns, risk-free rates, and market returns; Idiovolt is our measure of

idiosyncratic volatility; B/M is the book-to-market ratio. We present our results with and without

controls for year fixed effects. For instance, columns [1] and [2] respectively report the results

without and with controls for the year fixed effects when the dependent variable is defined as

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Spreadi,t while columns [3] and [4] present the regression estimates without and with controls

for year fixed effects when the dependent variable is defined as σ(spreadi,t). In each of the

columns, p-values are reported in parentheses and are obtained from standard errors that account

for two-dimensional clustering.

Results in Table 2 are qualitatively similar whether or not we control for year fixed

effects. Therefore, for brevity we will only discuss our findings in columns [1] and [3]. Column

[1] shows that mean spreads are inversely related to price, and directly related to market

capitalization. In addition, mean spreads are directly related to B/M ratios and idiosyncratic

volatility and inversely related to volume and beta. Similar results have been found generally in

the literature (see McInish and Wood (1992)).

Column [3] reports the results when spread volatility is defined as the dependent variable.

We also show that spread volatility is inversely related to price as the coefficient for β1 is -0.0016

(p-value = 0.000). Spread volatility is also positively related to market capitalization (estimate =

0.0653, p-value = 0.000) and B/M ratios (estimate = 0.0036, p-value = 0.013). We also find that

spread volatility is inversely related to volume and beta (estimates = -0.2706, -0.1229; p-values =

0.000, 0.000) and directly related to idiosyncratic volatility (estimate = 0.4290, p-value = 0.000).

The results in Table 2 show that spread volatility is related to several stock characteristics that

might also influence future stock returns. Therefore, we recognize the need to control for these

variables in our tests for a return premium associated with spread volatility.

4.2 The Relation between Spread Volatility and Future Returns: A Fama-MacBeth Approach

In this subsection, we begin testing for the presence of a return premium associated with

spread volatility by estimating the following equation using pooled stock-month observations.

Reti,t+1 = β0 + β1σ(spreadi,t) + β2Pricei,t + β3ln(sizei,t) + β4B/Mi,t + β5Reti,t + β6Reti,t-1 +

β7Reti,t-2 + β8Reti,t-3 + β9Betai,t + β10Idiovolti,t + β10ln(volumei,t) + β11Spreadi,t + εi,t+1 (2)

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The dependent variable is abnormal returns, which is the difference between the CRSP raw

return for stock i during month t+1 and the value-weighted CRSP index return (Chordia,

Subrahmanyam, and Ashuman, 2001). The independent variables include the following:

σ(spreadi,t) is the standard deviation of the daily closing spreads for each stock i during month t;

Price is the CRSP closing price at the end of each month; ln(sizei,t) is the natural log of market

capitalization using shares outstanding and closing prices at the end of each month; B/M is the

book-to-market ratio gathered from CRSP and Compustat; Reti,t is the CRSP return for stock i

during month t; Reti,t-1 is the CRSP return for stock i during month t-1; Reti,t-2 is the CRSP return

for stock i during month t-2; Reti,t-3 is the CRSP return for stock i during month t-3; Beta is

obtained from estimating a Capital Asset Pricing Model using daily returns, risk-free rates, and

market returns; Idiovolt is our measure of idiosyncratic volatility; ln(volumei,t) is the natural log

of monthly volume obtained from CRSP; and Spreadi,t is the average daily closing spread for

each stock i during month t. We estimate equation (2) using an approach similar to Fama and

MacBeth (1973) and provide heteroskedasticity-consistent standard errors using a Newey-West

adjustment.

Table 3 reports the results from the Fama-MacBeth regressions. We include different

combinations of independent variables to show robustness for our results. In column [1], we find

that spread volatility produces a positive and significant estimate (estimate = 0.2751, p-value =

0.001), which is consistent with the idea of a return premium associated with the variability of

bid-ask spreads. In economic terms, a one percent increase in spread volatility results in a 27.5

basis point increase in next month’s returns. Column [2] shows the results when we include

Price, ln(Size), and B/M with spread volatility. Again, we find that the coefficient on spread

volatility is positive and significant (estimate = 0.2155, p-value = 0.001). We also find that the

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natural log of size produces a reliably negative estimate, which is consistent with findings in

Banz (1981) and Fama and French (1992). In column [3], we also find past monthly returns

produce positive and statistically significant estimates while the coefficient on contemporaneous

monthly returns is negative and significant. These results are consistent with the presence of

momentum (Jegadeesh and Titman, 1993) in past returns and monthly price reversals in

contemporaneous returns (Bali, Cakici, and Whitelaw, 2011). When including these variables,

we still find that spread volatility is directly related to next-month’s returns (estimate = 0.2908,

p-value = <.0001). Column [4] shows that results when we control for both systematic and

idiosyncratic risk. Again, we find that estimate for spread volatility is positive and significant

(estimate = 0.3447, p-value = <.0001). In column [5], we include all of the control variables up

to this point and again find a positive and significant estimate for spread volatility (estimate =

0.2871, p-value = <.0001).

In the remaining columns, we include controls for liquidity. For instance, column [6]

extends column [5] by including the natural log of volume as an approximation for liquidity. We

again find that spread volatility produces a significantly negative estimate (estimate = 0.2871, p-

value = <.0001). In our final two estimations, we include mean bid-ask spreads as an additional

control The purpose in doing so is to account for the possibility that spread volatility is only

capturing the well-known return premium associated with illiquidity. The results in columns [7]

and [8] are qualitatively similar. So, for brevity, we only discuss our findings in column [8]. As

expected, we find that the estimate for mean spreads is positive and significant (estimate =

0.1565, p-value = <.0001). This result is consistent with findings in Amihud and Mendelson

(1986) and suggests that illiquidity, in the form a higher bid-ask spreads, is directly related to

future returns. However, after controlling for mean spreads, we still find a positive estimate for

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spread volatility (estimate = 0.0942, p-value = 0.034). In economic terms, the estimate for

spread volatility, although noticeably weaker in column [8] than in other columns, suggests that a

one percent increase in spread volatility is associated with a 9.4 basis point increase in future

next-month returns. These findings also suggest that, in addition to a return premium associated

with higher bid-ask spreads, there is also a significant return premium associated with greater

variability in bid-ask spreads.

We note that our results are robust to a variety of other specifications where we include

different combinations of independent variables. We also recognize the possibility that our

results in column [8] suffer from multicollinearity bias because of heavy correlation between

mean spreads and spread volatility. We estimate equation (2) using pooled OLS and estimate

variance inflation factors and find that factors for both mean spreads and spread volatility are

below three suggesting that multicollinearity is not that big of an issue. However, for additional

robustness, we use a dummy variable approach. Instead of including the mean spreads as a

continuous variable, we include an indicator variable that captures stock-month observations in

the highest quintile based on mean spreads. When including this indicator variable, we still find

that spread volatility produces a positive and significant estimate (estimate = 0.2276, p-value =

0.001). We also include a specification where we control for liquidity by using share turnover

and Amihud’s illiquidity measure. Results from these unreported tests are qualitatively similar

to those reported in Table 3. Finally, in unreported results, we control for the possibility that

distressed firms are influencing our results. For instances, distressed firms might have the

highest variability in bid-ask spreads, which may affect the relation between spread volatility and

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future next-month returns. Using a standard Altman’s Z-score, we control for distress firms and

still find that spread volatility predicts positive next-month returns.6

4.3 The Spread Volatility Premium: A Cross-Sectional Analysis

Next, we examine next-month returns across quintiles sorted by spread volatility. In particular,

we sort the stock-month observations into quintiles based on σ(spread) during month t and then

report various measures of returns during month t+1. Table 4 reports the results from this

analysis. Column [1] shows the results for next-month CRSP raw returns. Column [2] reports

abnormal returns, which is the difference between CRSP raw returns and the value-weighted

CRSP index. In columns [3] through [5] we report the alphas (α) from variants of the following

equation.

Reti,t – Rft = α + β1(Rmt – Rft) + β2SMBt + β3HMLt + β4UMDt + β5LIQt + εi,t (3)

Equation (3) is a common five-factor model, where risk factors are the market risk premium

from the standard Capital Asset Pricing Model (CAPM), the Fama and French (1996) small-

minus-big (SMB) factor, the Fama and French (1996) high-minus-low factor, the Carhart (1997)

up-minus-down factor, and the Pastor and Stambaugh (2003) liquidity risk factor. After sorting

stocks into quintiles based on σ(spread) during the previous month, we estimate variants of

equation (3) and report the estimated α across each quintile. Column [3] shows the estimated α

for the Fama-French 3-Factor regressions (FF3F Alpha) while columns [4] and [5] report the

estimated α for the Carhart 4-Factor regressions (FF4F Alpha) and the Pastor-Stambaugh 5-

Factor regressions (FF5F Alpha), respectively.

Column [1] shows that next-month raw returns are monotonically increasing across

increasing spread volatility quintiles. In the quintile with the largest spread volatility, next-

6 We also control for the decimalization time period using an indicator variable approach and find results that are qualitatively similar to those reported in Table 3.

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month raw returns are 1.53 percent. The difference between extreme quintiles is 2.17 percent

and is statistically different from zero. Said differently, stocks in the largest spread volatility

quintile outperform stocks in the smallest spread volatility quintile by 2.17 percent per month.

Results in column [2] are qualitatively similar to those in column [1].

Column [3] reports the next-month FF3F Alpha across quintiles sorted by spread volatility.

Again, we find that these alphas are monotonically increasing across quintiles. After controlling

for the risk factors described in Fama and French (1996), we find that stocks in the highest

spread volatility quintile produce an alpha of 1.7 percent per month, which is both statistically

and economically significant. The difference in alphas between extreme quintiles is 2.44

percent, which is statistically different from zero (p-value = 0.000). We are able to make similar

inferences when examining FF4F Alphas in column [4]. However, we recognize the need to

control for the Pastor-Stambaugh liquidity risk factor since our measure of spread volatility

could just be a proxy for the market-wide liquidity factor. Column [5] reports the alphas from

the 5-factor model. In general, the results are similar to those in previous columns. Stocks in the

quintile with the highest spread volatility have statistically and economically significant next-

month 5-Factor alphas. Although the 5-Factor alphas are not monotonically increasing in

quintiles I and II, the results in Table 4 provide further evidence of a significant return premium

associated with spread volatility.

4.4 The Spread Volatility Return Premium and Different Tick-Size Environments

As a measure of robustness, we conduct the analysis in the previous table for different

time periods. As mentioned previously, the major stock exchanges reduced the minimum tick

size from fractions of dollars to pennies during the first part of 2001. Smaller tradable price

increments may have influenced the level of spread volatility and its associated return premium.

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Table 5 panel A replicates the analysis in Table 4 for the pre-decimalization time period (January

1990 to January 2001).7 Panel B of Table 5 reports the results for the post-decimalization time

period (February 2001 to December 2011). We are able to draw similar conclusions in each

column so, for brevity, we only discuss the finding in column [1].

Panel A shows that next-month raw returns are increasing monotonically across quintiles

and that stocks in the largest spread volatility quintile significantly outperform stocks in the

smallest spread volatility quintile, on average. In fact, stocks in the largest spread volatility

quintile have next-month raw returns of 3.59 percent, which supports the idea that investors are

compensated for the risk of holding stocks with high spread volatility.

Panel B reports various measures of next-month returns for the post-decimalization

period. Again, each column produces results that are similar, so we only discuss the findings in

column [1]. Similar to panel A, we find that next-month returns are increasing monotonically

across quintiles and that stocks in the largest spread volatility quintile have an average raw return

of 1.53 percent while stocks in the smallest volatility quintile have an average raw return of -.64

percent. The difference of 2.17 percent is statistically and economically significant. We note,

however, that stocks with high spread volatility had much higher returns during the pre-

decimalization period than during the post-decimalization period. The difference between

extreme quintiles is 1.29 percent smaller during the post-decimalization period than during the

pre-decimalization period. The difference-in-differences is statistically significant (p-value =

0.000) in column [1] and suggests that while the return premium associated with spread volatility

was much larger when stocks traded on fractions of dollars, the return premium still exists during

the most recent tick-size environment and remains economically meaningful.

7While the NYSE reduced the minimum tick size to pennies in January 2001, Nasdaq did not reduce the minimum tick size until April 2001. In unreported tests, we use months before April 2001 as the pre-decimalization period and find qualitatively similar results to those reported in this paper.

17

We are able to draw similar conclusions when focusing on columns [2] through [5], but

there are some differences that are noteworthy. First, column [5] of both panels A and B shows

that the next-month FF5F Alpha is not monotonically increasing across the first two spread

volatility quintiles. Second, the difference between extreme quintiles in column [5] is only .23

percent smaller during the post-decimalization period than during the pre-decimalization. This

difference-in-difference is not statistically significant (p-value = 0.326). While there are notable

differences between time periods, we are able to conclude that the risk premium associated with

spread volatility has decreased during the most recent tick-size environment. However, a return

premium still exists and is both statistically and economically significant.

4.5 Double Sorted Tests: The Illiquidity Premium and the Spread Volatility Premium

Next, we double sort the stock-month observations – first by spread volatility, then by mean

spread. The purpose in doing so is to try and determine whether the return premium associated

with spread volatility is driven by stocks that are the most illiquid. Table 6 reports the results of

the analysis. Stock-month observations are sorted into quintiles (horizontally) based on spread

volatility and then, within each spread volatility quintile, are sorted into quintiles based on mean

spreads. After performing these double sorts, we then report our various measures of next-month

returns. Panel A, for instance, presents the next-month raw returns across double-sorted

quintiles. Panels B through E present the results using next-month abnormal returns, next-month

FF3F alphas, next-month FF4F alphas, and next-month FF5F alphas, respectively.

In panel A row 1, we find that for the most liquid stocks (i.e. stocks with the smallest

mean spreads), next-month raw returns are still increasing monotonically across spread volatility

quintiles. The difference between extreme quintiles in row 1 is positive and significant

18

(difference = 1.31 percent, p-value = 0.000). Similar results are found in rows 2 through 4. Row

5 represents stocks that are the most illiquid. We again find that the next-month returns are

monotonically increasing across spread volatility quintiles and the difference between extreme

quintiles is positive and significant (difference = 3.42 percent, p-value = 0.000). In fact, a closer

look at column [6] reveals that the differences between extreme spread volatility quintiles is

generally increasing, although not monotonically, across mean spread quintiles. At least two

interpretations exist. First, the spread volatility premium is directly related to the illiquidity

premium. This is not unexpected, given it is the second moment of the distribution. However,

the fact that the spread volatility premium still exists in the lowest mean spread quintile is

evidence that spread volatility contains explanatory power above and beyond the mean spread.

Second, and perhaps more importantly, stocks that are the most illiquid and have the highest

spread volatility have extremely large next-month returns. For instance, the intersection of the

largest spread volatility quintile and the largest mean spread quintile yields mean next-month

returns that are 4.3 percent, on average. Furthermore, the difference-in-differences (column [6],

row 6) is positive and statistically significant.

We are able to draw similar conclusions in panels B through D. In Panel E, we examine

next-month FF5F alphas across double-sorted quintiles. A few of the results in panel E are

noteworthy. First, we find that, after controlling for multiple risk factors, including the liquidity

risk factor, next-month alphas are monotonically increasing across spread volatility quintiles in

row 1 (the quintile with the lowest mean spreads). In fact, next-month FF5F alphas are

increasing monotonically across spread volatility quintiles in each row except for row 5, which

represents the quintile with the largest mean spreads. These results suggest that when we control

for the Pastor-Stambaugh liquidity risk factor, the direct monotonic relation between spread

19

volatility and next-month alphas exists in most mean spread quintiles. However, we again find

that the intersection between the largest spread volatility quintile and the largest mean spread

quintile yields the largest next-month FF5F alpha.

4.6 Double Sorted Tests: The Spread Volatility Premium and Other Measures of Liquidity

Volatility

In this section, we examine the robustness of our results to other measures of liquidity volatility

reported in Chordia, Subrahmanyam, and Anshuman (2001) and Pereira and Zhang (2010). In

particular, we examine FF5F alphas across double sorted quintiles – first by spread volatility,

and second by other measures of liquidity volatility. Pereira and Zhang (2010) use three

measures of liquidity volatility, two of which are similar to those used in Chordia,

Subrahmanyam, and Anshuman (2001). The first measure is the standard deviation of volume,

which we denote as σ(volume). The second measure is the standard deviation of turnover, which

is denoted as σ(turn). It should be noted that turnover is the ratio of daily trade volume to shares

outstanding. The third and final measure is the standard deviation of the Amihud’s (2002)

illiquidity, which we term σ(illiq). Amihud’s illiquidity is the ratio of the absolute value of the

daily returns relative to the total trade volume. We take the standard deviation of the daily

values of volume, turnover, and illiquidity at the monthly level.

Table 7 reports the FF5F alphas across double-sorted quintiles. We note that our results

are robust to the other measures of future returns used in the previous table. However, for

brevity we only report the FF5F alpha results. Panel A of Table 7 shows in column [1] that

next-month alphas are decreasing across increasing std_vol quintiles. This result is similar to the

general results reported in Chordia, Subrahmanyam, and Anshuman (2001) and Pereira and

Zhang (2010) that show that returns are negatively related to the standard deviation of volume.

20

We find similar results in columns [2] and [3]. However, in column [4], we find that returns are

no longer decreasing across increasing σ(vol). In fact, the difference between extreme quintiles

(row 6) in column [4] is positive and marginally significant (difference = 0.0038, p-value =

0.073). We again find that the difference between extreme quintiles is positive and significant in

column [5].

As we look across rows, we find that next-month returns are generally increasing across

increasing spread volatility quintiles. In particular, we find that the positive relation between

next-month returns and spread volatility is monotonic in rows 3 through 5. In column [6], we

also show that the difference between extreme spread volatility quintiles is increasing

monotonically across σ(vol) quintiles. These results suggest that while prior research finds a

negative relation between the standard deviation of volume and future returns, we show that the

positive spread volatility premium is increasing in the level of σ(vol).

Panel B shows the results when the second sort is the standard deviation of share

turnover, which is also used as a measure of liquidity volatility in Pereira and Zhang (2010). The

results in panel B are similar to those in panel A. In particular, we find a negative relation

between next-month returns and std_turn in columns [1] through [3]. However, we again find a

return premium associated with spread volatility across each row. We do note that the

differences between extreme spread volatility quintiles (column [6]) are not increasing

monotonically, although the difference in differences is positive and significant in column [6]

row 6 (difference = 0.0142, p-value = 0.000).

In panel C, we do not find a robust relation between next-month returns and the standard

deviation of Amihud’s illiquidity measure. In fact, the relation is generally positive in column

[2], but unstable in other columns. However, we still find a positive and monotonic relation

21

between spread volatility and next-month returns in rows 1 through 3 and row 5. Further, we

find that the difference between extreme spread volatility quintiles is positive and significant in

each row. Another noteworthy result is the difference in differences is not statistically

significant. While we are able to conclude that the spread volatility return premium exists in

each σ(illiq) quintile, we do not find a relation between the magnitude of the premium and the

standard deviation of Amihud’s illiquidity measure.

4.7 Double Sorted Tests: The Spread Volatility Premium and Other Sorts

In our final set of tests, we examine the relation between the spread volatility premium and other

factors that might influence the premium. We first sort by spread volatility and then separately

sort by market capitalization, idiosyncratic volatility, and trading volume. Table 8 panel A

reports next-month FF5F alphas across double-sorted quintiles, first by spread volatility and

then by size.8 Prior research suggests that smaller stocks are generally less liquid (see McInish

and Wood (1992)) and have less market making capacity (Hong, Lim, and Stein (2000) and Roll

and Subrahmanyam (2010)).

The first row of Panel A shows that next-month FF5F alphas increase monotonically

across spread volatility quintiles. Row 1 represents the smallest stocks (in terms of market

capitalization). We show that in this row, the return premium associated with spread volatility is

extremely large. For instance, stocks in the largest spread volatility quintile have next-month

FF5F alphas that are nearly 5 percent. The difference between extreme spread volatility

quintiles in the smallest size quintile is positive and both statistically and economically

significant. We find that next-month FF5F alphas are also increasing monotonically across

8 As before, we replicate Table 8 using next-month raw returns, next-month abnormal returns, next-month FF3F alphas, and next-month FF4F alpha. The results from these unreported tests are qualitatively similar to those reported in this paper that use FF5F alphas. We report FF5F alphas since it is the most stringent model we consider and also controls for marketwide risk.

22

spread volatility quintiles in the second row. The difference between extreme quintiles in this

row is also positive and significant. In row three, we do not find that the next-month FF5F

alphas are monotonically increasing. Stocks in the largest spread volatility quintile in this row is

positive, but not statistically different from zero (alpha = 0.33 percent, p-value = 0.413). Even

though the alpha in the largest spread volatility quintile is not statistically different in row three,

the difference between extreme quintiles is still positive and significant (difference = 1.68

percent, p-value = 0.000). We find some evidence that next-month alphas are generally

increasing across spread volatility quintiles (although not monotonically) in rows four and five.

In fact, in the largest market capitalization quintile (row five), we do not find much of a relation

although the difference between extreme spread volatility quintiles is positive and significant

(difference = 0.0060, p-value = 0.096). The results in panel A suggest that the return premium

associated with spread volatility is strongest in small-cap stocks, which is expected. We find

some, albeit weak evidence that the spread volatility premium still exists in the quintile of stocks

with the largest market capitalization.

In panel B, we report next-month FF5F alphas across double-sorted quintiles, first by

spread volatility, then by idiosyncratic volatility. The purpose for conditioning the spread

volatility premium on idiosyncratic volatility is because spread volatility might, in some way

represent higher idiosyncratic volatility. Given the theoretical and empirical relation between

idiosyncratic volatility and future returns found in Merton (1987) and Ang, Hodrick, Xing, and

Zhang (2006, 2009) conditioning the spread volatility premium on higher idiosyncratic volatility

might be important. We find that next-month alphas are not monotonically increasing across

spread volatility quintiles in row one. We find that next-month alphas are 74 percent higher in

the largest spread volatility quintile than in the smallest spread volatility quintile. However, the

23

difference between extreme quintiles (in column [6]) is not statistically significant (difference =

0.28 percent, p-value = 0.204). We do find that next-month alphas increase monotonically

across idiosyncratic volatility quintiles in rows two through four. In row five, which represents

the quintile of stocks that have the highest idiosyncratic volatility, we find that next-month

alphas are not monotonically increasing in columns [1] and [2], but are generally increasing

otherwise. In fact, stocks in the largest spread volatility quintile significantly outperform stocks

in the smallest spread volatility quintile by a larger amount than any other row in panel B. The

results in panel B suggest that there is direct relation between the spread volatility premium and

idiosyncratic volatility. This is consistent with Han and Lesmond (2011), which find that much

of the pricing ability attributed to idiosyncratic volatility can be explained by zero returns and

bid-ask spreads. We also note, however, that a weak premium still exists in the quintile with the

lowest idiosyncratic volatility.

In panel C, we show next-month FF5F alphas across double-sorted quintiles, first by

spread volatility and then by monthly trading volume. The purpose in sorting spread volatility

quintiles into additional quintiles based on volume is driven by the empirical relation between

the distribution of liquidity and trading volume discussed in Roll and Subrahmanyam (2010).

Stocks with higher trading volume are generally thought to have higher market making capacity,

which might lead to a more stable liquidity provision. In each row of panel C, we find that next-

month alphas are generally increasing across spread volatility quintiles. In column [5], we find

that next-month alphas are significantly large in each row suggesting that volume is unrelated to

the presence of a spread volatility return premium. Further, the difference between extreme

quintiles (column [6]) is positive and significant in each row and does not appear to be increasing

24

or decreasing across rows. These results again suggest that the spread volatility premium is

unrelated to level of trading volume.

We note that the results reported in Table 8 are not only robust to the other measures of

next-month returns that we have used earlier in the analysis, but the results are also robust to

sorting first by size (or volatility or volume) and then by spread volatility. These unreported

tests show that the return premium associated with spread volatility is stronger in smaller cap

stocks and stocks with higher idiosyncratic volatility and is unrelated to the level of trading

volume.

5. CONCLUSION

While the importance of liquidity in markets is undisputed, the relative importance of the

different dimensions of liquidity is not as clear. In this paper, we examine, what we denote as

spread volatility. We define spread volatility as the standard deviation of the bid-ask spread and

find that it is associated with a large premium in expected stock returns. In general, we find that

the return premium associated with spread volatility is statistically significant and economically

meaningful. In particular, we examine the relation between expected returns and spread

volatility by estimating Fama MacBeth regressions and find that spread volatility has explanatory

power for future returns after controlling for mean bid-ask spreads as well as several other

factors that might influence future returns. We then examine the alphas associated with stocks

sorted by spread volatility and find a clear relation between alphas and the level of spread

volatility in stocks.

The significant return premium is robust to different tick-size regimes. We also show

that, while the spread volatility premium is highest in stocks with the largest mean bid-ask

spreads, the premium still exists in the stocks with the lowest mean bid-ask spreads. Additional

25

robustness tests reveal that the spread volatility return premium robust to other measures of

liquidity volatility and is related to idiosyncratic volatility and size, but unrelated to volume.

However, after controlling for these other variables, the spread volatility return premium still

persists.

26

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29

Table 1 Summary Statistics The table reports a summary of statistics of the variables used throughout the analysis during the entire time period. Spread is the average daily closing spread taken at the monthly level. σ(spread) is the spread volatility or the standard deviation of the daily closing spreads taken at the monthly level. Price is the CRSP closing price at the end of each month while Size if the market capitalization using shares outstanding and closing prices at the end of each month. Volume is the monthly volume obtained from the CRSP. Beta is obtained from estimating a Capital Asset Pricing Model using daily returns, risk-free rates, and market returns. Idiovolt is a measure of idiosyncratic volatility and is obtained by taking the standard deviation of the daily residual returns from the daily CAPM estimation. B/M is the book-to-market ratio gathered from CRSP. Panel A reports the summary statistics during the entire time period (1990 to 2011). Panel B reports the summary statistics during the 1/8th tick-size environment that existed from Jan 1990 to June 1997. Panel C presents the summary statistics during the 1/16th environment, which is from July 1997 to January 2001. Panel D reports the statistics during the period of decimalization, which existed from February 2001 to December 2011. P-values are reported below each correlation coefficient.

Panel A. Entire Time Period

Mean Median Std. Deviation Min Max

[1] [2] [3] [4] [5]

Spread

σ(spread)

Price

Size

Volume

IdioVolt

Beta

B/M

0.0348 0.0134

16.44

1,345,547,365 89,002.95

0.0389 0.7462 0.3609

0.0208 0.0090

12.56

157,087,538 17,543.59

0.0336 0.7190 0.0658

0.0476 0.0144

18.65

7,692,313,931 354,423.63

0.0246 0.6496 5.0380

0.0002 0.0001

0.03

127,444 0.00

0.0030 2.2687 -0.5337

0.9545 0.1775

749.57

340,486,006,813 17,023,115.44

0.6213 9.2430

412.1772

Panel B. 1/8th Environment (Jan 1990 – June 1997)

Spread

σ(spread)

0.0567 0.0144

0.0404 0.0103

0.0585 0.0134

0.0027 0.0008

0.9545 0.1701

Panel C. 1/16th Environment (July1997 – Jan 2001)

Spread

σ(spread)

0.0381 0.0156

0.0267 0.0111

0.0437 0.0152

0.0004 0.0003

0.8421 0.2894

Panel D. 0.01 Environment (Feb 2001 – Dec 2011)

Spread

σ(spread)

0.0191 0.0115

0.0080 0.0055

0.0295 0.0156

0.0006 0.0001

0.4017 0.2655

30

Table 2 Panel Regression Results The table reports the results from estimating the following equation using pooled stock-month observations. Spreadi,t or σ(spreadi,t) = β0 + β1Pricei,t + β2ln(sizei,t) + β3B/Mi,t + β4ln(volumei,t) + β5Betai,t + β6Idiovolti,t + εi,t

The dependent variable is either the average daily closing spread for each stock i during month t (Spreadi,t) or the standard deviation of the daily closing spreads for each stock i during month t (σ(spreadi,t)). The independent variables include the following: Price is the CRSP closing price at the end of each month; ln(sizei,t) is the market capitalization using shares outstanding and closing prices at the end of each month; ln(volumei,t) is the natural log of monthly volume obtained from the CRSP; Beta is obtained from estimating a Capital Asset Pricing Model using daily returns, risk-free rates, and market returns; Idiovolt is a measure of idiosyncratic volatility and is obtained by taking the standard deviation of the daily residual returns from the daily CAPM estimation; B/M is the book-to-market ratio gathered from CRSP. Columns [1] and [2] report the results without and with controls for the year fixed effects when the dependent variable is defined as Spreadi,t while columns [3] and [4] present the regression estimates without and with controls for year fixed effects when the dependent variable is defined as σ(spreadi,t). In each of the columns, p-values are reported in parentheses and are obtained from standard errors that account for two-dimensional clustering. *,**,*** represent statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Spreadi,t σ(spreadi,t)

[1] [2] [3] [4]

Intercept

Pricei,t

ln(sizei,t)

B/Mi,t

ln(volumei,t)

Betai,t

IdioVolti,t

Adj R2 Year Fixed Effects Clustering

0.0112* (0.083)

-0.0049*** (<.0001)

0.4374*** (<.0001) 0.0122** (0.023)

-1.0861*** (<.0001)

-0.3092*** (<.0001)

1.2145*** (<.0001)

0.6066

No Yes

0.0093 (0.194)

-0.0059*** (<.0001)

0.4862*** (<.0001) 0.0141** (0.016)

-0.9850*** (<.0001)

-0.3594*** (<.0001)

1.2327*** (<.0001)

0.6544

Yes Yes

0.0114*** (<.0001)

-0.0016*** (<.0001)

0.0653*** (<.0001) 0.0036** (0.013)

-0.2706*** (<.0001)

-0.1229*** (<.0001)

0.4290*** (<.0001)

0.6489

No Yes

0.0108*** (<.0001)

-0.0015*** (<.0001)

0.0718*** (<.0001) 0.0035** (0.013)

-0.2912*** (<.0001)

-0.1224*** (<.0001)

0.4334*** (<.0001)

0.6563

Yes Yes

31

Table 3 Fama MacBeth Regressions The table reports the results from estimating the following equation using Fama-MacBeth (1973) regressions.

Reti,t+1 = β0 + β1Spreadi,t + β2σ(spreadi,t) + β3Betai,t + β4ln(sizei,t) + β5B/Mi,t + β6Reti,t-1 + β7Reti,t-2 + β8Reti,t-3 β9Idiovolti,t + β10ln(volumei,t) + β11Pricei,t + εi,t+1

The dependent variable is CRSP raw return for stock i during month t+1. The independent variables include the following: Spreadi,t is the average daily closing spread for each stock i during month t; σ(spreadi,t) is the standard deviation of the daily closing spreads for each stock i during month t; Beta is obtained from estimating a Capital Asset Pricing Model using daily returns, risk-free rates, and market returns; ln(sizei,t) is the market capitalization using shares outstanding and closing prices at the end of each month; B/M is the book-to-market ratio gathered from CRSP; Reti,t-1 is the CRSP return for stock i during month t-1; Reti,t-2

is the CRSP return for stock i during month t-2; Reti,t-3 is the CRSP return for stock i during month t-3; Idiovolt is a measure of idiosyncratic volatility and is obtained by taking the standard deviation of the daily residual returns from the daily CAPM estimation; ln(volumei,t) is the natural log of monthly volume obtained from the CRSP; Price is the CRSP closing price at the end of each month. P-values are reported in parentheses below each estimate. *,**,*** represent statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

[1] [2] [3] [4] [5] [6] [7] [8]

Intercept

σ(spread)i,t

Pricei,t

ln(sizei,t)

B/Mi,t

Reti,t

Reti,t-1

Reti,t-2

Reti,t-3

Betai,t

IdioVolti,t

ln(volumei,t)

Spreadi,t

0.1983 (0.588)

0.2751*** (0.000)

3.2709*** (0.002)

0.2155*** (0.000) 0.0070 (0.101)

-0.1639*** (0.002) -0.0367 (0.245)

-0.2703 (0.334)

0.2908*** (<.0001)

-0.0206*** (0.002)

0.2179*** (0.000)

0.0714*** (0.000) 0.0063* (0.081)

0.2535 (0.397)

0.3447*** (<.0001)

0.0582 (0.582) -0.0663 (0.247)

2.1171*** (0.009)

0.2384*** (<.0001) 0.0064** (0.031)

-0.1212*** (0.002) -0.0156 (0.661)

-0.0248*** (<.0001)

0.2180*** (<.0001)

0.0723*** (<.0001) 0.0071** (0.017) 0.0459 (0.548) -0.0558 (0.147)

4.9136*** (<.0001)

0.2871*** (<.0001)

0.0133*** (<.0001)

-0.4085*** (<.0001) -0.0126 (0.717)

-0.0241** (<.0001)

0.2180*** (<.0001)

0.0729*** (<.0001)

0.0083*** (0.003) 0.0050 (0.942)

-0.1162*** (<.0001)

0.2962*** (<.0001)

1.5799* (0.059)

0.0905** (0.047)

0.0057** (0.045)

-0.0941** (0.018) -0.0093 (0.789)

-0.0244*** (<.0001)

0.2180*** (<.0001)

0.0725*** (<.0001)

0.0072*** (<.0001) 0.0488 (0.513)

-0.0759* (0.067)

0.1091*** (0.000)

4.5134*** (<.0001) 0.0942 (0.034)

0.0136*** (<.0001)

-0.4182*** (<.0001) -0.0170 (0.671)

-0.0229*** (<.0001)

0.2181*** (<.0001)

0.0732*** (<.0001)

0.0084*** (0.003) 0.0094 (0.891)

-0.1711*** (<.0001)

0.3596*** (<.0001)

0.1565*** (<.0001)

32

Table 4 Next-Month Returns Across Liquidity Quintiles The table reports various measures of next-month returns across quintiles sorted by spread volatility at the end of each month. Column [1] contains next-month CRSP Raw Returns while column [2] reports next-month Abnormal

Returns across quintiles, which are calculated as the difference between Raw Returns and value-weighted market returns. Column [3] reports the alpha obtained from estimating a Fama-French 3-Factor model in each quintile. Column [4] presents the alpha obtained from estimating a Fama-French-Carhart 4-Factor model in each quintile. Column [5] presents the alpha obtained from estimating a Fama-French-Carhart-Pastor-Stambaugh 5-Factor model in each quintile. P-values are reported in parentheses. *,**,*** represent statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Raw Returns Abnormal

Returns

FF3F Alpha FF4F Alpha FF5F Alpha

[1] [2] [3] [4] [5]

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0029

-0.0000

0.0046

0.0086

0.0210

0.0239*** (<.0001)

-0.0095

-0.0078

-0.0026

0.0013

0.0134

0.0229*** (<.0001)

-0.0074

-0.0047

0.0011

0.0061

0.0170

0.0244*** (<.0001)

-0.0071

-0.0041

0.0016

0.0076

0.0177

0.0248*** (<.0001)

-0.0079

-0.0093

0.0012

0.0039

0.0188

0.0267*** (<.0001)

33

Table 5 Next-Month Returns Across Liquidity Quintiles – Pre- and Post-Decimalization Periods The table reports various measures of next-month returns across quintiles sorted by spread volatilities during the pre-decimalization period (panel A) and the post-decimalization period (panel B). Column [1] contains next-month CRSP Raw Returns while column [2] reports next-month Abnormal Returns across quintiles, which are calculated as the difference between Raw Returns and value-weighted market returns. Column [3] reports the alpha obtained from estimating a Fama-French 3-Factor model in each quintile. Similarly column [4] presents the alpha obtained from estimating a Fama-French-Carhart 4-Factor model in each quintile. Column [5] presents the alpha obtained from estimating a Fama-French-Carhart-Pastor-Stambaugh 5-Factor model in each quintile. Panel A reports the results when sorting by mean spreads while panel B presents the results when sorting by spread volatilities. P-values are reported in parentheses. *,**,*** represent statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Panel A. Sort by σ(spread) – Pre-Decimalization

Raw Returns Abnormal

Returns

FF3F Alpha FF4F Alpha FF5F Alpha

[1] [2] [3] [4] [5]

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

0.0013

0.0058

0.0098

0.0129

0.0359

0.0346*** (<.0001)

-0.0085

-0.0042

0.0008

0.0034

0.0272

0.0357*** (<.0001)

-0.0017

0.0019

0.0108

0.0136

0.0353

0.0370*** (<.0001)

-0.0005

0.0038

0.0145

0.0173

0.0493

0.0498** (<.0001)

-0.0008

-0.0014

0.0091

0.0111

0.0297

0.0305*** (<.0001)

Panel B. Sort by σ(spread) – Post-Decimalization

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0064

-0.0041

0.0009

0.0074

0.0153

0.0217*** (<.0001)

-0.0074

-0.0065

-0.0013

0.0046

0.0113

0.0187** (<.0001)

-0.0056

-0.0038

0.0002

0.0062

0.0119

0.0175*** (<.0001)

-0.0052

-0.0038

0.0001

0.0064

0.0116

0.0168*** (<.0001)

-0.0127

-0.0177

-0.0083

0.0017

0.0155

0.0282*** (<.0001)

Diff in panels -0.0129 (<.0001) -0.0170 (<.0001) -0.0195 (<.0001) -0.0330 (<.0001) -0.0023 (0.326)

34

Table 6 Next-Month Returns Across Two-Way Liquidity Sorts The table reports various measures of next-month returns across double-sorted quintiles. Stock-month observation are sorted (horizontally across columns) by spread volatilities and then (vertically across rows) by mean spreads. Panel A contains next-month CRSP Raw Returns while panel B reports next-month Abnormal Returns across quintiles, which are calculated as the difference between Raw Returns and value-weighted market returns. Panel C reports the alpha obtained from estimating a Fama-French 3-Factor model for the observations in each double-sorted quintiles. Panel D presents the alpha obtained from estimating a Fama-French-Carhart 4-Factor model for the observations in each double-sorted quintile. Panel E presents the alpha obtained from estimating a Fama-French-Carhart-Pastor-Stambaugh 5-Factor model in each quintile. P-values are reported in parentheses. *,**,*** represent statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Panel A. First sort by σ(spread), Second Sort by Mean Spread - Raw Returns

Q I

(Low)

Q II

Q III

Q IV

Q V

(High)

Q V – Q I

[1] [2] [3] [4] [5] [6]

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0051

-0.0053

-0.0043

-0.0008

0.0088

0.0139*** (<.0001)

0.0005

0.0006

0.0051

0.0045

0.0069

0.0064*** (0.002)

0.0034

0.0049

0.0065

0.0091

0.0128

0.0094*** (<.0001)

0.0054

0.0083

0.0096

0.0099

0.0145

0.0091*** (<.0001)

0.0080

0.0154

0.0193

0.0213

0.0430

0.0350*** (<.0001)

0.0131*** (<.0001)

0.0207*** (<.0001)

0.0236*** (<.0001)

0.0221*** (<.0001)

0.0342*** (<.0001)

0.0211*** (<.0001)

Panel B. First sort by σ(spread), Second Sort by Mean Spread – Abnormal Return

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0099

-0.0113

-0.0091

-0.0055

0.0014

0.0113*** (<.0001)

-0.0061

-0.0063

-0.0019

-0.0026

-0.0010

0.0051** (0.015)

-0.0042

-0.0018

0.0001

0.0020

0.0053

0.0095*** (<.0001)

-0.0017

0.0011

0.0019

0.0023

0.0071

0.0088*** (<.0001)

0.0003

0.0085

0.0119

0.0139

0.0364

0.0360*** (<.0001)

0.0102*** (0.001)

0.0198*** (<.0001)

0.0210*** (<.0001)

0.0194*** (<.0001)

0.0350*** (<.0001)

0.0248*** (<.0001)

35

Panel C. First sort by σ(spread), Second Sort by Mean Spread – FF3F alpha

Q I

(Low)

Q II

Q III

Q IV

Q V

(High)

Q V – Q I

[1] [2] [3] [4] [5] [6]

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0098

-0.0095

-0.0069

-0.0044

0.0033

0.0131*** (<.0001)

-0.0037

-0.0034

0.0007

0.0003

0.0015

0.0052*** (<.0001)

-0.0002

0.0015

0.0026

0.0050

0.0072

0.0074*** (<.0001)

0.0020

0.0054

0.0070

0.0083

0.0098

0.0078*** (<.0001)

0.0035

0.0131

0.0137

0.0176

0.0403

0.0368*** (<.0001)

0.0133*** (<.0001)

0.0226*** (<.0001)

0.0206*** (<.0001)

0.0220*** (<.0001)

0.0370*** (<.0001)

0.0237*** (<.0001)

Panel D. First sort by σ(spread), Second Sort by Mean Spread – FF4F alpha

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0105

-0.0091

-0.0070

-0.0042

0.0041

0.0146*** (<.0001)

-0.0034

-0.0036

0.0007

0.0018

0.0026

0.0060*** (<.0001)

0.0005

0.0033

0.0025

0.0058

0.0092

0.0087*** (<.0001)

0.0024

0.0087

0.0102

0.0114

0.0127

0.0103*** (<.0001)

0.0050

0.0159

0.0190

0.0177

0.0436

0.0386*** (<.0001)

0.0155*** (<.0001)

0.0250*** (<.0001)

0.0260*** (<.0001)

0.0219*** (<.0001)

0.0395*** (<.0001)

0.0240*** (<.0001)

Panel E. First sort by σ(spread), Second Sort by Mean Spread – FF5F alpha

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0086

-0.0069

-0.0037

-0.0034

0.0026

0.0112*** (<.0001)

-0.0068

-0.0054

-0.0024

-0.0008

0.0031

0.0099*** (<.0001)

-0.0030

0.0004

-0.0018

0.0059

0.0049

0.0079*** (<.0001)

0.0035

0.0060

0.0076

0.0129

0.0105

0.0070*** (0.008)

0.0058

0.0169

0.0060

0.0147

0.0372

0.0314*** (<.0001)

0.0144*** (<.0001)

0.0238*** (<.0001)

0.0097*** (0.003)

0.0181*** (<.0001)

0.0346*** (<.0001)

0.0202*** (<.0001)

36

Table 7 Next-Month Returns Across Two-Way Sorts The table reports the next-month Fama-French-Carhart-Pastor-Stambaugh 5-Factor alphas across double-sorted quintiles. In panel A, stock-month observation are sorted (horizontally across columns) by spread volatility and then (vertically across rows) by the standard deviation of other liquidity measures. In panel A, the second sort is by the standard deviation of volume (std_vol). In panel B, the second sort standard deviation of share turnover (std_turn). Turnover is the ratio of trading volume to shares outstanding. In panel C, the second sort is the standard deviation of Amihud’s (2002) daily illiquidity measure (std_illiq). Amihud’s illiquidity measure is the ratio of the absolute value of daily returns to the total trade volume. P-values are reported in parentheses. *,**,*** represent statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Panel A. First sort by σ(spread), Second Sort by std_vol – FF5F alpha

Q I

(Low)

Q II

Q III

Q IV

Q V

(High)

Q V – Q I

[1] [2] [3] [4] [5] [6]

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

0.0015

-0.0004

-0.0008

-0.0079

-0.0077

-0.0092*** (0.002)

0.0028

0.0010

-0.0001

-0.0035

-0.0011

-0.0039* (0.090)

0.0033

0.0090

0.0016

0.0019

-0.0030

-0.0063*** (0.002)

0.0018

0.0057

0.0053

0.0032

0.0056

0.0038* (0.073)

0.0140

0.0136

0.0180

0.0135

0.0215

0.0075*** (0.007)

0.0125*** (<.0001) 0.0132** (<.0001)

0.0188*** (<.0001)

0.0214*** (<.0001)

0.0292*** (<.0001)

0.0167*** (<.0001)

Panel B. First sort by σ(spread), Second Sort by std_turn – FF5F alpha

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0013

0.0016

0.0015

0.0009

-0.0071

-0.0058*** (0.003)

0.0036

-0.0015

0.0010

-0.0020

-0.0043

-0.0079*** (<.0001)

0.0058

0.0032

0.0024

0.0065

0.0015

-0.0043** (0.021)

0.0053

0.0026

0.0103

0.0029

0.0083

0.0030 (0.138)

0.0126

0.0155

0.0103

0.0144

0.0210

0.0084*** (0.002)

0.0139*** (<.0001)

0.0139*** (<.0001)

0.0088*** (0.001)

0.0135*** (<.0001)

0.0281*** (<.0001)

0.0142*** (<.0001)

Panel C. First sort by σ(spread), Second Sort by std_illiq– FF5F alpha

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0114

-0.0057

-0.0101

0.0058

-0.0009

0.0105*** (<.0001)

-0.0075

-0.0049

-0.0012

-0.0010

0.0001

0.0076*** (<.0001)

0.0001

0.0028

0.0051

0.0032

0.0028

0.0027 (0.190)

0.0048

0.0065

0.0069

0.0058

0.0088

0.0040 (0.100)

0.0142

0.0168

0.0131

0.0161

0.0205

0.0063* (0.055)

0.0256*** (<.0001)

0.0225*** (<.0001)

0.0232*** (<.0001)

0.0103*** (0.001)

0.0214*** (<.0001)

-0.0042 (0.200)

37

Table 8 Next-Month Returns Across Two-Way Sorts The table reports the next-month Fama-French-Carhart-Pastor-Stambaugh 5-Factor alphas across double-sorted quintiles. In panel A, stock-month observation are sorted (horizontally across columns) by spread volatilities and then (vertically across rows) by size. Similarly, panel B shows the results when stock-month observation are sorted (horizontally across columns) by spread volatilities and then (vertically across rows) by idiosyncratic volatility. Finally, in panel C, stock-month observation are sorted (horizontally across columns) by spread volatilities and then (vertically across rows) by trading volume. P-values are reported in parentheses. *,**,*** represent statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Panel A. First sort by σ(spread), Second Sort by Size – FF5F alpha

Q I

(Low)

Q II

Q III

Q IV

Q V

(High)

Q V – Q I

[1] [2] [3] [4] [5] [6]

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0040

-0.0074

-0.0135

-0.0023

-0.0068

-0.0028 (0.443)

-0.0019

-0.0057

-0.0049

-0.0015

-0.0131

-0.0112*** (<.0001)

0.0120

-0.0003

-0.0036

-0.0038

-0.0013

-0.0133*** (<.0001)

0.0151

0.0101

0.0076

0.0046

0.0035

-0.0116*** (<.0001)

0.0490

0.0171

0.0033

0.0067

-0.0008

-0.0498*** (<.0001)

0.0530*** (<.0001)

0.0245*** (<.0001)

0.0168*** (<.0001) 0.0090** (0.010) 0.0060* (0.094)

-0.0470***

(<.0001)

Panel B. First sort by σ(spread), Second Sort by IdioVolt – FF5F alpha

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

0.0038

0.0030

-0.0011

-0.0031

-0.0071

-0.0109*** (<.0001)

0.0084

0.0044

0.0034

-0.0001

-0.0074

-0.0158*** (<.0001)

0.0072

0.0053

0.0047

0.0010

-0.0014

-0.0086*** (<.0001)

0.0067

0.0091

0.0047

0.0074

0.0023

-0.0044** (0.049)

0.0066

0.0121

0.0152

0.0126

0.0191

0.0125*** (<.0001)

0.0028 (0.204)

0.0091*** (<.0001)

0.0163*** (<.0001)

0.0157*** (<.0001)

0.0262*** (<.0001)

0.0234*** (<.0001)

Panel C. First sort by σ(spread), Second Sort by Volume – FF5F alpha

Q I (Low)

Q II

Q III

Q IV

Q V (High)

Q V – Q I

-0.0014

-0.0003

-0.0019

-0.0044

-0.0092

-0.0078* (0.050)

0.0047

0.0017

0.0026

-0.0040

-0.0082

-0.0129*** (<.0001)

0.0056

0.0068

0.0002

0.0013

-0.0018

-0.0074*** (0.001)

0.0052

0.0054

0.0069

0.0060

0.0071

0.0019 (0.407)

0.0223

0.0123

0.0121

0.0151

0.0175

-0.0048* (0.085)

0.0237*** (<.0001)

0.0126*** (<.0001)

0.0140*** (<.0001)

0.0195*** (<.0001)

0.0267**** (<.0001)

0.0030 (0.392)

38

Figure 1. The table reports the average daily closing spread (Spread) during each year of the sample time period as well as the standard deviation of the daily closing spread during each year.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08Spreads and Spread Volatilities Across Time

Spread Spread Volatility