he empirical results presented in this paper suggest a strong role for liquidity in explaining higher raw and excess returns realized by investors in less liquid stocks. Size effect has been studied extensively and it has been suggested that it may be a proxy for another unobserved factor. Our results strongly suggest that liquidity may be that unobserved factor explaining a large part but not all of the size premium.

1. Does Liquidity Masquerade as Size?
Size effect, initially reported by Banz (1981) and Reinganum (1981) has been researched
extensively. Fama and French (1992, 1993) , for example have proposed a three factor model
which incorporates size and value as two value factors augmenting the traditional CAPM.
However, the original question posed by Banz; “It is not known whether size per se is
responsible for the effect or whether size is just a proxy for one or more true unknown factors” is
still unanswered.
A parallel stream of research starting around the same time has examined the role of liquidity in
explaining asset returns. Liquidity risk has been recognized as a significant factor in asset
pricing. Constantinides (1986) hypothesized that illiquid assets need to offer higher returns
as compared to similar risky assets in order to compensate for the higher risks associated with
lack of liquidity. Grossman and Miller (1988) followed up with the concept that residual
demand curve facing active traders is not infinitely elastic and price concessions are necessary to
accommodate order flows. Earlier studies of liquidity studied the role of transaction costs for
stocks traded on the New York Stock Exchange. Perhaps the most influential study of liquidity in
asset pricing is that of Amihud and Mendelson (1986), exploring the relationship between market
micro structure and asset pricing, by showing that bid-ask spread and asset returns are positively
related. This study spawned a large body of literature dealing with bid-ask spreads in explaining
stock returns as well as on the determinants of bid-ask spread. Amihud (1989), Chalmers and
Kadlec (1998), and Jones (2001) found positive relationship between stock returns and bid-ask
spreads. Heaton and Lucas (1996), Vayanos (1998), and Lo, Mamaysky, and Wang (2001),
among others, explore the relationship between liquidity and asset prices and show that

2. significant price discounts exist for less liquid but otherwise comparable assets. Brennan,
Chordia and Subrahmanyam (1998) separated the cost of transactions into a variable and a fixed
cost and found that illiquidity tends to result in higher stock returns. Similar results have been
reported by researchers using different proxies for liquidity. For example, while the bid-ask
spread measure used in Amihud and Mendelson (1986) relates to the trading cost dimension;
Pastor and Stambaugh (2003) construct their measures based on the concept of price impact to
capture the price reaction to trading volume. Amihud (2002) used the ratio of absolute stock
returns to dollar volume as a proxy liquidity measure for the price pressure. These studies
reported that even after controlling for common risk factors stocks' liquidity and returns
remained negatively related. Using various approaches, these studies come to similar
conclusions, essentially confirming that significant price discounts exist for less liquid but
otherwise comparable assets. The recent financial credit crisis, (2007-9) has dramatically
illustrated the impact that lack of liquidity can have on entire economies.
At the macro level more recent studies have started addressing the role of market liquidity and
the sensitivity of the individual asset to the market level of liquidity as components of the
illiquidity risk premium analogous to the equity risk premium. Chordia, Roll and
Subrahmanyam (2000) show that there is a common component of liquidity that should be
considered as systematic risk factor within a market. Pastor and Stambaugh (2003) and Porter
(2008) examine individual stocks' sensitivity to aggregate market liquidity and explore the
relationship between stock returns and changes in market wide liquidity. Both studies report that
stocks with high sensitivity to aggregate liquidity offered substantially higher returns. Acharay
and Pedersen (2003) estimated liquidity risks of individual stocks by studying their sensitivity to
market conditions and market liquidity. Predictive accuracy for expected returns has been shown

3. to improve with inclusion of liquidity as an explanatory factor. Jones (2001) finds empirically
that the expected annual stock market return increases with the previous year‟s bid-ask spread
and decreases with the previous year‟s turnover. Amihud (2002) finds that illiquidity predicts
excess return both for the market and for size-based portfolios. These results strongly suggest
that liquidity risks provide valuable insight and should be considered in asset pricing.
A cross-sectional analysis of relationship between liquidity and returns can be potentially
contaminated by existence of risk factors other than liquidity. Any discussion of a liquidity
premium, therefore, would be incomplete without accounting for security risk, Amihud and
Mendelson (1986), for example adjust for risk by analyzing asset returns in a CAPM framework.
Fama-French three-factor model (Fama and French, 1993, 1996), adjustment for risk factors is
used by Brennan and Subrahmanyam (1996). Both studies find that asset returns include a
significant premium for illiquidity, even after accounting for the market risk and in case of
Brennan and Subrahmanyam, adjusting for market risk, size premium and market value/book
value ratio. The incremental impact of liquidity as a pricing factor is assessed inside an
Arbitrage Pricing Theory framework for its contribution to the required risk premium for holders
of illiquid assets.
This paper presents a simple measure of liquidity, uncorrelated with unit stock price, which can
be used to measure the relative role of liquidity and size in explaining asset returns and address
this fundamental question. Our results suggest that between size and liquidity, liquidity may be
the dominant factor in asset pricing. The rest of this paper is organized as follows. Section II
describes the data sources and empirical methodology employed. Section III presents our

4. empirical results, and section IV presents our conclusions and some suggestions for further
research.
Section II. Data and Methodology.
The data set consists of 1,468,108 firm- month observations spanning all listed securities for the
three equity markets (NYSE, AMEX, and NASDAQ) for January 1993 to December 2008.
Market capitalization, bid, ask, closing price, total returns, shares outstanding, and trading
volume for all stocks traded on the three exchanges were obtained from CRSP data base
provided by the Center for Research in Security Prices at the University of Chicago. This time
period was selected since the reporting of trading volume was standardized across the three
equity markets only in June 1992. The trading volume reported by NASDAQ before June 1992
was the aggregate of volume reported by all dealers in the security, leading to inflated counts as
dealers/market makers reported each buy and sell transaction separately.
Underlying data for 1993-2010 are retrieved from the CRSP data set provided by the Centre for
Research in Security Prices (CRSP) at University of Chicago. This data set provides daily and monthly
price (High Low Close Bid Ask), return, trading volume, and shares outstanding, among others.
CRSP advises that reporting of NASDAQ trading volumes was standardized in June 1992.
Therefore we start our analysis in January 1993. The time period is appropriate as it covers two
cycles of Pre Bubble, Bubble, and Post Bubble data, allowing us to observe significant changes
in liquidity and pricing behavior. We calculate geometric annual returns for each stock as well
as the market indices starting with every month.
Our measure of liquidity is based on a constant flow model. The shares outstanding and monthly
trading volume are used to construct our liquidity measure λ. This Liquidity Measure (λ) takes

5. in to account both the trading volume and shares outstanding. It is a natural log transformation of
the turnover measure.
Given
The stock holding at time t is St
Volume for one time period time t is Vt
The stock holding at time t +1 is St+1 = St - Vt
Assuming that the rate of deal flow is constant (λ) at time t
St+1 = St e- λ
Or λ = Logn (St) - Logn (St+1)
Half life, or the time a dollar invested in the stock/portfolio is held before being reinvested, is
simply Log (2)/ λ.
Firms with an IPO or delisting during the month are excluded from the sample. This results in
reassigned monthly portfolios containing 1,367,204 firm-month observations. High and Low
stock portfolios based on monthly levels of market value and liquidity are formed at the end of
each month. In addition, sub-portfolios are formed using alternate sort orders (size followed by
liquidity/ liquidity followed by size) and used to measure the between and within portfolio return
differentials. A comparison is made between the observed geometric annual returns following
the portfolio assignment. Size and liquidity premiums are calculated following the Fama French
procedure as the difference between larger stocks and smaller stocks, and between stocks with
higher liquidity and lower liquidity. Further, similar differences are calculated for each of the
size and liquidity portfolios further sorted by liquidity and size and averaged to generate size
adjusted liquidity premium and liquidity adjusted size premium. Our sample consists of 202
monthly portfolios in each series. The first portfolio formation month is February 1993 and the

6. last is December 2009. Descriptive statistics for the dataset are summarized below by size and
liquidity classifications as follows.
Table 1. Data Summary for Monthly Reassigned Portfolios
Variable Mean Std Dev Minimum Maximum N t Value Pr > |t|
Geometric Annual 0.111451 0.215817 -0.44354 0.7741343 202 7.36 <.0001
Return Total Sample
Mean M V ( ‘000) 1910918 820567.7 653160.9 3483087 202 33.1 <.0001
Total Sample
Mean Market Liquidity 0.094208 0.041466 0.042014 0.2586027 202 32.29 <.0001
Total Sample
Geometric Annual 0.111726 0.24255 -0.46664 0.9032731 202 6.55 <.0001
Return Small Stocks
Mean M V ( ‘000) 69310.86 36174.11 26623.81 145138 202 27.23 <.0001
Small Stocks
Mean Liquidity 0.06295 0.023204 0.032006 0.1398093 202 38.56 <.0001
Small Stocks
Geometric Annual 0.110255 0.197388 -0.42034 0.7443907 202 7.94 <.0001
Return Large Stocks
Mean M V (‘000) 3754879 1612351 1276473 6840916.4 202 33.1 <.0001
Large Stocks
Mean Liquidity 0.125464 0.061295 0.052029 0.3776782 202 29.09 <.0001
Large Stocks
Geometric Annual 0.120236 0.21552 -0.4524 0.7948197 202 7.93 <.0001
Return
Low Liquidity Stocks
Mean M V (‘000) 923711.2 511426.7 291640.6 2254601.2 202 25.67 <.0001
Low Liquidity Stocks
Mean Liquidity 0.02272 0.007969 0.011158 0.048765 202 40.52 <.0001
Low Liquidity Stocks
Geometric Annual 0.101599 0.225568 -0.43464 0.8107023 202 6.4 <.0001
Return
High Liquidity Stocks
Mean M V (‘000) 2901860 1320912 792130 5594250.5 202 31.22 <.0001
High Liquidity Stocks
Mean Liquidity 0.165962 0.075647 0.072962 0.4689387 202 31.18 <.0001
High Liquidity Stocks

7. Table 2. Geometric Annual Returns for portfolios sorted by size and liquidity
Geometric Annual Return
Size sorted by liquidity N Mean Std Dev Minimum Maximum t Value Pr > |t|
Small Size Low Liquidity 340563 0.122961 0.6245659 -0.9953528 5 114.89 <.0001
Small Size High Liquidity 340658 0.0935327 0.7156676 -0.9955132 5 76.28 <.0001
Large Size Low Liquidity 340207 0.1101057 0.4382259 -0.9975142 4.9999999 146.55 <.0001
Large Size High Liquidity 340302 0.1111275 0.5755055 -0.9963801 5 112.64 <.0001
Geometric Annual Return
Liquidity sorted by Size N Mean Std Dev Minimum Maximum t Value Pr > |t|
Low Liquidity Small Size 341083 0.1240464 0.6705963 -0.9949096 5 108.03 <.0001
Low Liquidity Large Size 341179 0.1139869 0.4705356 -0.9954839 4.9941635 141.5 <.0001
High Liquidity Small Size 339684 0.087717 0.7005652 -0.9963801 5 72.97 <.0001
High Liquidity Large Size 339784 0.1118893 0.5136302 -0.9975142 4.9999998 126.98 <.0001
Table 3. Size and Liquidity Premiums
Variable N Mean Std Dev Minimum Maximum t Value Pr > |t|
Size Premium 202 0.0014714 0.0913712 -0.1580823 0.3077134 0.23 0.8192
Liquidity Premium 202 0.018637 0.0872153 -0.2337889 0.2695761 3.04 0.0027
Average Size 202 -0.003779 0.096042 -0.1755517 0.3373916 -0.56 0.5767
Premium across
Liquidity
Average Liquidity 202 0.0121216 0.0943331 -0.284534 0.2957275 1.83 0.0693
Premium across Size
Data distribution follows the expected pattern. Mean market value and liquidity differentials are
high when compared across size and liquidity sorted portfolios. Larger market value and higher
liquidity portfolios exhibit lower returns as compared to portfolios with smaller market value and
low liquidity. The difference between mean returns on size sorted portfolios is considerably
smaller than the difference between mean returns on liquidity sorted portfolios. High returns
generated by a portfolio would indicate initial under pricing, and low returns generated by a
portfolio would, conversely, indicate initial overpricing. The observed returns indicate that while
larger stocks may not show significant differences between high and low liquidity portfolio

8. returns, small stocks may exhibit significant over pricing for high liquidity and significant under
pricing for low liquidity portfolios. Overall liquidity premium is significant and positive, and the
average liquidity premium after adjusting for size is also significant and positive, indicating that
less liquid stocks are underpriced. Overall size premium, as well as the size premium after
adjusting for liquidity is insignificant. This suggests that the origins of „size effect‟ may lie in the
small stock/low liquidity quadrant, and it may simply be a manifestation of the „liquidity‟ effect.
We find that the relative liquidity and returns differential between large and small stocks is
dwarfed by the considerably higher relative liquidity and returns differential between liquid and
illiquid stocks. The data appear to indicate that liquidity impact may be much stronger that size
impact in explaining the excess returns generated by the stocks.
Section III. Empirical Analysis
Data summary presented in section II indicates that between size and liquidity, liquidity may be
the dominant factor explaining the realized returns. Table 4. Below presents results of regression
models with stock excess returns as the dependent variables and a choice of size and liquidity
premiums in addition to the equally weighted market excess returns as the explanatory variables.
Liquidity premium is significant and has a positive coefficient for the entire sample, as well as
the small and large stock samples. (models 1,3,4) Size premium is insignificant for the entire
sample, has a significant positive coefficient for low liquidity and a significant negative
coefficient for high liquidity stocks. (models 2,5,6). The reversal of sign for size premium in
models 5 and 6 is interesting. While smaller low liquidity stocks appear to generate higher
returns, indicating under pricing, size premium has a negative and significant coefficient for high
liquidity stocks. This suggests that liquid small stocks may be experiencing overpricing and
generate low returns. This supports overreaction hypothesis for smaller stocks.

9. Table 4. Regression Results Dependent Variable Stock Excess Return
Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Full Sample Full Sample Small Large Low High Liquidity
stocks Stocks Liquidity
Intercept -0.0066 2.10E-05 -0.021 0.0078 0.0179 -0.0179
t -12.56 0.04 -25.05 12.28 25.18 -23.86
Equally Weighted 0.87065 0.85032 0.98583 0.75628 0.75457 0.94648
Market Excess Return
t 433.63 370.14 307.81 313.13 239.06 284
Liquidity Premium 0.25685 0.47945 0.03473
t 46.05 53.99 5.17
Size Premium -0.0058 0.27544 -0.2879
t -0.92 31.91 -31.59
F-Value 95585.4 94378.4 47534.9 51412.9 45654.5 49928.5
Adj R-Sq 0.1231 0.1217 0.1225 0.1313 0.118 0.1281
Following Fama French procedure we form size averaged liquidity premium and liquidity
averaged size premium. Regression results for the full sample using size premium and liquidity
premium as well as augmented models with liquidity premium averaged across size segmented
samples and size premium averaged across liquidity segmented samples are presented in table 5
below. Once again, liquidity premium is positive and significant across all specifications,
indicating that less liquid stocks are underpriced and generate higher returns across all size
segments. Size premium is insignificant by itself, and has a negative and significant coefficient
in conjunction with liquidity. These regression results confirm that liquidity premium is
significant in explaining stock excess returns. Size premium is significant only in conjunction
with liquidity premium and has a negative coefficient. This suggests that the origins of the
previously observed size premium, neglecting liquidity, may in fact lie in the small illiquid stock
quadrant.

10. Table 5. Augmented Regression Models Dependent Variable Stock Excess Return
Variable Model 1 Model 1A Model 2 Model 2A
Full Full Full Full
Sample Sample Sample Sample
Intercept -0.0066 -0.0138 0.000021 -0.0123
t -12.56 -23.77 0.04 -21.99
Equally Weighted Market Excess 0.87065 0.93408 0.85032 0.93858
Return
t 433.63 314.87 370.14 341.62
Liquidity Premium 0.25685 0.28442
t 46.05 50.29
Size Premium -0.0058 -0.0979
t -0.92 -15.13
Average Size Premium across Liquidity -0.219
t -29.04
Average Liquidity Premium across Size 0.35174
t 58.4
F-Value 95585.4 64044.1 94378.4 64213.4
Adj R-Sq 0.1231 0.1236 0.1217 0.1239
Liquidity risk is a priced factor markets and has a positive economically significant contribution
to expected returns. In periods of crises as a flight to safety occurs liquidity premium is expected
to rise. Regression results presented in Table 6. below show that liquidity premium is negatively
related to the level of prevailing market liquidity as well as the market returns as expected. In
periods of low liquidity and economic downturns, preference for liquidity creates a larger
discount for illiquid stocks, resulting in subsequent higher returns. This effect is significant
across the entire sample, as well as the sub samples partitioned across small and large sizes.
These results suggest that liquidity effect is economically significant in explaining the realized
returns. A naïve strategy investing in long position in illiquid stocks and short position in liquid
stocks would generate significant positive economic returns.

11. Table 6. Regression Results Dependent Variable Liquidity Premium
Variable Full Sample Small Stocks Large Stocks
Intercept 0.05648 0.05655 0.05641
t 306.54 217.03 216.49
Equally Weighted Excess -0.0861 -0.08656 -0.08564
Returns
t -289.97 -205.82 -204.26
Mean Market Liquidity -0.33036 -0.33122 -0.32952
t -180.72 -128.11 -127.46
F Value 55926.3 28116.3 27811.6
Adj. R-Square 0.0759 0.0763 0.0756
The returns would not be significant for a naïve strategy shorting large stocks and going long in
small stocks. Role of size effect in generating larger returns is not supported by this analysis.
Previously reported size effect thus may be a manifestation of the liquidity effect.
Section IV. Conclusions and Suggestions for Further Research
The empirical results presented in this paper suggest a strong role for liquidity in explaining
higher raw and excess returns realized by investors in less liquid stocks. Size effect has been
studied extensively and it has been suggested that it may be a proxy for another unobserved
factor. Our results strongly suggest that liquidity may be that unobserved factor. We introduce a
new measure of liquidity, unaffected by the stock price per share and find that it provides an
effective indicator. While market level liquidity and sensitivity of individual stock liquidity has
been studied primarily in price impact there is considerable work that needs to be done in
assessing predictability of future returns based on historic liquidity. This paper is a first step in
that direction.

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