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Uncertainty elasticity of liquidity and the associated premium of China's A-shares

Abstract We investigate what determines a stock’s uncertainty elasticity of liquidity (UEL: the change in the stock’s liquidity given the change in the market return volatility) and whether UEL is priced for China’s A-shares. We find that stocks with higher UEL have lower share price, smaller market capitalization, lower stock liquidity, less investor attention, and higher market risk and liquidity risk. From May 2004 to April 2018, our results show that the highest UEL equally-weighted decile portfolio significantly outperforms the lowest UEL equally-weighted decile portfolio by 0.88% per month and that the UEL premium only exists when the market risk premium is positive. Moreover, we find that the size premium mainly drives the UEL premium in the China’s A-shares market. Finally, our results show that UEL provides additional explanatory power for stock returns after we control for transaction cost, market risk, and liquidity risk, demonstrating that, in additional to market return and market liquidity, market uncertainty also plays an important role in determining individual stocks’ liquidity and the associated premium. JEL classification: G12, G15 Keywords: market uncertainty; stock liquidity; liquidity risk; stock returns; A-shares

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1. Introduction

Do investors care about the stock market volatility when they trade stocks? If the

stock market uncertainty proxied by the stock market volatility can influence a stock’s

liquidity, how does the uncertainty elasticity of liquidity (UEL: the change in the stock’s

liquidity given the change in the stock market volatility) of the stock vary with the

expected stock return? We study these two research questions for China’s A-share

market from 2004 to 2017 in this study. Chung and Chuwonganant (2014) find that the

stock market uncertainty exerts a greater impact on stock liquidity in the U.S. market

when public traders play a greater role and market makers play a reduced role in

liquidity provision. Because there is no market maker to provide liquidity and

individual investors play an important role in the order-driven China’s A-share market,

China’s A-share market becomes a good candidate to study the UEL and its associated

premium.

Previous studies have shown that market liquidity, return, and volatility influence

an individual stock’s liquidity. Chordia, Roll, and Subrahmanyam (2000) first

document that an individual stock’ liquidity co-moves with market- and industry-wide

liquidity. Acharya and Pedersen (2005) derive a liquidity-adjusted capital asset pricing

model and show that the covariation between an individual stock’s liquidity innovation

and the stock market return is an important dimension of liquidity risk.1 Chung and

1 Hameed, Kang, and Viswanathan (2010) find that negative market returns decrease stock liquidity, especially during times of tightness in the funding market.

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Chuwonganant (2014) find that the effect of VIX on individual stock liquidity is greater

than the effects of other liquidity determinants and that the uncertainty elasticity of

liquidity increases after regulatory changes to increase the role of public traders of

liquidity provision.

Since both China’s economy and equity market are currently ranked second in

the world and MSCI already includes big firms of China’s A-shares into the emerging

markets index starting from June 2018, in addition to stock market liquidity and return

which have shown their influences on individual stocks’ liquidity in the international

financial markets as documented by Lee (2011), it becomes important to know whether

stock market volatility also plays an important role to influence individual stocks’

liquidity of China’s A-shares from institutional investors’ international diversification

perspective. 2 Furthermore, exploring whether the stock market uncertainty can

influence investors’ trading behavior is interesting because the sensitivity of stock

liquidity to the stock market volatility may provide another channel for us to better

understand the equity risk premium. Bansal, Kiku, Shaliastovich, and Yaron (2014) find

that an increase in macroeconomic volatility is associated with an increase in discount

rates and a decline in consumption. Hence, investors may hesitate to buy a stock until

the price is lower enough to provide the expected return which can cover its transaction

costs when the stock market is volatile. Under this circumstance, investors may require

2 Lee (2011) documents a security’s required rate of return depends on the covariance of its own liquidity with aggregate local market liquidity and the covariance of its own liquidity with local and global market returns in international financial markets.

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an additional risk premium for holding stocks with higher uncertainty elasticity of

liquidity.

Our findings for the uncertainty elasticity of liquidity and the associated premium

of China’s A-shares from 2004 to 2017 are as follows. First of all, we find that the

significant determinants of UEL include share price level, market capitalization, stock

liquidity variables, and investor attention variables. Specifically, stocks with higher

UEL are associated with lower share price, smaller market capitalization, higher

Amihud (2002)’s illiquidity ratio, lower institutional ownership, lower analyst coverage,

and fewer employees and shareholders. In addition, stocks with higher UEL also have

higher market risk and liquidity risk according to Acharya and Pedersen (2005)’s

liquidity-adjusted capital asset pricing model, suggesting that the higher covariation

between individual stock return and market return and the higher covariation between

individual stock liquidity and market liquidity signal the higher covariation between

individual stock liquidity and market volatility.

Secondly, after we sort stocks into decile portfolios based on the UEL and

calculate equally-weighted returns for each decile portfolio, we find the highest UEL

decile portfolio outperforms the lowest UEL decile portfolio by 0.88% per month of the

168 months from May 2004 to April 2018. Interestingly, the highest UEL decile

portfolio outperforms the lowest UEL decile portfolio by 1.62% per month when the

market risk premium is positive and the highest UEL decile portfolio has similar

performance to the lowest UEL decile portfolio when the market risk premium is

negative during our sample period. This result suggests that, for China’s A-shares,

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investors who bear the UEL risk will be rewarded when the market performs well while

those investors may not lose more money than other stocks when the market is bad.

Moreover, the Fama and French (2018) 6-factor model explains the UEL premium well

and shows that the size premium mainly accounts for the UEL premium.

Thirdly, we examine the UEL premium of portfolios sorted by different firm

characteristics. We find that there is no UEL premium for portfolios sorted by market

capitalization, suggesting that size premium is highly correlated with UEL premium for

China’s A-shares. In addition, we find that the UEL premium is more significant in the

portfolios with lower liquidity, lower investor attention, higher market risk, and higher

liquidity risk, indicating that investors require an additional return for holding stocks

whose liquidity are sensitive to market volatility in those portfolios.

Finally, we investigate whether UEL provides additional explanatory power for

cross-sectional stock returns under the Acharya and Pedersen (2005)’s LCAPM

framework. Our findings show that, after controlling for transaction cost, market risk,

and liquidity risk, UEL significantly and positively explains stock returns, consistent

with Chung and Chuwonganant (2014)’s conjecture that the market volatility-induced

liquidity risk is also priced.

Our study contributes to the market microstructure literature in the China’s A-

shares market in the following ways. First, we show that investors do care about the

stock market volatility when they trade stocks. On average, there is a monthly premium

of 0.88% required by investors for holding stocks with high uncertainty elasticity of

liquidity. Second, we find that stocks with higher UEL are smaller in size, less liquid,

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and attract less investor attention, indicating that liquidity of stocks with lower

institutional ownership, fewer analysts following, and lower number of employees and

shareholders is more sensitive to market uncertainty. Third, there is no UEL premium

for portfolios sorted by size, suggesting that the UEL premium is highly associated with

the size premium. Finally, in addition to market risk and liquidity risk, UEL provides

additional explanatory power for cross-sectional stock returns, showing that market

uncertainty also plays an important role in determining individual stocks’ liquidity and

the associated premium in the China’s A-shares market.

The rest of the paper is organized as follows. Section 2 briefly describes the

market microstructure in China’s A-share market. Section 3 describes our data and

variable construction. Section 4 shows our empirical methodology and results. Section

5 concludes our paper.

1. Market microstructure in the China’s A-shares market

As of April 2018, there are four boards in China’s A-shares market. The Shanghai

Main Board (with stock id 6xxxxx) was launched on December 19, 1990. The Shenzhen

Main Board (with stock id 0xxxxx) was launched on July 3, 1991 and stopped listing

new firms after the launch of the Small and Medium Sized Enterprises Board from 2004.

The Shenzhen Small and Medium Sized Enterprises Board (with stock id 002xxx) was

launched on May 17, 2004. The Shenzhen Growth Enterprise Market Board (with stock

id 3xxxxx) was launched on October 30, 2009.

The market opening days are from Monday to Friday and the daily trading period

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is from 9:30 am to 11:30 am in the morning and 1:00 pm to 3:00 pm in the afternoon.

The minimum price tick size is 0.01 RMB for A-shares. Since December 16, 1996, the

stock price starts having a daily fluctuation limit of 10%. During our sample period

from 2004 to 2017, the annual average number of trading days in the China’s A-shares

market is 242 days, which is about 10 days less than the annual average number of

trading days in the U.S. stock market. The major reason for this number of trading days’

difference is due to three major holiday weeks – the Chinese New Year week in

February, the Labor Day week in early May, and the National Day golden week in early

October. One specific feature of the China’s A-shares market is the trading halt

mechanism. When a listed firm has an important event such as merger & acquisition,

seasoned equity offering, or restructuring to announce, there will be a trading halt for

the stock and the date to resume stock trading will be uncertain. In addition, if a stock’s

price closes at positive 10% upper limit for consecutive three days, the regulatory

agency such as China Securities Regulatory Commission (CSRC) may require the stock

to have a trading halt to examine whether there is any non-public material information

to be disclosed. Therefore, investors of China’s A-shares bear the trading discontinuity

risk due to the national holidays, price limit, and trading halt mechanisms.

Unlike the U.S. stock market, there are no market makers in the China’s A-shares

market and the trading mechanism is an order-driven system. According to Madhavan

(1992), a quote-driven system is where dealers post prices before order submission and

an order-driven system is where traders submit orders before prices are determined.

Under the order-driven system, the A-shares’ daily opening price is determined by a

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periodic auction from 9:15 am to 9:25 am and starts a continuous auction after 9:30 am.

During the five minutes from 9:25 am to 9:30 am, traders cannot submit new orders nor

withdraw their previous submitted orders.

According to Liao, Liu, and Wang (2014), the Chinese stock market has a unique

split-share structure, a legacy of China’s initial share issue privatization (SIP), in which

state-owned enterprises (SOEs) went public to issue minority tradable shares to

institutional and individual investors. Meanwhile, the Chinese government withheld

control of these listed SOEs by owning majority non-tradable shares. In 2005, the Split-

Share Structure Reform was initiated to dismantle the dual share structure by converting

non-tradable shares into tradable shares. Liao et al. (2014) argue that the Split-Share

Structure Reform adopted a market mechanism that played an effective information

discovery role in aligning the interests of the government and public investors.

Nevertheless, many newly listed stocks still have a higher percentage of non-tradable

shares than tradable shares and the seasoned equity offering shares also have a non-

tradable period. Therefore, we also apply the percentage of tradable shares as one of

our liquidity measures.

2. Data and variable construction

We use the China Stock Market and Accounting Research (CSMAR) database to

collect A-shares’ data from 2004 to 2017.3 Because listed A-shares are required to

3 Because CSMAR starts reporting institutional ownership from June 2003, we start our sample period from April 2004 and use institutional ownership in December 2003 as our first institutional ownership measure.

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report their annual reports by the end of April in the following year, we classify May in

year t-1 to April in year t as a year to construct our variables.

Since individual stock liquidity is a major variable in our study, we require our

sample stocks to have at least 180 trading days from May in year t-1 to April in year t.

In addition, because the CSMAR database starts reporting the number of shareholders

and the institutional ownership information from the annual report of 2003, our sample

period starts from April 2004 when the 2003’s annual report is released. Furthermore,

since we require a stock to have 60 months’ observations (at least 36 months) to

calculate its individual uncertainty elasticity of liquidity and liquidity risk measures,

our return observations start from May 1999 and we use the period from May 1999 to

April 2004 to construct stocks’ first individual UEL and liquidity risk measures in April

2004 in our study.

2.1. Amihud (2002)’s illiquidity ratio

We use Amihud’s (2002) illiquidity ratio ,i tILLIQ to be the major liquidity

variable used in our study. Specifically, as shown in equation (1), where TD is the

number of trading days in a month; and ,i sR and ,i sVOL are stock i’s absolute return

and dollar trading volume (in million RMB), respectively, on day s.

,,

1 ,

1 TDi s

i tsT i s

RILLIQ

D VOL=

= ∑ (1)

Many research papers provide evidence to show that Amihud (2002)’s illiquidity

ratio is a valid proxy to measure a stock’s liquidity. Acharya and Pedersen (2005) use

Amihud (2002)’s illiquid ratio to measure a stock’s transaction cost. Goyenko, Holden,

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and Trzcinka (2009) run horse races of annual and monthly liquidity estimates and

conclude that Amihud (2002)’s illiquidity ratio does well in measuring price impact.

Lou and Shu (2017) find that the pricing of the Amihud (2002)’s measure is driven by

its trading volume component instead of its construct of the ratio of absolute return to

volume. Because Amihud (2002)'s illiquidity ratio, dollar trading volume, and turnover

(shares traded divided by shares outstanding) all include similar trading information,

we only use Amihud (2002)'s illiquidity ratio to construct UEL and liquidity risk

measures. In each trading day during our sample period, we winsorize our sample

stocks’ illiquidity ratio at 99% to avoid extreme values to affect our liquidity

measurement. For the market liquidity measure, we take the equally-weighted average

of each sample stock’s monthly illiquidity ratio to be the market illiquidity.

Table 1 reports the descriptive statistics of the illiquidity ratio ILLIQ of our

sample. ILLIQ has a mean of 0.0017 and a median of 0.0005, suggesting that illiquid

stocks account for a small part of our sample stocks.

2.2. Uncertainty elasticity of liquidity

To calculate UEL, we use Amihud (2002)’s illiquidity ratio to be the liquidity

measure. Since there is no similar stock market uncertainty measure such as VIX in the

China’s A-shares market, for each month from May 1999 to April 2018, we follow Naes,

Skjeltorp, and ØDegaard (2011) and take the cross-sectional average volatility of the

sample stocks to be the market volatility _ tMkt Vola , where volatility of each

individual stock VOLA is calculated as the standard deviation of daily returns over the

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month.

As shown in equation (2) and (3), we take the logarithm of each stock’s monthly

illiquidity ratio divided by previous month’s illiquidity ratio and the logarithm of the

market volatility divided by previous month’s market volatility to measure the change

in the individual stock illiquidity ratio and the change in the market volatility,

respectively.

1( / )t t tdILLIQ log ILLIQ ILLIQ −= (2)

1_ ( _ / _ )t t tdMkt Vola log Mkt Vola Mkt Vola −= (3)

We then calculate each individual stock’s uncertainty elasticity of liquidity as

shown in equation (4), the coefficient on dMkt_Volat is defined as UELi. A qualified

stock in our sample needs to have past 60 months’ (at least 36 months) observations of

both dILLIQt and dMkt_Volat in the end of April from 2004 to 2017.

, * _i t i i t idILLIQ UEL dMkt Vola eα= + + (4)

To avoid the errors-in-variables problem, we use the portfolio approach to

calculate the individual stock’s Port_UEL. Specifically, in the end of April in each year

from 2004 to 2017, we first sort stocks into 10 size (market capitalization) sorted

portfolios. Within each size decile portfolio, we further sort stocks into 10 individual

UEL sorted portfolios. We then apply each stock's size rank and UEL rank into the

following year from May in year t to April in year t+1 to form 100 equally-weighted

portfolios and calculate each portfolio’s change in illiquidity ratio. Next, we calculate

each portfolio’s UEL during the sample period from May 2004 to April 2018. Finally,

we assign the portfolio’s UEL back to individual stocks based on their size rank and

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UEL rank. Table 1 shows Port_UEL has a mean of 0.85 and a median of 0.84.

2.3. Firm characteristics

In order to understand the determinants of a stock's Port_UEL, we include the

following firm characteristics. PRC is a firm’s average daily share price from May in

year t-1 to April in year t. SIZE is a firm’s market capitalization in the end of April. BM

is a firm’s book to market equity ratio in the end of December in year t-1. GP is a firm’s

gross profitability defined as dividing the difference between sales and cost of goods

sold by the firm’s lagged total asset in the end of December in year t-1. INV is a firm’s

asset growth rate in the end of December in year t-1. RET(-12,-2) is a firm’s cumulative

stock return from May in year t-1 to March in year t. VOLA is a firm’s daily return

volatility from May in year t-1 to April in year t.4

Table 1 shows the descriptive statistics of those firm characteristics in our sample.

PRC has a mean of 11.81 RMB per share and a median of 9.04 RMB per share,

suggesting that stocks with high share price account for a small part in our sample. SIZE

has a mean of 12.67 billion RMB and a median of 4.54 billion RMB, implying big firms

account for a small part in our sample. BM has a mean of 0.48 and a median of 0.39,

suggesting that firms with higher book to market ratio account for a smaller portion in

4 Fama and French (1992) find that size and book to market capture the cross-sectional variation in average stock returns associated with market beta, size, leverage, book to market equity, and earnings-price ratio. Novy-Marx (2013) shows that gross profitability significantly and positively explains future stock returns in the U.S. market. Cooper, Gulen, and Schill (2008) document a negative relationship between asset growth and future stock returns in the U.S. market. Jegadeesh and Titman (1993) document a strategy that buying stocks that have performed well in the past and selling stocks that have performed poorly in the past can generate significant and positive returns over 3- to 12-month holding periods.

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our sample. GP has a mean of 3.91% and a median of 2.61%, implying that firms with

higher gross profitability account for a smaller portion in our sample. INV has a mean

of 26.42% and a median of 9.47%, suggesting that firms pursuing higher asset growth

account for a small part in our sample. RET(-12,-2) has a mean of 20.91% and a median

of 2.11%, implying that a smaller part of our sample has good past price performance.

VOLA has a mean of 2.98%, a median of 2.77%, and standard deviation of 0.98%,

showing that individual volatility exhibits a distribution similar to the normal

distribution in our sample.

2.4. Other liquidity measures

Because of the specific trading halt feature and the existence of non-tradable

shares for China's A-shares, in addition to Amihud (2002)'s illiquidity ratio, we also

include the number of trading days and the percentage of tradable shares to measure a

stock's liquidity. Specifically, TRD is the firm’s number of trading days from May in

year t-1 to April in year t. FLOAT is the firm’s daily average tradable shares’ percentage

from May in year t-1 to April in year t.

Table 1 shows the descriptive statistics of those two liquidity measures. TRD has

a mean of 235.80 and a median of 240, suggesting that most stocks in our sample do

not have a long period of trading halt. FLOAT has a mean of 71.94% and a median of

75.58%, showing that the tradable percentage of shares exhibits a distribution similar

to the normal distribution in our sample.

2.5. Investor attention variables

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Because Chung and Chuwonganant (2014) use investor attention variables such

as institutional ownership and analyst coverage to explain UEL, we also include four

investor attention variables used by Hou and Moskowitz (2005) to explain Port_UEL

in our study. Specifically, IO is a firm’s institutional ownership including ownership of

mutual funds, QFIIs, security companies, insurance companies, social security funds,

trust funds, financial companies, banks, and non-financial public firms in the end of

December in year t-1. ANA is a firm’s unique number of analysts who provide earnings

forecasts in year t-1. EMP is a firm’s number of employees in the end of December in

year t-1. SH is a firm’s number of shareholders in the end of December in year t-1.5

Table 1 reports the descriptive statistics of those investor attention variables. IO

has a mean of 4.61% and a median of 2.60%, suggesting that only a small percentage

of our sample firms attract institutional investors’ attention. ANA has a mean of 5.07

and a median of 2.00, also implying that a small percentage of our sample firms has

analyst following. EMP has a mean of 6605 and a median of 2200, suggesting that firms

with a higher number of employees account for a small percentage in our sample. SH

has a mean of 63876 and a median of 39000, implying that stocks which attract a higher

number of shareholders only account for a small percentage in our sample.

2.6. Liquidity risk

Pastor and Stambaugh (2003) first propose the concept of liquidity risk and

5 Armstrong et al. (2011) use the number of shareholders to measure the extent to which equity market is competitive to study the importance of information asymmetry on a firm's cost of equity capital.

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document that stocks with returns most sensitive to market liquidity innovation

outperform stocks with returns least sensitive to market liquidity innovation by 7.5%

annually from 1966 through 1999 in the U.S. stock market. Acharya and Pedersen (2005)

then derive a liquidity-adjusted capital asset pricing model and show that two additional

sensitivities: covariation between individual stock liquidity innovation to market

liquidity innovation and covariation between individual stock liquidity innovation to

market return also explain expected stock returns well.

Similar to the idea of Pastor and Stambaugh (2003), Liu (2006) applies the

turnover adjusted non-trading days’ as the liquidity measure to create a liquidity factor

and finds that his liquidity-augmented capital asset pricing model explains size, book

to market, long-term contrarian investment, and fundamental to price ratios related

equity risk premium well. Lam and Tam (2011) also show that liquidity is an important

factor for pricing returns in Hong Kong after taking well-documented asset pricing

factors into consideration. Lee (2011) applies Lesmond, Ogden, and Trzcinka (1999)

zero-return probability as the transaction cost proxy and uses Acharya and Pedersen

(2005) liquidity-adjusted capital asset pricing model to examine the price of liquidity

risk in the global stock markets.

Since stocks in the China’s A-shares market always have trading volume when

the stock is eligible for trading, we apply Amihud (2002)’s illiquidity ratio to be the

stocks’ transaction cost proxy. Similar to Acharya and Pedersen (2005) and Lee (2011),

we use equation (5), (6), (7), (8), and (9) to calculate the covariation between the stock

return and market return 1β , stock liquidity innovation and market liquidity innovation

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correlation risk 2β , the covariation between stock return and market liquidity

innovation 3β , the covariation between stock liquidity innovation and market return

4β , and the total liquidity risk 5β .

( )( )

1cov ,

var

i Mt t

i M Mt t

r r

r cβ =

− (5)

( )( )

2cov ,

var

i Mt t

i M Mt t

c c

r cβ

∆ ∆=

− (6)

( )( )

3cov ,

var

i Mt t

i M Mt t

r c

r cβ

∆=

− (7)

( )( )

4cov ,

var

i Mt t

i M Mt t

c r

r cβ

∆=

− (8)

5 2 3 4i i i iβ β β β= − − (9)

where itr represents the individual stock return, M

tr represents the market return, itc∆

represents the individual stock's liquidity innovation, and Mtc∆ represents the market

liquidity innovation. To calculate stocks’ beta (1 to 4) in the April end from 2004 to

2017, we require our sample stock to have 60 months’ (at least 36 months) return and

Amihud (2002)’s illiquidity ratio. We follow Pastor and Stambaugh (2003), Acharya

and Pedersen (2005), and Liu (2006) to use the AR(2) model as shown in equation (10)

to calculate a stock’s liquidity innovation itc∆ or the market’s liquidity innovation

Mtc∆ .

( )( ), 1 ( ), 1 2 ( ), 2* * i M

i M t i M t i M t tILLIQ ILLIQ ILLIQ cα β β− −= + + + ∆ (10)

Similar to the way we use to calculate individual stocks’ UEL, we use the

portfolio approach to calculate the individual stocks’ Port_Beta1, Port_Beta2,

Port_Beta3, and Port_Beta4. Specifically, in the end of April in year t from 2004 to

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2017, we sort stocks into decile portfolios by their market capitalization. Within each

size sorted decile portfolio, we then sort stocks based on stocks’ individual beta (1 to 4)

and apply their size rank and beta rank to the following year from May in year t to April

in year t+1 to form 100 equally-weighted portfolios and calculate each portfolio’s

return, portfolio’s liquidity innovation, and market liquidity innovation through the

whole sample period from May 2004 to April 2018. We then calculate each portfolio’s

beta (1 to 4) and assign each portfolio’s beta back to individual stocks based on their

size rank and beta (1 to 4) rank.

Table 1 reports the descriptive statistics of those risk measures. Port_Beta1 has a

mean of 1.08 and a median of 1.10. Port_Beta2 has a mean of 0.00026 and a median of

0.00013, suggesting that tocks with higher liquidity commonality account for a small

part in our sample. Port_Beta3 has a mean of -0.00364 and a median of -0.00384,

exhibiting a distribution similar to the normal distribution. Port_Beta4 has a mean of -

0.00374 and a median of -0.00277, implying a small part of our sample stocks have

higher flight to liquidity risk. The overall liquidity risk Port_Beta5 has a mean of

0.00764 and a median of 0.00649.

(Insert Table 1 here)

3. Empirical methodology and results

We perform our empirical analysis of UEL and the UEL premium for China’s A-

shares as follows. We first examine what determines a stock’s UEL. Next, we

investigate whether there is a UEL premium for China’s A-shares and perform a six-

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factor (Fama and French (2015) five factor plus a momentum factor) model analysis

for the UEL premium. We further examine the UEL premium of portfolios sorted by

different firm characteristics. Finally, under the Acharya and Pedersen (2005)’s

LCAPM framework, we investigate whether UEL provides additional explanatory

power for future stock returns in addition to transaction cost, market risk, and liquidity

risk.

3.1. Average firm characteristics of portfolios sorted by Port_UEL

Table 2 reports the average firm characteristics of decile portfolios sorted by

stocks’ Port_UEL of our sample from 2004 to 2017. Port_UEL increases from 0.46 of

the lowest Port_UEL portfolio to 1.25 of the highest Port_UEL portfolio.

From the univariate analysis, the stock price PRC shows a decreasing trend as

the Port_UEL rank increases, showing that stocks with higher uncertainty elasticity of

liquidity normally have a lower share price for China’s A-shares. Similarly, the market

capitalization of stocks SIZE also decreases as the Port_UEL rank increases, showing

that stocks with higher UEL tend to be smaller in size. The book to market ratio BM

decreases as the Port_UEL rank increases, showing that stocks with higher UEL tend

to be growth firms. The gross profitability GP also decreases as the Port_UEL rank

increases, indicating that stocks of higher UEL have lower profitability. The asset

growth INV decreases as the Port_UEL rank increases, showing that stocks with higher

UEL are more conservative in expanding their total assets. The past year return skipping

one month RET(-12,-2) has a decreasing trend as the Port_UEL rank increases, showing

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that stocks with higher UEL tend to be loser stocks in the past year. Finally, individual

stock volatility VOLA increases as the Port_UEL rank increases, showing that stocks

with higher UEL also have higher total risk.

As for the three liquidity measures used in our study, Amihud (2002)’s illiquidity

ratio ILLIQ increases as the Port_UEL rank increases, showing that stocks with higher

UEL are less liquid. The number of trading days TRD does not show a trend as the

Port_UEL rank increases, suggesting that trading continuity has a negligible impact on

stocks’ UEL. Interestingly, tradable percentage FLOAT demonstrates an increasing

trend as the Port_UEL rank increases, indicating that stocks with higher UEL also have

a higher percentage of tradable shares, consistent with what Chung and Chuwonganant

(2014) find that uncertainty exerts a greater impact on stock liquidity when public

traders play a greater role.

For the four investor attention variables, those variables all exhibit a decreasing

trend as the Port_UEL rank increases. Therefore, our results show that stocks with

higher UEL for China’s A-shares have lower institutional ownership IO, few analysts

following ANA, and lower number of employees EMP and shareholders SH. Because

stocks with less investor attention also have higher information asymmetry, our results

also suggest that investors pay more attention to market uncertainty when they trade

stocks with higher information asymmetry.

Finally, for risk measures under the Acharya and Pedersen (2005)’s liquidity-

adjusted capital asset pricing model (LCAPM) framework, stocks with higher UEL

have higher market risk Port_Beta1, liquidity commonality risk Port_Beta2, and flight

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to liquidity risk Port_Beta4 (since Port_Beta4 is generally negative, the more negative

the Port_Beta4 means the higher flight to liquidity risk). However, stocks with higher

UEL exhibit lower absolute value of the covariation between individual stock return

and market liquidity innovation Port_Beta3 (Port_Beta3 is also generally negative)

although the difference is relatively small. Overall, our results show that stocks with

higher UEL have higher market risk and liquidity risk Port_Beta5 under the LCAPM

framework, suggesting that higher covariation between individual stock return and

market return and higher covariation between individual stock liquidity innovation and

market liquidity innovation also signal that individual stock liquidity is also more

sensitive to market uncertainty.

(Insert Table 2 here)

3.2. Determinants of Port_UEL

Table 3 reports the Fama and MacBeth (1973) regression results for the

determinants of Port_UEL from 2004 to 2017. The regression equations for Model 1

Model 2, Model 3, and Model 4 are shown in equation (11a), (11b), (11c), and (11d) as

follows.

, 1 , 2 , 3 ,

4 , 5 , 6 , 7 , ,

_ * ( ) * ( ) * ( )* * * ( 12, 2) *

i t i t i t i t

i t i t i t i t i t

Port UEL log PRC log SIZE log BMGP INV RET VOLA e

α β β ββ β β β

= + + + ++ + − − + + (11a)

, 8 , 9 , 10 , ,_ * * ( ) *i t i t i t i t i tPort UEL ILLIQ log TRD FLOAT eα β β β= + + + + (11b)

, 11 , 12 ,

13 , 14 , ,

_ * * (1 )* ( ) * ( )

i t i t i t

i t i t i t

Port UEL IO log ANAlog EMP log SH e

α β ββ β

= + + + ++ + (11c)

21

, 1 , 2 ,

3 , 4 , ,

_ * _ 1 * _ 2* _ 3 * _ 4

i t i t i t

i t i t i t

Port UEL Port Beta Port BetaPort Beta Port Beta e

α β ββ β

= + + ++ + (11d)

Model 1 of Table 3 shows that, among firm characteristics, only share price PRC

and market capitalization SIZE significantly and negatively explain Port_UEL,

demonstrating that liquidity of stocks with lower share price level or smaller firm size

is more sensitive to market uncertainty. As for liquidity measures, as shown in Model

2 of Table 3, Amihud (2002)’s illiquidity ratio ILLIQ significantly and positively

explains Port_UEL, demonstrating that illiquid stocks’ liquidity is more sensitive to

market uncertainty. However, number of trading days TRD and tradable shares’

percentage FLOAT also significantly and positively explain Port_UEL, showing that,

in the trading continuity dimension, liquidity of stocks with more continuous trading is

more sensitive to market uncertainty. Model 3 of Table 3 shows that, all investor

attention variables significantly and negatively explain Port_UEL, showing that

liquidity of stocks with lower investor attention is more sensitive to market uncertainty.

Model 4 of Table 3 shows that, risk measures under Acharya and Pedersen

(2005)’s LCAPM framework all significantly explain Port_UEL. The market risk

measure Port_Beta1 positively explains Port_UEL, showing that liquidity of stocks

with returns more sensitive to market returns is more sensitive to market uncertainty.

For the three liquidity risk measures, the liquidity commonality risk Port_Beta2

positively explains Port_UEL, showing that liquidity of stocks with individual liquidity

more sensitive to market liquidity is also more sensitive to market uncertainty. Both the

covariation between individual stock return and market liquidity innovation Port_Beta3

22

Port_UEL and the flight to liquidity risk Port_Beta4 negatively explain Port_UEL.

Since stocks with more negative Port_Beta3 and Port_Beta4 have higher liquidity risk,

this result also shows that liquidity of stocks with higher liquidity risk is more sensitive

to market uncertainty. Overall, our findings show that liquidity of stocks with higher

market risk or liquidity risk comoves more with the market volatility.

(Insert Table 3 here)

3.3. Portfolio returns and 6-factor model analysis for portfolios sorted by Port_UEL

In the end of April from 2004 to 2017, we sort stocks on the basis of their

Port_UEL and apply their Port_UEL rank to the following year from May in year t to

April in year t+1. We then calculate equally-weighted returns for those 10 decile

portfolios for the 168 months from May 2004 to April 2018. Among those 168 months,

there are 94 months when the market excess return MKTRF is positive and there are 74

months when the market excess return MKTRF is negative for China’s A-shares.

Table 4 reports the return analysis results for portfolios sorted by Port_UEL.

Panel A reports the summary statistics of raw returns for those 10 portfolios sorted by

Port_UEL. Generally, we find the portfolio return increases as the Port_UEL rank

increases. The highest UEL portfolio significantly outperforms the lowest UEL

portfolio by 0.88% per month during our sample period. Interestingly, once we separate

our sample period into sub-periods based on the sign of MKTRF, we find that the return

difference between the highest UEL portfolio and the lowest UEL portfolio becomes

higher at 1.62% per month when the market is good while the return difference is close

23

to 0 when the market is bad. This finding suggests that, by holding stocks with higher

UEL, investors can increase the upside potential of their investment without bearing

additional downside risk. We further study the UEL premium of stocks sorted by

different firm characteristics in Table 5.

Because Barillas and Shanken (2018) find that Fama and French (2015) five

factor model is dominated by a variety of models that include a momentum factor, we

add the momentum factor to Fama and French (2015) five factor model to analyze the

UEL premium as shown in equation (12).

, , 0 1 2 3 4 5

6 ,

p t f t t t t t t

t p t

R r MKTRF SMB HML RMW CMAUMD e

α β β β β β

β

− = + + + + + +

+ (12)

In the end of April from 2004 to 2017, we use the 2x3 method described in Table

3 of Fama and French (2015) to construct those factors. Rp is the Port_UEL sorted

decile portfolio return. rf is the risk-free rate defined as the monthly rate of the 1-year

certificate of deposit rate. MKTRF is the value-weighted A-share stock return in excess

of the risk-free rate. SMB is the return difference between small and big stocks. HML

is the return difference between high and low book to market stocks. RMW is the return

difference between robust and weak operating profitability stocks. CMA is the return

difference between conservative and aggressive in asset growth stocks. UMD is the

return difference between winner (up) and loser (down) stocks.

Panel B of Table 4 reports the six-factor model analysis for portfolio excess

returns sorted by Port_UEL. After the 6-factor risk adjustment, although portfolios with

higher UEL still have significant and positive abnormal returns, we find that the risk-

24

adjusted UEL premium becomes insignificant, showing that the 6-factor model can

subsume the UEL premium. Furthermore, our result shows that the highest UEL

portfolio has a significantly higher factor loading on SMB but lower factor loadings on

both RMA and CMA than the lowest UEL portfolio. During our sample period from

May 2004 to April 2018, SMB factor has an average value of 0.89% at 5% significance

level, RMW factor has an insignificant average value of 0.19%, and CMA factor has an

insignificant average value of -0.03%. Therefore, our finding shows that the UEL

premium is mainly due to the size premium.

(Insert Table 4 here)

3.4. UEL premium of portfolios sorted by firm characteristics

We further study the UEL premium for China’s A-shares in this section.

Specifically, in the April end from 2004 to 2017, we first sort stocks based on one

specific firm characteristic into quintile portfolios. Within each characteristic-sorted

quintile portfolio, we further sort stocks on the basis of Port_UEL into five portfolios

and then apply the firm characteristic rank and Port_UEL rank in the following year

from May in year t to April in year t+1. For the 168 months from May 2004 to April

2018, we calculate the average return difference between the highest UEL quintile

portfolio and the lowest UEL quintile portfolio within each characteristic-sorted

quintile portfolio to get the UEL premium.

Table 5 reports the UEL premium for different characteristic-sorted quintile

portfolios. Our focus here is examining the statistical significance of each UEL

25

premium. One noticeable result of Panel A of Table 5 is that, the UEL premium of SIZE

sorted quintile portfolio does not exhibit any statistical significance, demonstrating that

UEL premium is highly correlated with the size premium for China’s A-shares.

Panel B of Table 5 shows that, the UEL premium is the most significant for the

highest ILLIQ portfolio and for the lowest FLOAT portfolio, demonstrating that

investors require additional return for holding stocks with higher UEL for illiquid stocks.

Panel C of Table 5 shows that, the UEL premium is more significant in quintile

portfolios with lower institutional ownership IO, lower analyst coverage ANA, fewer

employees EMP, and fewer shareholders SH, demonstrating that, for stocks with less

investor attention, investors require a premium to hold stocks with higher UEL.

Panel D of Table 5 shows that, the UEL premium is more significant for higher

market risk Port_Beta1 and liquidity commonality risk Port_Beta2 portfolios,

demonstrating that, for stocks with higher covariation between individual stock return

and market return and higher covariation between individual liquidity innovation and

market liquidity innovation, investors require a premium to hold stocks with higher

UEL.

(Insert Table 5 here)

3.5. UEL, liquidity risk, and the cross-section of stock returns

Because Chung and Chuwonganant (2014) find that UEL is greater than liquidity

commonality in the U.S. market, they conjecture that UEL will also be priced in the

cross-section of stock returns. We add UEL to the Acharya and Pedersen (2005)’s

26

LCAPM model and run Fama and MacBeth (1973) regressions to empirically explore

this conjecture for China’s A-shares as shown in equation (13) from May 2004 to April

2018.

, , 1 , 2 , 3 ,

4 , 5 , 6 ,

7 , ,

* _ * _ 2 * _ 3* _ 4 * _ 5 * _ 1*

i t f t i y i y i y

i y i y i y

i y i t

r r Port UEL Port Beta Port BetaPort Beta Port Beta Port BetaILLIQ e

α β β β

β β β

β

− = + + + +

+ + +

+

(13)

where ri is the monthly individual stock return and rf is the risk-free rate defined as the

monthly rate of one-year certificate of deposit. We use market risk Port_Beta1 and

illiquidity ratio ILLIQ as control variables in our regressions.

Table 6 reports the regression results. Model 1 of Table 6 shows that, without any

control variable, Port_UEL significantly and positively explains future stock returns,

demonstrating that there exists an UEL premium for China’s A-shares. After we control

for market risk and transaction cost proxied by Amihud (2002)’s illiquidity ratio, Model

2 of Table 6 shows that UEL still maintains its significantly explanatory power for stock

returns.

Model 3 to Model 6 of Table 6 examine the liquidity risk premium for China’s

A-shares. Our results show that only the liquidity commonality risk Port_Beta2 and the

overall liquidity risk Port_Beta5 demonstrate significantly explanatory power on future

stock returns, indicating that liquidity commonality risk is the most important

dimension of liquidity risk for China’s A-shares.

By adding Port_UEL into the regression equations with liquidity risk measures,

from Model 7 to Model 10, we find that Port_UEL still maintains its explanatory power

on future stock returns, showing that, in addition to traditional liquidity risk measures,

27

the comovement between individual stock liquidity and market uncertainty is also an

important dimension which cannot be ignored to price cross-sectional stock returns.

(Insert Table 6 here)

4. Conclusion

We examine whether investors care about market uncertainty when they trade

stocks and whether the uncertainty elasticity of liquidity is priced in the China’s A-

shares market. We find stocks with higher UEL are associated with lower share price,

smaller size, lower stock liquidity, and less investor attention. In addition, stocks with

higher UEL also have higher market risk and liquidity risk. Furthermore, the highest

UEL decile portfolio significantly outperforms the lowest UEL decile portfolio by 0.88%

per month from May 2004 to April 2018 for China’s A-shares. Our results further show

that the UEL premium is highly correlated with the size premium. Moreover, the UEL

premium matters most for illiquid, less investor attention, high market risk, and high

liquidity risk stocks. Finally, our findings show that, in addition to transaction cost,

market risk, and liquidity risk under the Acharya and Pedersen (2005)’s LCAPM

framework, UEL provides additional explanatory power for cross-sectional stock

returns.

Since there is no market maker to provide liquidity in the China’s A-shares

market, our finding that investors require a UEL premium in such a public trader

dominated stock market implies a similar finding may also exist in a market without

market makers. We leave this interesting investigation for future research.

28

References Acharya, V.V., Pedersen, L.H., 2005. Asset pricing with liquidity risk. Journal of Financial Economics 77, 375 – 410. Amihud, Y., 2002. Illiquidity and stock returns: cross-section and time-series effects. Journal of Financial Markets 5, 31 – 56. Armstrong, C.S., Core, J.E., Taylor, D.J., Verrecchia, R.E., 2011. When does information asymmetry affect the cost of capital? Journal of Accounting Research 49, 1–40. Bansal, R., Kiku, D., Shaliastovich, I., Yaron, A., 2014. Volatility, the macroeconomy, and asset prices. Journal of Finance 69, 2471 – 2511. Barillas, F., Shanken, J., 2018. Comparing asset pricing models. Journal of Finance 73, 715 – 754. Chordia, T., Roll, R., Subrahmanyam, A., 2000. Commonality in liquidity. Journal of Financial Economics 56, 3 – 28. Chung, K.H, Chuwonganant, C., 2014. Uncertainty, market structure, and liquidity. Journal of Financial Economics 113, 476 – 499. Cooper, M.J., Gulen, H., Schill, M.J., 2008. Asset growth and the cross-section of stock returns. Journal of Finance 63, 1609 – 1651. Fama, E.F., MacBeth, J.D., 1973. Risk, return, and equilibrium: empirical tests. Journal of Political Economy 81, 607 – 636. Fama, E.F., French, K.R., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427 – 465. Fama, E.F., French, K.R., 2015. A five-factor asset pricing model. Journal of Financial Economics 116, 1 – 22. Fama, E.F., French, K.R., 2018. Choosing factors. Journal of Financial Economics 128, 234 – 252. Goyenko, R.Y., Holden, C.W., Trzcinka, C.A., 2009. Do liquidity measures measure liquidity? Journal of Financial Economics 92, 153 – 181. Hameed, A., Kang, W., Viswanathan, S., 2010. Stock market declines and liquidity.

29

Journal of Finance 65, 257 – 293. Hou, K., Moskowitz, T.J., 2005. Market frictions, price delay, and the cross-section of expected returns. Review of Financial Studies 18 (3), 981-1020. Lee, K.H., 2011. The world price of liquidity risk. Journal of Financial Economics 99, 136 – 161. Lesmond, D.A., Ogden, J.P., Trzcinka, C.A., 1999. A new estimate of transaction costs. Review of Financial Studies 12, 1113 – 1141. Liao, L., Liu, B., Wang, H., 2014. China’s secondary privatization: perspectives from the split-share structure reform. Journal of Financial Economics 113, 500 – 518. Liu, W., 2006. A liquidity-augmented capital asset pricing model. Journal of Financial Economics 82, 631 – 671. Lam, K., Tam, L., 2011. Liquidity and asset pricing: evidence from the Hong Kong stock market. Journal of Banking and Finance 35, 2217 – 2230. Lou, X., Shu, T., 2017. Price impact or trading volume: Why is the Amihud (2002) measure priced? Review of Financial Studies 30, 4481 – 4520. Madhavan, A., 1992. Trading mechanism in securities markets. Journal of Finance 47, 607 – 641. Naes, R., Skjeltorp, J.A., ØDegaard, B.A., 2011. Stock market liquidity and the business cycle. Journal of Finance 66, 139 – 176. Novy-Marx, R., 2013. The other side of value: The gross profitability premium. Journal of Financial Economics 108 (1), 1-28. Pastor, L., Stambaugh, R.F., 2003. Liquidity risk and expected stock returns. Journal of Political Economy 111, 642 – 685.

30

Table 1 Descriptive statistics This table reports descriptive statistics of China’s A-shares in the end of April from 2004 to 2017. From May in year t-1 to April in year t during 2004 to 2017, we require our sample A-shares to have at least 180 trading days and positive book equity in the latest annual report. To estimate individual UEL or betas in the April end of each year from 2004 to 2017, we require our sample firms to have past 60 months’ (at least 36 months) return observations. Port_UEL is the uncertainty elasticity of liquidity (change in Amihud (2002)’s illiquidity ratio in response to change in market volatility) estimated by the portfolio approach with 100 size and individual UEL sorted portfolios from May 2004 to April 2018. PRC is a firm’s average daily share price from May in year t-1 to April in year t. SIZE is a firm’s market capitalization in the end of April in year t. BM is a firm’s book to market equity ratio in the end of December in year t-1. GP is a firm’s gross profitability defined as dividing the difference between sales and cost of goods sold by the lagged total asset in the end of December in year t-1. INV is a firm’s asset growth rate in the end of December in year t-1. RET(-12,-2) is a firm’s cumulative stock return from May in year t-1 to March in year t. VOLA is a firm’s daily return volatility from May in year t-1 to April in year t. ILLIQ is a firm’s daily average Amihud (2002)’s illiquidity ratio defined as absolute return divided by dollar trading volume in millions from May in year t-1 to April in year t. TRD is a firm’s number of trading days from May in year t-1 to April in year t. FLOAT is a firm’s daily average tradable shares’ percentage from May in year t-1 to April in year t. IO is a firm’s institutional ownership including mutual funds, QFIIs, security companies, insurance companies, social security funds, trust funds, financial companies, banks, and non-financial public firms in the end of December in year t-1. ANA is a firm’s unique number of analysts who provide earnings forecasts in year t-1. EMP is a firm’s number of employees in the end of December in year t-1. SH is a firm’s number of shareholders in the end of December in year t-1. We follow Acharya and Pedersen (2005)’s liquidity capital asset pricing (LCAPM) model, apply Amihud (2002)’s illiquidity ratio as the liquidity measure, and use the portfolio approach with 100 size and individual beta sorted portfolios to estimate a firm’s following betas from May 2004 to April 2018. Market beta Port_Beta1 is the correlation between individual stock return and market return. Liquidity commonality Port_Beta2 is the correlation between individual stock liquidity innovation and market liquidity innovation. Port_Beta3 is the correlation between individual stock return and market liquidity innovation. Port_Beta4 is the correlation between individual stock liquidity innovation and market return. Port_Beta 5 = Port_Beta2 – Port_Beta3 – Port_Beta4.

Variable Mean 1st Quartile Median 3rd Quartile SD Port_UEL 0.85 0.67 0.84 0.99 0.23 PRC 11.81 5.98 9.04 14.24 10.28 SIZE 12674.19 2301.00 4540.51 9494.40 51645 BM 0.48 0.24 0.39 0.61 0.54 GP 3.91% 0.10% 2.61% 6.54% 15.25% INV 26.42% 0.67% 9.47% 22.13% 341.21% RET(-12,-2) 20.91% -21.03% 2.11% 41.49% 65.99% VOLA 2.98% 2.28% 2.77% 3.49% 0.98% ILLIQ 0.0017 0.0002 0.0005 0.0014 0.0035 TRD 235.80 236 240 242 11.40 FLOAT 71.94% 49.51% 75.58% 99.49% 25.79% IO 4.61% 0.43% 2.60% 6.70% 6.10% ANA 5.07 0.00 2.00 7.00 7.00 EMP 6605 980 2200 5000 24580 SH 63876 22000 39000 70000 91690 Port_Beta1 1.08 1.06 1.10 1.13 0.09 Port_Beta2 0.00026 0.00006 0.00013 0.00028 0.00051 Port_Beta3 -0.00364 -0.00494 -0.00384 -0.00280 0.00183 Port_Beta4 -0.00374 -0.00513 -0.00277 -0.00135 0.00619 Port_Beta5 0.00764 0.00471 0.00649 0.00955 0.00670 Firm-year observations

17781

31

Table 2 Average firm characteristics of portfolios sorted by portfolio UEL This table reports average firm characteristics of portfolios sorted by portfolio UEL in the end of April from 2004 to 2017. Port_UEL is the uncertainty elasticity of liquidity estimated from the portfolio approach. Firm characteristics include share price PRC, market capitalization SIZE, book to market ratio BM, gross profitability GP, asset growth INV, cumulative stock return from past year skipping one month RET(-12,-2), and individual stock return volatility VOLA. Liquidity measures include illiquidity ratio ILLIQ, number of trading days TRD, and tradable shares’ percentage FLOAT. Investor attention variables include institutional ownership IO, analyst coverage ANA, number of employees EMP, and number of shareholders SH. Liquidity capital asset pricing model (LCAPM) risk measures include the following betas. Port_Beta1 measures the correlation between individual stock return and market return. Port_Beta2 measures the correlation between individual stock liquidity innovation and market liquidity innovation. Port_Beta3 measures the correlation between individual stock return and market liquidity innovation. Port_Beta4 measures the correlation between individual stock liquidity and market return. Port_Beta 5 = Port_Beta2 – Port_Beta3 – Port_Beta4. t-statistics are in the parentheses. ***, **, * denote statistical significance at 1%, 5%, and 10% level respectively.

Port_UEL Rank

0 (low) 1 2 3 4 5 6 7 8 9 (high) 9 – 0

Port_UEL 0.46 0.61 0.68 0.74 0.81 0.87 0.94 1.00 1.09 1.25 0.79*** (214.82)

Firm Characteristics

PRC 15.40 13.85 13.03 12.82 11.58 10.04 9.73 9.28 9.05 9.07 -6.33*** (-7.02)

SIZE 50216.93 13380.75 13042.41 16435.76 5876.33 4322.93 4210.60 3061.29 2930.61 2438.86 -47778.07*** (-5.67)

BM 0.60 0.47 0.49 0.48 0.47 0.49 0.47 0.45 0.45 0.42 -0.18*** (-3.62)

GP 7.45% 7.92% 5.72% 5.32% 4.61% 2.70% 2.12% 0.94% 0.90% 0.30% -7.15%*** (-12.45)

INV 26.87% 59.99% 30.49% 35.29% 36.46% 13.94% 13.10% 10.53% 9.95% 14.75% -12.12%* (-1.98)

RET(-12,-2) 24.61% 26.16% 25.36% 25.34% 21.68% 20.93% 19.43% 17.32% 17.77% 15.21% -9.40%* (-2.04)

VOLA 2.77% 2.96% 2.94% 3.00% 3.04% 3.05% 3.04% 3.08% 3.07% 3.09% 0.32%*** (5.10)

Liquidity Measures

ILLIQ 0.0008 0.0011 0.0012 0.0015 0.0017 0.0021 0.0025 0.0029 0.0028 0.0032 0.0024** (2.77)

TRD 236.43 235.25 235.26 235.60 235.14 235.82 235.95 235.46 235.39 235.12 -1.31 (-1.10)

FLOAT 66.56% 65.34% 67.67% 67.20% 67.76% 69.64% 70.18% 70.50% 69.59% 70.36% 3.80%** (2.52)

32

Investor Attention

IO 6.17% 6.55% 5.96% 5.24% 4.79% 3.93% 3.70% 3.29% 2.93% 2.78% -3.40%*** (-9.96)

ANA 11.10 7.10 6.86 5.91 4.64 3.26 2.97 2.01 1.79 1.62 -9.48*** (-7.40)

EMP 22861 6950 7376 8621 3676 3085 2759 2295 2102 2000 -20860*** (-5.90)

SH 147541 74714 73739 74116 54087 48096 45980 37694 38220 31718 -115823*** (-9.82)

LCAPM Risk

Port_Beta1 1.03 1.07 1.06 1.07 1.08 1.09 1.09 1.11 1.10 1.11 0.07*** (19.58)

Port_Beta2 0.00007 0.00011 0.00014 0.00018 0.00015 0.00022 0.00028 0.00052 0.00035 0.00055 0.00048*** (22.30)

Port_Beta3 -0.00397 -0.00347 -0.00335 -0.00354 -0.00334 -0.00344 -0.00373 -0.00387 -0.00371 -0.00392 0.00005 (1.47)

Port_Beta4 -0.00149 -0.00205 -0.00260 -0.00299 -0.00312 -0.00388 -0.00417 -0.00618 -0.00472 -0.00610 -0.00461*** (-22.06)

Port_Beta5 0.00553 0.00563 0.00609 0.00672 0.00661 0.00754 0.00818 0.01057 0.00878 0.01056 0.00503*** (25.16)

33

Table 3 Determinants of Port_UEL This table reports the Fama-MacBeth (1973) regression results of determinants of Port_UEL from 2004 to 2017. Port_UEL is the uncertainty elasticity of liquidity estimated from the portfolio approach. Log(PRC) is the logarithm of share price. Log(SIZE) is the logarithm of market capitalization. Log(BM) is the logarithm of book to market ratio. GP is the gross profitability. INV is the asset growth. RET(-12,-2) is the cumulative stock return from May in year t-1 to March in year t. VOLA is individual stock return volatility. ILLIQ is Amihud (2002)’s illiquidity ratio. Log(TRD) is the logarithm of number of trading days. FLOAT is the tradable shares’ percentage. IO is the institutional ownership. Log(1+ANA) is the logarithm of 1 plus analyst coverage. Log(EMP) is the logarithm of number of employees. Log(SH) is the logarithm of number of shareholders. Port_Beta1 measures the correlation between individual stock return and market return. Port_Beta2 measures the correlation between individual stock liquidity innovation and market liquidity innovation. Port_Beta3 measures the correlation between individual stock return and market liquidity innovation. Port_Beta4 measures the correlation between individual stock liquidity and market return. Newey-West adjusted t-statistics (with lag = 3) are reported in the parenthesis. ***, **, * denote statistical significance at 1%, 5%, and 10% level respectively.

Model 1 Model 2 Model 3 Model 4 Intercept 2.2943***

(41.31) -0.4409 (-1.18)

1.8222*** (39.80)

0.2204*** (11.37)

Log(PRC) -0.0153*** (-4.70)

Log(SIZE) -0.1682*** (-30.96)

Log(BM) -0.0006 (-0.35)

GP -0.0103 (-0.46)

INV 0.0025 (1.00)

RET(-12,-2) 0.0021 (0.43)

VOLA 0.0466 (0.12)

ILLIQ 216.3400** (3.01)

Log(TRD) 0.1927** (2.90)

FLOAT 0.2027*** (3.48)

IO -0.3419*** (-16.50)

Log(1+ANA) -0.0886*** (-7.71)

Log(EMP) -0.0172*** (-4.69)

Log(SH) -0.0695*** (-25.93)

Port_Beta1 0.5295*** (30.29)

Port_Beta2 94.6975*** (20.63)

Port_Beta3 -2.5468*** (-4.37)

Port_Beta4 -5.3466*** (-16.06)

ADJ-RSQ 0.4997 0.2098 0.3139 0.1388 Observations 17781

34

Table 4 Portfolio returns and 6-factor model analysis for portfolios sorted by Port_UEL This table reports equally-weighted portfolio returns and 6-factor model analysis for portfolios sorted by Port_UEL from May 2004 to April 2018. Panel A reports the average portfolio returns for the whole period (168 months), the period when the market risk premium MKTRF is greater or equal to zero (94 months), and the period when the market risk premium is less than zero (74 months). Panel B reports the 6-factor (Fama and French (2015) five factors plus the momentum factor) model analysis for the portfolio excess return for the whole period. Alpha is the intercept term. MKTRF is the market risk premium. SMB is the return difference between small and big stocks. HML is the return difference between high book to market and low book to market stocks. RMW is the return difference between robust operating profitability and weak operating profitability stocks. CMA is the return difference between conservative in asset growth and aggressive in asset growth stocks. UMD is the return difference between past winner (up) and past loser (down) stocks. Newey-West adjusted t-statistics (with lag = 4) are reported in the parenthesis. ***, **, * denote statistical significance at 1%, 5%, and 10% level respectively. Panel A

Port_UEL Rank

0 (low) 1 2 3 4 5 6 7 8 9 (high) 9 – 0

RAW (whole period, 168 months)

1.44%** (2.00)

1.48%* (1.92)

1.49%* (1.94)

1.59%** (2.01)

1.54%* (1.88)

1.92%** (2.29)

2.01%** (2.41)

2.18%** (2.50)

2.09%** (2.42)

2.32%** (2.60)

0.88%** (2.06)

RAW (MKTRF>=0, 94 months)

7.46%*** (11.31)

7.82%*** (10.57)

7.75%*** (10.52)

7.97%*** (10.31)

8.06%*** (10.11)

8.38%*** (9.54)

8.53%*** (10.12)

8.85%*** (9.52)

8.68%*** (9.54)

9.09%*** (9.51)

1.62%** (2.61)

RAW (MKTRF<0, 74 months)

-6.21%*** (-8.26)

-6.57%*** (-8.29)

-6.45%*** (-8.11)

-6.53%*** (-8.05)

-6.74%*** (-7.61)

-6.28%*** (-7.27)

-6.28%*** (-7.12)

-6.27%*** (-6.93)

-6.27%*** (-6.94)

-6.27%*** (-6.74)

-0.05% (-0.10)

Panel B

Port_UEL Rank

0 (low) 1 2 3 4 5 6 7 8 9 (high) 9 – 0

Alpha 0.0028 (1.48)

0.0013 (0.64)

0.0008 (0.47)

0.0007 (0.44)

-0.0014 (-0.85)

0.0017 (1.17)

0.0022 (1.60)

0.0030** (2.45)

0.0022* (1.66)

0.0041*** (3.08)

0.0013 (0.87)

MKTRF 1.0197*** (28.39)

1.0243*** (26.33)

0.9945*** (29.90)

0.9934*** (25.00)

0.9913*** (25.72)

0.9810*** (34.58)

0.9784*** (31.88)

0.9888*** (42.44)

0.9832*** (40.98)

0.9854*** (41.64)

-0.0343 (-1.44)

SMB 0.1199** (2.20)

0.3712*** (4.81)

0.4635*** (6.81)

0.5803*** (8.20)

0.7586*** (11.30)

0.8572*** (13.90)

0.8897*** (15.89)

1.0080*** (21.42)

0.9943*** (16.36)

1.0577*** (19.38)

0.9378*** (24.03)

HML 0.2464*** (2.83)

0.1585 (1.35)

0.1765* (1.86)

0.2629** (2.53)

0.2994*** (3.08)

0.3292*** (4.25)

0.3170*** (3.76)

0.2343*** (3.55)

0.2555*** (3.28)

0.2416*** (3.54)

-0.0049 (-0.09)

RMW -0.2307 (-1.58)

-0.3736*** (-2.69)

-0.3743*** (-2.94)

-0.4397*** (-3.37)

-0.4050*** (-3.02)

-0.4625*** (-3.76)

-0.4041*** (-3.39)

-0.4515*** (-5.18)

-0.4091*** (-4.47)

-0.5119*** (-5.03)

-0.2812*** (-2.79)

CMA 0.1171 (0.82)

-0.0160 (-0.09)

0.0329 (0.23)

-0.1711 (-1.02)

-0.1166 (-0.66)

-0.1867 (-1.36)

-0.1453 (-1.26)

-0.1478* (-1.66)

-0.0814 (-0.66)

-0.1456 (-1.55)

-0.2627** (-2.05)

UMD 0.1648** (2.41)

0.1846** (2.24)

0.2486*** (3.86)

0.1594** (1.99)

0.2603*** (4.05)

0.2678*** (4.69)

0.1623*** (2.77)

0.0260 (0.39)

0.1008* (1.91)

0.0908** (1.99)

-0.0740 (-1.11)

ADJ-RSQ 0.9351 0.9346 0.9430 0.9426 0.9496 0.9594 0.9628 0.9723 0.9724 0.9740 0.9039 Observations 168

35

Table 5 UEL premium of portfolios sorted by firm characteristics This table reports UEL premium of portfolios sorted by firm characteristics from May 2004 to April 2018. In the April end from 2004 to 2017, within each quintile portfolio sorted by firm characteristic, we further sort stocks into quintile portfolios on the basis of Port_UEL, apply each stock’s firm characteristic rank and Port_UEL rank to May in year t to April in year t+1, and calculate equally-weighted portfolio returns of those 25 portfolios, and take the return difference between high UEL ranked and low UEL ranked portfolio return within each firm characteristic group. Panel A reports UEL premium for portfolios sorted by basic firm characteristics. Firm characteristics include share price PRC, market capitalization SIZE, book to market ratio BM, gross profitability GP, asset growth INV, cumulative stock return from past year skipping one month RET(-12,-2), and individual stock return volatility VOLA. Panel B reports UEL premium for portfolios sorted by liquidity measures. Liquidity measures include illiquidity ratio ILLIQ, number of trading days TRD, and tradable shares’ percentage FLOAT. Panel C reports UEL premium for portfolios sorted by investor attention variables. Investor attention variables include institutional ownership IO, analyst coverage ANA, number of employees EMP, and number of shareholders SH. Liquidity capital asset pricing model (LCAPM) risk measures include the following betas. Panel D reports UEL premium for portfolios sorted by liquidity capital asset pricing model (LCAPM) risk measures. Port_Beta1 measures the correlation between individual stock return and market return. Port_Beta2 measures the correlation between individual stock liquidity innovation and market liquidity innovation. Port_Beta3 measures the correlation between individual stock return and market liquidity innovation. Port_Beta4 measures the correlation between individual stock liquidity and market return. Port_Beta 5 = Port_Beta2 – Port_Beta3 – Port_Beta4. t-statistics are in the parentheses. ***, **, * denote statistical significance at 1%, 5%, and 10% level respectively. Panel A Firm characteristics

Characteristic rank 0 1 2 3 4 PRC group UEL premium

0.57% (1.51)

0.88%** (2.42)

0.75%*** (2.65)

0.55% (1.49)

0.55% (1.31)

SIZE group UEL premium

0.21% (1.11)

-0.15% (-0.85)

0.09% (0.60)

0.04% (0.22)

0.09% (0.38)

BM group UEL premium

0.72%* (1.66)

0.99%** (2.58)

0.98%*** (3.05)

0.74%** (2.11)

0.54% (1.30)

GP group UEL premium

0.66%* (1.95)

0.71%* (1.94)

0.70%** (2.11)

1.14%*** (3.15)

0.54% (1.54)

INV group UEL premium

0.81%** (2.28)

0.91%** (2.62)

0.89%** (2.38)

0.65%* (1.69)

0.86%** (2.12)

RET(-12,-2) group UEL premium

0.73%* (1.82)

1.12%*** (2.96)

0.87%** (2.50)

0.74%** (2.11)

0.51% (1.31)

VOLA group UEL premium

0.84%** (2.02)

0.80%** (2.13)

1.00%*** (2.75)

1.21%*** (3.38)

0.74%* (1.76)

Panel B Liquidity measures

Characteristic rank 0 1 2 3 4 ILLIQ group UEL premium

-0.05% (-0.11)

0.12% (0.49)

0.27% (0.96)

0.47%** (2.30)

0.70%*** (2.86)

TRD group UEL premium

0.72%** (1.99)

0.82%** (2.14)

0.58% (1.46)

0.90%** (2.14)

0.86%** (2.36)

FLOAT group UEL premium

1.26%*** (2.98)

0.64%* (1.68)

0.61% (1.52)

0.38% (1.03)

0.83%** (2.24)

36

Panel C Investor attention variables Characteristic rank 0 1 2 3 4 IO group UEL premium

0.83%*** (3.42)

0.86%** (2.38)

0.94%** (2.58)

0.45% (1.03)

0.48% (1.21)

ANA group UEL premium

0.95%*** (3.71)

0.94%*** (3.55)

1.15%*** (4.05)

0.68%* (1.88)

0.44% (1.09)

EMP group UEL premium

0.79%** (2.60)

0.78%*** (2.73)

0.89%*** (2.81)

0.59%* (1.75)

0.65% (1.54)

SH group UEL premium

1.21%*** (2.90)

0.59%* (1.80)

0.55%* (1.86)

0.43% (1.25)

0.32% (0.75)

Panel D LCAPM risk measures

Characteristic rank 0 1 2 3 4 Port_Beta1 group UEL premium

0.50% (1.25)

0.62%* (1.80)

0.65%** (1.99)

0.96%*** (2.81)

1.46%*** (2.99)

Port_Beta2 group UEL premium

0.05% (0.18)

0.15% (0.65)

0.27% (1.29)

0.40%** (2.19)

0.62%*** (2.62)

Port_Beta3 group UEL premium

0.83%* (1.96)

0.70%* (1.96)

0.91%** (2.04)

0.54% (1.50)

0.75%*** (3.15)

Port_Beta4 group UEL premium

0.42%** (1.99)

0.25% (1.33)

0.14% (0.73)

-0.01% (-0.06)

1.19%** (2.22)

Port_Beta5 group UEL premium

0.68% (1.53)

0.56% (1.49)

0.51% (1.43)

0.25% (1.12)

0.36%* (1.82)

37

Table 6 Fama-MacBeth regression results of excess returns on UEL and liquidity risk measures This table reports Fama-MacBeth (1973) regression results of stock excess returns (raw return minus monthly 1-year certificate of deposit rate) on UEL and Acharya and Pedersen (2005)’s liquidity capital asset pricing model (LCAPM) risk measures from May 2004 to April 2018. Port_UEL measures the uncertainty elasticity of liquidity (change in Amihud (2002)’s illiquidity ratio in response to change in market volatility). Port_Beta1 measures the correlation between individual stock return and market return. Port_Beta2 measures the correlation between individual stock liquidity innovation and market liquidity innovation. Port_Beta3 measures the correlation between individual stock return and market liquidity innovation. Port_Beta4 measures the correlation between individual stock liquidity and market return. Port_Beta 5 = Port_Beta2 – Port_Beta3 – Port_Beta4. ILLIQ is Amihud (2002)’s illiquidity ratio. Newey-West adjusted t-statistics (with lag = 4) are reported in the parenthesis. ***, **, * denote statistical significance at 1%, 5%, and 10% level respectively.

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9 Model 10 Intercept 0.0047

(0.50) 0.0074 (0.93)

0.0108 (1.39)

0.0089 (1.10)

0.0102 (1.32)

0.0094 (1.22)

0.0084 (1.05)

0.0065 (0.78)

0.0077 (0.97)

0.0072 (0.91)

Port_UEL 0.0133** (2.58)

0.0084** (2.08)

0.0078** (1.98)

0.0084** (2.07)

0.0080** (2.04)

0.0078** (2.01)

Port_Beta2 2.2211*** (2.61)

1.8298** (2.47)

Port_Beta3 -0.1923 (-0.98)

-0.1905 (-0.95)

Port_Beta4 -0.0658 (-1.64)

-0.1144* (-1.85)

Port_Beta5 0.0794** (2.14)

0.1292** (2.22)

Port_Beta1 -0.0014 (-0.14)

0.0012 (0.11)

0.0023 (0.22)

0.0015 (0.14)

0.0016 (0.15)

-0.0020 (-0.19)

-0.0011 (-0.11)

-0.0016 (-0.16)

-0.0016 (-0.15)

ILLIQ 5.2900** (2.13)

5.4807* (1.71)

6.2831* (1.77)

5.9626* (1.80)

5.8066* (1.76)

4.6363** (2.04)

5.2293** (2.10)

5.0582** (2.13)

4.9368** (2.09)

ADJ-RSQ 0.0174 0.0309 0.0238 0.0240 0.0240 0.0239 0.0317 0.0323 0.0316 0.0316 Observations 207380