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Investor Sentiment and the Fragility of Liquidity

Chunmei Lin1

November, 2011

Abstract

This paper studies the relationship between investor sentiment and the fragility of liquidity: the

property that a small funding shock to the investors’ capital can lead to a large jump in stock

illiquidity. I argue that investors’ negative sentiment plays an important role in amplifying the

market liquidity impact of funding shocks to investors. I test this hypothesis using data on

monthly outflows from mutual fund investors of a large cross-section of US stocks over the

period 1991-2009. I define the variable OutFlow to present the percent of the shares of a given

stock owned by mutual funds that is subjected to mutual fund outflows. Using a vector

autoregression (VAR) framework, I find that an OutFlow equivalent to 1% of a stock`s market

value leads to a 22% increase in Amihud illiquidity. Given the same level of mutual fund

outflows, a one-standard-deviation increase in negative sentiment leads to an additional 33%

jump in illiquidity. In the cross-section of stocks, liquidity is more fragile among stocks which

are more sensitive to shifts in investor sentiment. Furthermore, I find economically significant

returns for liquidity provision during periods of negative sentiment.

1 Chunmei Lin is from the Department of Finance, NUS Business School, National University of Singapore. I thank Xi Dong, Lily Fang, Allaudeen Hameed, Wenjin Kang, Lilian Ng, David Thesmar and Hong Zhang for their comments. I acknowledge the Doctoral Dissertation Support Award from University of Michigan-Dearborn Betty F. Elliott Initiative. All errors are my own.

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1. Introduction

The liquidity spiral induced by the feedback effect between funding liquidity (i.e., the ease with

which investors can obtain funding) and market liquidity (i.e., the ease with which stock is traded)

presents a significant challenge for institutional managers. The mutual reinforcement between

funding constraint and the price impact of liquidations creates an amplification mechanism that

is powerful enough to lead to fragility in the stock market. For example, Brunnermeier and

Pederson (2009) describes a mechanism in which negative funding shocks force speculators to

de-lever their positions in times of crisis, leading to the disappearance of liquidity. In

equilibrium, it is possible that a small funding shock to the investors can lead to a sharp

reduction in stock liquidity. In this paper, (following Brunnermeier and Pederson (2009)), I use

the term “fragility of liquidity” to refer to the elasticity of stock liquidity with respect to investors’

funding shock. A stock’s market liquidity is more fragile if the same funding shock triggers a

larger reduction in liquidity.

This paper proposes a behavioral amplification mechanism for the relationship between

funding liquidity and market liquidity ,using capital outflow as a proxy for shocks to funding

available to mutual fund investors. During market turmoil, financial intermediaries such as hedge

funds and mutual funds face tighter financing conditions. These include both higher margin

requirements (in the case of hedge funds) and an erosion of the capital base through net fund

withdrawals from mutual funds. I argue that investors’ negative sentiment plays an important

role in amplifying the market liquidity impact of funding shocks to a stock’s mutual fund

investors, which I call the “fragility of liquidity”.

Investor sentiment, as proposed by Baker and Wurgler (2006), refers to fluctuations in risk

tolerance or to overly optimistic or pessimistic cash flow forecasts. In either case, sentiment

should have an impact on stock market that is distinct from the impact of fundamentals (changes

in the investment opportunity set, “rational” cash flow forecasts, interest rates, etc.). Investor

sentiment is generally attributed to individual, retail investors (see, for example, Lee, Shleifer,

and Thaler (1991)).The role of investor sentiment comes into play at both the demand and supply

of market liquidity. In the demand side, negative sentiment can cause investors to withdraw

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money from mutual funds and cause mutual funds to liquidate their portfolio, creating demand

for liquidity. By offering on-demand withdrawals, mutual funds expose themselves to investor

actions that are affected by investor sentiments. Indeed, a few studies use mutual fund flows as

proxy of investor sentiment because most of mutual fund investors are generally considered to be

the least informed investors in the market and they delegate their investment management to

fund managers (Brown et al. (2005), Frazzini and Lamont (2008)). In the supply side, Kaniel,

Saar and Titman (2008) document that contrarian tendency of individuals leads them to act as

liquidity providers to institutions that require immediacy. In a sense, individuals act as the

irrational market makers as modeled in Baker and Stein (2004). As these market makers are not

formally required to continuously provide market-making services, their supply of liquidity

could easily be withdrawn when they are pessimistic about the stock market.

I focus on the liquidity shocks induced by outflows from open-ended mutual funds. Open-

ended mutual funds, though not leveraged as hedge funds, are extremely reliant on outside

capital to fund its investment opportunities. Because most funds are evaluated against all-equity

benchmarks, few maintain significant cash balances (see, for example, Coval and Stafford

(2007)). When capital is in immediate demand, mutual funds without significant cash reserves

have no choice but to sell holdings quickly, creating demand of liquidity (e.g., Ben-Rephael,

Coval and Stafford (2007), Edelen and Warther (2001), Kandel and Wohl (2011), Lou (2010)).

The demand for liquidity calls for its supply; if investor sentiment deteriorates, retail investors

tend to follow the crowd to sell instead of acting as liquidity providers. Furthermore, the fear of

experiencing future liquidity shocks themselves can actually induce potential arbitrageurs to sell

(rather than purchase) and the market becomes illiquid just when liquidity is most needed.

Liquidity dry-ups are not caused by funding liquidity shocks per se, but by the fear when

investor confidence wanes. With a limited supply of liquidity in the market during a general

crisis of confidence, this sudden reduction in liquidity accelerates the decline in asset prices and

induces more withdrawal of capital. This suggests that negative investor sentiment would

amplify the market liquidity impact of funding shocks to mutual fund investors.

I first investigate the interaction between mutual fund outflows and stock market liquidity

for individual stocks traded in NYSE/Amex over the period 1991–2009. To capture the percent

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of the shares of a given stock owned by mutual funds that is subjected to mutual fund outflows, I

construct the monthly time-series of OutFlow for each stock. The idea is that capital flows are

from individual investors to mutual funds and then from mutual funds to individual stocks base

on funds` portfolio holding. I define the precise formula of OutFlow later, but the following

example shows the basic idea. Suppose at month 0, a stock is held by three funds: fund A with

$10 billion in assets, fund B with $40 billion and fund C with $20 billion. Suppose at month 1,

fund A has an outflow of $1 billion; fund B fund has an outflow of $2 billion, while fund C has

an inflow. Suppose that at month 0 we observe that fund A has 10% of its assets in the stock;

fund B has 5% of its assets in the stock; fund C has 5% of its assets in t he stock. Assume that

outflows pass to the stock according to the holding portfolios of funds. The outflow passing to

the stock from fund A is $1 billion, from fund B is $2 billion and from fund C is 0. The

aggregate mutual fund outflow passing to the stock is $3 billion. If the stock has $12 billion in

market capitalization in month 0, the stock level OutFlow is 25% of the stock`s market value.

Next, I construct the Amihud (2002) price impact of trade measure to capture liquidity. This

measure is the absolute return divided by dollar trading volume. Thus it measures the price

impact of trading. The higher is this measure, the higher is the price impact, and the lower the

liquidity. This measure is consistent with theoretical research such as Grossman and Miller (1988)

which defines liquidity based on price impact as a result of buying and selling pressure. I

formulate a VAR system with three endogenous variables: OutFlow, illiquidity, and return as the

benchmark model. I include return in VAR system because previous studies identify an

important relation of both mutual fund flows and illiquidity with stock returns. I control for any

endogenous interaction with returns in all my analyses. I find that, on average, an OutFlow

equivalent to 1% of a stock`s market capitalization leads to a 22% standard deviation increase in

illiquidity, after controlling the effect of market liquidity, market return and the TED spread, a

proxy for the market wide funding liquidity.

I then proceed to estimate the VAR model with the presence of the interaction variable

negative sentiment. I use both the Baker and Wurgler (2006) investor sentiment index and the

University of Michigan Consumer Confidence Index as measures of investor sentiment. To

remove the effect of fundamentals from the University of Michigan’s consumer confidence index,

I regress the Consumer Sentiment Index on a set of variables that proxy for fundamental

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economic activity and take the residuals as the Orthogonalized Consumer Confidence Index. I

multiply both sentiment indexes by -1 and denote them as negative sentiment. I discover a

critical role for negative investor sentiment in the outflow-illiquidity relationship. Given an

OutFlow of 1% of a stock`s market capitalization, a one-standard-deviation increase in negative

sentiment leads to an additional 33% (38%) jump in illiquidity using the Baker and Wurgler

sentiment measure (Orthogonalized University of Michigan Consumer Confidence Sentiment).

An important assumption common to all noise trader models is that uninformed noise

trader demand aggregates across a population of individuals, that is, individuals buy or sell in

concert with each other (See e.g., DeLong, Shleifer, Summers, and Waldmann (1990), Kumar

and Lee (2006)). Thus a small observed outflow from mutual fund investors may be interpreted

as a big selling pressure in the stocks they hold because irrational investors might overreact to

this pseudo-signal and follow the mutual funds to sell the stocks when they are pessimistic.

Moreover, arbitrageurs know that noise traders are pessimistic today and there will be resale

price risk caused by the possibility that noise trader will become even more pessimistic in the

future. Hence arbitrageurs will be less willing to provide liquidity to stocks that are more subject

to whims of investor sentiment. Base on these arguments, stocks that are more sensitive to shifts

in investor sentiment should be more fragile in liquidity. To directly test this hypothesis, I

construct the sentiment beta on the basis of Baker and Wurgler (2006, 2007) methodology. I find

that stocks with high sentiment beta are more fragile in liquidity and hence outflows have

stronger impacts on liquidity.

Finally, using a zero-cost contrarian investment strategy as the measure of the return to

provide liquidity, I examine whether the cost of supplying liquidity depends on the state of

investor sentiment. The cost of providing liquidity is reflected in the temporary decrease in price

accompanying heavy trading and the subsequent increase as prices revert to fundamental values.

(e.g. Avramov, Chordia and Goyal (2006), Hameed, Kang and Viswanathan(2010)). The zero-

cost contrarian investment strategy yields an economically significant return of 0.88% (74%) per

week when conditioned on negative sentiment states for the Baker and Wurgler sentiment

measure (Orthogonalized University of Michigan Consumer Confidence Sentiment). This return

to provide liquidity is much higher than the unconditional return of 0.54%. Furthermore, I

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condition the return to provide liquidity on both state of investor sentiment and the state of

market returns, and find that the negative sentiment combined with down market give rise to a

weekly contrarian profit of 1.09% (1.13%) using the Baker and Wurgler sentiment measure

(Orthogonalized University of Michigan Consumer Confidence Sentiment). These numbers are

much higher than the 0.67% (0.66%) when the sentiment is positive in the down market. Overall,

my findings are consistent with the hypothesis that the cost of providing liquidity is much higher

when investor sentiment is negative.

This paper contributes to the recent literature on the amplification mechanisms in liquidity

crises .Numerous theoretical models point to liquidity shocks as a cause of financial crises.

(Adrian and Shin (2008, 2010), Brunnermeier and Pedersen (2009), Diamond and Rajan (2009),

Froot (2009), Gromb and Vayanos (2002), and Krishnamurthy (2010)). During periods of

financial crisis, a reinforcing mechanism between market liquidity and funding liquidity leads to

liquidity spirals and fragility—the property that a small shock can lead to a large jump in

illiquidity. Literature has proposed several explanations for the illiquidity amplification

mechanism. For example, binding margin constraints (Brunnermeier and Pederesen (2009)) and

the risk of experiencing future shocks, due to outflows (Shleifer and Vishny (1997)) can lead

investors to liquidate their holdings at the same time. During these episodes it is also hard to find

potential liquidity providers. As Duffie (2010), and Duffie and Strulovici (2011) show, the

frictions (such as the time to raise capital by intermediaries, the reputation concerns of fund

managers and the delays in processing information) preventing buying capital to move quickly to

temporary undervalued stocks are most significant during episodes of severe market turmoil. A

few empirical works focus on problems at hedge funds, which are thought to drive down stock

prices as they respond to margin call with liquidation. Boyson, Stahel, and Stulz (2010) link

hedge fund contagion in returns to liquidity shocks. Sadka (2010) shows that hedge funds with

high exposure to liquidity risk underperform during liquidity crises. Aragon and Strahan (2011)

argue that the failure of Lehman caused funding problems and losses at hedge funds that used it

as a prime broker. All these studies assume investors at play are rational. The role of irrational

investors in this illiquidity amplification mechanism, however, has not been a prime subject of

inquiry. This paper fills this gap by investigating the role of investor sentiment in the illiquidity

amplification mechanism. This paper also complements the empirical work by investigating a

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different channel for the feedback effect of funding liquidity and market liquidity, using mutual

fund outflows as the demand shocks to funding liquidity.

Second, the evidence presented in this paper pertains to the emerging literature on the

effect of investor sentiment on stock market outcomes. Baker and Wurgler (2006), Brown and

Cliff (2004), Lemmon and Portnaiguina (2006), Qiu and Welch (2004), and other papers have

investigated the role of investor sentiment in stock market returns. Yu and Yuan (2011) show

that sentiment has major effects on the mean-variance relationship in the stock market, with the

tradeoff between risks and expected returns emerging only in low sentiment periods. Baele,

Bekaert, and Inghelbrecht (2010) discuss sentiment and the time-series relationships between

government bond and stock market returns. Hwang (2011) provides evidence that a country’s

popularity among Americans affects U.S. investors’ demand for securities from that country and

causes security prices to deviate from their fundamental values. This paper contributes by

providing evidence on the amplification effect of negative sentiment on the interaction between

mutual fund outflows and stock market liquidity.

The results in this paper also complement a number of studies on the price impact of mutual

fund flows. Previous studies find that aggregate capital flows to mutual funds in a particular

sector or in a particular investment style affect both the contemporaneous and subsequent sector

returns or style returns.(See e.g., Warther (1995), Edelen and Warner (2001), Gompers and

Metrick (2001), Goetzmann and Massa (2003), Teo and Woo (2004)). Coval and Stafford (2007)

examine the price impact of extreme flows on individual stocks. Most of these studies focus on

the impact of mutual fund flows on stock return. This paper indentifies liquidity as an important

channel of the price impact of mutual fund flows.

The paper outline is as follows: Section II describes the sample, data sources, and key

variables. The methodology and results on the inter-temporal impact of negative sentiment on the

interaction of mutual fund flows and market liquidity are presented in Section III. Section IV

investigates the cross sectional relationship between sentiment and the fragility of liquidity.

Section V examines the cost of providing liquidity during different states of investor sentiments.

Section VI concludes.

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II. Data and Variables Construction

A. Investor sentiment index

I use two measures of investor sentiment in this paper. The first measure is the Baker and

Wurgler (2006) investor sentiment index. The data are obtained from Jeffrey Wurgler’s website

at www.stern.nyu.edu/_jwurgler. Baker and Wurgler (2006) form a composite sentiment index

that is the first principal component of six measures of investor sentiment. The six measures are

the closed-end fund discount, the NYSE share turnover, the number of IPOs, the average first-

day return of IPOs, the equity share in new issues, and the dividend premium. To remove

business cycle information, Baker and Wurgler (2006) first regress each of the raw sentiment

measures on a set of macroeconomics variables and use the residuals to build the sentiment index.

Baker and Wurgler (2007) show that the sentiment index has a highly significant correlation of

0.36 with speculative demand. This correlation is particularly suggestive that the overall

sentiment indexes do, to a large extent, capture a prevailing “greed” versus “fear” or “bullish”

versus “bearish” notion. The monthly composite Baker and Wurgler sentiment index is plotted in

Figure 1. This index reaches its most recent peak in the internet bubble. However, the index ends

at December 2007.

To capture the sentiment during the 2008-2009 crisis periods, I use the University of

Michigan Consumer Sentiment Index as the second measure for investor sentiment. I obtain the

University of Michigan Consumer Sentiment Index measure from the University Of Michigan

Surveys Of Consumers at www. Sca.isr.umich.edu. The consumer confidence index is measured

using survey methodology. The respondents are asked questions about their assessment of the

current and future economic conditions. Lemmon and Portniaguina (2006) use this measure to

explain the cross-section of the 25 Fama_French portfolios. Billet, Jiang and Rego (2010) show

that consumer sentiment contributes to investor sentiment in the market.

The consumer sentiment survey values reflect consumers beliefs about the fundamentals of

the economy as well as their over optimism or pessimism (investor sentiment). Since we need to

measure the excess optimism or pessimism, I remove the effect of fundamentals from the raw

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survey values. Specifically, I regress the University of Michigan’s Consumer Sentiment Index

on a set of variables that proxy for fundamental economic activity as the following equation:

�� 3 � �� (1)

�� is the original University of Michigan Consumer Sentiment Index. Industry production

growth rate (IP) is quarterly change in the natural logarithm of industry production. Default

spread (DEF) is measured at a monthly frequency, and is the difference between the yield to

maturity on Moody’s Baa-rated and Aaa-rated bonds, taken from the Federal Reserve Bank of St.

Louis.YLD3 is the monthly yield on the three-month Treasury bill. GDP is the GDP growth

measured as the quarterly change in the natural logarithm of adjusted GDP. Consumption growth

(CONS) is measured as the quarterly change in the natural logarithm of personal consumption

expenditures. Unemployment rate (URATE) is the monthly and seasonally adjusted values as

reported by the Bureau of Labor Statistics. The inflation rate (CPI) is measured monthly and

obtained from CRSP. Consumption-to-wealth ratio (CAY) is taken from data provided by Lettau

and Ludvigson (2001).

[Insert Figure 1 about here]

To account for investor’s belief about future economics, I take the leading 12 month

moving average of the residual from the above equation as the Orthogonalized University of

Michigan Consumer Confidence Sentiment. I standardize the series to have mean 0 and standard

deviation 1. The residual denotes the excess optimism or pessimism of consumers and is my

second measure for investor sentiment. The monthly index is plotted in Figure 1. The correlation

between the Baker and Wurgler index and the Orthogonalized University of Michigan Consumer

Confidence Sentiment is 51%.

B. Mutual Fund Data

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The mutual fund sample is constructed by merging the CRSP Survivorship Bias Free Mutual

Fund Database with the Thompson Financial CDA/Spectrum holdings database using MFLink

provided by WRDS. The CRSP mutual fund database includes information on fund returns, total

net assets and other fund characteristics. Monthly total net assets are available for most funds

from 1991. Hence the sample period in this study starts from 1991. The CDA/Spectrum mutual

funds database includes all registered domestic mutual funds filing with the SEC. The holdings

constitute almost all the equity holdings of the funds. Most mutual funds in the database report

their holdings on a quarterly basis; I adjust the holdings for stock splits reported in the CRSP

stock files.

I require the ratio of equity holdings to total net assets to be between 0.75 and 1. The lower

bound is to make sure that the return from the equity portfolio accounts for a significant portion

of the total fund return while the upper bound is to get rid of some apparent data errors.

Summary statistics of more than 5000 mutual fund portfolios over the period 1991 -2009 are

presented in Table 1, Panel A. The average fund has Total net assets (TNA) of $914 million over

the sample period.

[Insert Table 1 about here]

C. Stock outflows

One central variable in this study is the stock level outflow, the percent of the shares of a given

stock owned by mutual funds that is subjected to fund outflows. I first calculate mutual fund

flows using the CRSP Mutual Fund Database. Since we do not observe flows directly, I infer

flows from fund returns and TNA as reported by CRSP. Let ��!" be the total net asset of a fund

k and let Rt be its return between month t -1 and month t. Following the standard practice in the

literature (e.g., Zheng (1999), Sapp and Tiwari (2004), Frazzini and Lamont (2008)), I compute

flows for fund k in month t, �#$%�&'(!" using

�#$%�&'(!" � ��!" ) ��!*�" +1 � �!"- ) .��!" (2)

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where .��!" is the increase in total net assets due to mergers during month t. I handle mergers

by assuming that investors in the merged funds place their money in the surviving fund. I assume

that inflows and outflows occur at the end of the month, and that existing investors reinvest

dividends and other distributions in the fund. I assign an initial TNA value of zero to funds that

were newly created, while funds that die have outflows equal to their terminal TNA.

Following Frazzini and Lamont (2008), I assume that fund flows pass to stocks according

to the holding portfolios of funds. This formulation assumes that all trades were made on the last

day of the month. Thus, I have a formula for stock flow by fund k in month t:

�/'01�&'(2,!" � �#$%�&'(!" 4 Proportion of stock in portfolio 1 (3)

I then aggregate StockFlow over all mutual funds that experience outflow to create a total

outflow for each stock i. For comparability among stocks, I scale the StockFlow by the market

value ( .10AB2,!) of each stock.

�#/�&'(2,! � ∑ DE!FG"HIFJK,LM DM 4NOHPQRHIFJLMSTUV"GWXK,L (4)

Where O�#$%�&'(!" Y 0U is a dummy variable with the value of one when �#$%�&'(!" Y 0 and zero otherwise.

Combine equation (2) to (4), for stock i at month t, �#/�&'(2,! can be expressed as

�#/�&'(2,! � ∑ [\]^LM*\]^L_`M +�abLM-*Vc]LM[4NOHPQRHIFJLMSTU\]^L_`M 4 dFIR2QeK,LMEfFP!K,L" (5)

g'&%h$i2,!" is the most recent reported number of shares of stock i hold by mutual fund k at

month t. the Shout is stock i ‘s number of shares outstanding.

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I also construct the stock level InFlow in the same way except O�#$%�&'(!" Y 0U is

replaced with O�#$%�&'(!" j 0U . Figure 2 depicts the monthly stock level mutual fund

OutFlow and InFlow over the sample period.


D. Other Data and variables

Shares outstanding, stock returns, share codes, exchange codes , prices, market capitalization and

trading volume for all stocks come from the Center for Research on Security Prices (CRSP)

daily and monthly files. In the current analysis, I focus on ordinary common shares of firms

incorporated in the United States that traded on the NYSE and Amex . Throughout, ADRs, units,

REITs, Americus Trust components, closed-end funds and preferred stocks are excluded– that is,

stocks that do not have a CRSP share type code of 10 or 11. I exclude NASDAQ stocks because

their trading protocols are different .The stock should also have at least 60 months of valid

observations during the sample period. After applying all the above filters, the final database

includes about 4000 stocks over 19 years.

I construct the Amihud (2002) illiquidity measure using the daily return, volume and price.

The Amihud proxy is designed to capture the marginal impact of a unit of trading on the stock

price. For each stock i for each month t, it is calculated as follows:

�&&hk2,! � �N ∑ [bK,l[NFImFIPnoK,lNRp� (6)

Where D is the number of days in month t. �2,R is the daily stock return and '&q'&#rs2,R is the

daily dollar trading volume. Following Amihud (2002), I use the logarithmic transformation of

illiquidity. Hasbrouck (2009) finds that among various price impact measures, the Amihud

illiquidity measure has the highest correlation to the measures of price impact constructed from

high-frequency data.

Summary statistics of more than 4000 stocks over the period 1991 -2009 are presented in

Table 1, Panel B. The stocks have average monthly return of 0.85% and average monthly

OutFlow of 0.08% over the sample period.

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III. Investor Sentiment and the Fragility of Liquidity

I start by examining the relationship between mutual fund outflows and the stock market

illiquidity. To avoid imposing a priori restrictions on the dynamic interaction of outflows,

illiquidity, and returns, I adopt a vector autoregression (VAR) methodology following Vagias

and Van Dijk (2011). Vagias and Van Dijk (2011) use the VAR system with international

capital flows, market liquidity and market return as endogenous variables to study the impact of

international capital flows on local market liquidity.

The general form of an unrestricted VAR model of order p with m endogenous variables

and n exogenous factors is as follows:

�! � � � ∑ tI �!*IXIp� � � u! � v! (7)

where �! � Oy1, t, , y2, t, … , ym, tU´ is an m×T matrix of jointly determined dependent

variables assumed to be covariance stationary, u! � Ox1, t, x2, t, … , xn, tU´ is an n×T vector of

exogenous variables, A is an m×1 vector of intercepts, and tI O& � 1,2, … , BU and C are the

m×m and m×n coefficient matrices to be estimated. In this paper, �! consists of three variables

(defined for each stock i): monthly outflows of mutual investors weighted by their percentage

holding of the stock (�#/�&'(2,!), monthly stock returns (�2,!), and the monthly Amihud

illiquidity (�&&hk2,!).

Suppressing exogenous factors, the stock -specific VAR model can be expressed as follows:

} �2,!�#/�&'(2,!�&&hk2,! ~ � }�2��2��2�~ � }��2 ��2 ��2��2 ��2 ��2��2 ��2 ��2 ~ } �2,!*��#/�&'(2,!*��&&hk2,!*� ~ � � v2bv2�P!HIFJv2�II2� � (8)

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� v2bv2�P!HIFJv2�II2� � ~��0, ∑2�, ∑2 � �� O�2bU� �2b,�P!�IFJ �2b,�II2��2�P!�IFJ,b +�2�P!HIFJ-� �2�P!�IFJ,�II2�

�2�II2�,b �2�II2�,�P!�IFJ +�2�II2�-� ��

Besides the endogenous variables, I take several external factors to control for other

sources of inter-temporal variation in liquidity, return and mutual fund outflows. I account for

changes in market wide funding liquidity conditions by including the TED spread (the spread

between LIBOR and U.S. Treasury bills). I also include market average returns and market

average liquidity as exogenous factors in the VAR specifications. Market illiquidity is calculated

as the cross-sectional equal-weighted average of individual stock illiquidity in that month. It

should be noted that I exclude firm i in the computation of market illiquidity and market return.

For each stock, I estimate the VAR model using the 5-year window rolled forward every 6

months. To decide upon the optimal lag length p, I use the Hannan-Quinn Information Criterion

(HQC) for the stock-specific VARs. I find an optimal lag length equal to one month for the

majority of the stocks. Consequently, for the sake of parsimony I use a lag length of one month

in all VARs. I require each regression has at least 40 observations.


Table 2 presents the results. Panel A reports the baseline VAR model with only

endogenous variables. Panel B reports the VAR estimation including exogenous variables. The

estimated coefficients are averaged over time and then across firms.

The coefficients ��2 of the VAR model are the primary interest of this study. These

coefficients describe the market liquidity impact of funding shocks, measured by mutual fund

outflows. The coefficients ��2 indicate that fund outflow positively predicts illiquidity for the

stock the funds hold. In Panel B, an OutFlow corresponding to 1% of the market capitalization of

a stock on average leads to 22% SD jump in illiquidity. Furthermore, the OutFlow

coefficients on �&&hk ��2 indicate the positive feedback effect of market illiquidity on OutFlow.

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Returns display negative monthly autocorrelation, on average across the stocks after

controlling the effect of outflow and illiquidity. The return coefficient on lagged illiquidity is

positive and statistically significant. The evidence herein suggests the liquidity premium. The

results also resonate with Hameed, Kang and Viswanathan (2010) that decrease in stock returns

and market returns increases stock illiquidity. The coefficients on TED spread are positive and

significant, indicating that market liquidity is negatively impacted by widening TED spreads, a

proxy for market wide funding liquidity.


Denoting the coefficient ��2 from the VAR model as fragility of liquidity, I take the

average of fragility of liquidity across stocks and plot the time-series variation of the average

fragility in liquidity. Figure 3 shows significant time-series variation in the fragility of liquidity

over the sample period 1995 to 2009. Recall that I estimate the VAR model with 5 years rolling

windows, so the fragility of liquidity starts from 1995. We observe spikes in fragility associated

with periods of liquidity crisis. For example, the highest levels of fragility in liquidity in Figure 3

coincide with liquidity dry-ups during the subprime crisis (2007-2008) when investor sentiment

is also very low. However, liquidity seems to be fragile during 1991-1995 even there were no

crisis and we don’t see major mutual fund outflows. Interestingly, this period is accompanied by

negative sentiments, highlighting the impact of investor sentiment on liquidity.

To directly examine how investors’ negative sentiment affects the dynamic relationship

between outflows and market liquidity, I interact the three endogenous variables with sentiment

index,

�! � � � � �!*� � � �si�s$/!*� �!*� � v! (9)

Where �!= {R, OutFlow, Illiq}. �si�s$/!*� is the Baker and Wurgler sentiment index or

the Orthogonalized University of Michigan Consumer Confidence Sentiment multiplied by -1.

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Table3 presents the results. The coefficients of negative sentiment interacting with OutFlow

for the illiquidity equation measure the incremental impact of OutFlow on stock market

illiquidity when investors’ negative sentiment is 1 SD higher than the mean. Given an OutFlow

corresponding to 1% a stock’s market value, a 1 SD increase in negative sentiment leads to an

additional 33% SD (38% SD) jump in illiquidity using the Baker and Wurgler sentiment index

measure (Orthogonalized University of Michigan Consumer Sentiment index). Negative

sentiment also amplifies the feedback effect of illiquidity on mutual fund outflows. The

coefficients of negative sentiment interacting with illiquidity for the OutFlow equation are

mostly positive and significant.

Coval and Stafford (2007) document that funds with significant capital inflows tend to

increase their existing holdings much like the funds experiencing significant outflows tend to

reduce their existing positions. In other words, funds facing significant inflows behave as if they

too are constrained. If many funds are simultaneously forced to buy the same securities when

few others are willing to sell—what we will call inflow-driven price pressure can also cause a

decline in liquidity. To see whether inflows have the same impact on market liquidity as

outflows and how investor sentiment affects this relationship, I run the VAR estimation replacing

OutFlow with InFlow.


Table 4 reports the results. First, I do find that InFlow also has a positive impact on market

illiquidity. However, the magnitude of impact is much smaller compared to that of OutFlow.

This finding is consistent with Campbell, Ramadorai and Schwartz (2009) that institutions

demand more liquidity when they sell than when they buy. Not surprisingly, negative sentiment

attenuates the impact of inflows on market liquidity. This evidence is also in line with Brennan,

Chordia, Subrahmanyam and Tong (2009) that the demand for immediacy is stronger for sellers

of securities than for buyers since investors are more likely to have a pressing need to raise cash

than to exchange cash for securities.

17

Overall, the results suggest that both mutual outflows and inflows create the demand for

liquidity. Nevertheless, investors’ negative sentiment amplifies the mutual reinforcing effect of

mutual fund outflows and stock market illiquidity, but attenuates the impact of inflows on market

illiquidity.

IV. Cross Sectional Determinants of Fragility of Liquidity

Baker and Wurgler (2006, 2007) show that broad waves of sentiment have greater effects on

hard to arbitrage and hard to value stocks; these stocks will exhibit high sensitivity to sentiment.

Do we expect these hard to arbitrage and hard to value stocks to be more fragile in liquidity? To

examine the firm-specific determinants of the fragility of liquidity, I sort varieties of stock

characteristics on the fragility of liquidity based on semiannual breakpoints. Table 5 shows the

result. Smaller firms are more fragile, which is not surprising given that smaller firms usually

have high retail concentration. The same category applies for stocks with low institutional and

mutual fund ownership. Highly volatile stocks usually have high speculative appeal and hence

relatively hard to value and relatively hard to arbitrage, making them especially prone to

fluctuations in sentiment. The result shows that Volatile stocks are more fragile in liquidity. The

number of analysts serves as a proxy for the mass of informed agents as suggested by Brennan

and Subrahmanyam (1995). Low analyst coverage stocks are hard to value and they show to be

more fragile in liquidity. Earnings surprises serve as the proxy for the extent of estimation

uncertainty about fundamental values. However, the result shows that stocks with high negative

earnings surprises are more fragile than stocks with positive earnings surprises. A natural

interpretation is that negative earnings surprises may indicate distress.


However, results with respect to book-to-market do not seem to align well with hard to

arbitrage and hard to value stocks, at least, at the first glance. Literature shows that growth stocks

are usually more subject to sentiment shift. My finding shows that liquidity is more fragile for

high book-to-market stocks. One possible explanation is that high book-to-market can also be

associated with distress. Overall, for the set of stocks for which sentiment is most likely to

operate I find the impact of outflows on market liquidity is the strongest.

18

It is interesting to ask whether the cross-sectional variation among stocks’ fragility in

liquidity is persistent over time. After all, if fragility of liquidity is closely related to investor

sentiment, it should be a persistent characteristic since firm characteristics play a key role in how

investor sentiment affects stocks. To answer this question, I sort stocks into quintiles based on

their fragility measures in June and December, and examine the evolution of their fragility

quintiles for the next 10 years. Figure 4 plots the evolution of fragility quintiles over time and

reveals that fragility of liquidity is relatively persistent, especially for the lower quintiles. Thus,

fragility of liquidity appears to be a persistent characteristic of the stock.


To directly examine whether investor sentiment explains why some stocks are more

vulnerable to funding shocks to their mutual fund investors, I first define the sentiment loading

of a stock following Baker and Wurgler (2006, 2007) and I denote the loading as sentiment beta.

The idea of sentiment beta is similar to that of Shefrin and Statman (1994) where they develop a

behavioral asset-pricing theory as an analog to the standard CAPM. In their BAPM model the

expected returns of securities are determined by their “behavioral betas”.


Specifically, I estimate the sentiment betas based on the following model:

�2,! ) �� 2 � �Vb�\,2�!Vb�\ � �dV�,2g.�! � �EV�,2�.t! � ��VN,2�. ! � �E�]\,2 �� u!*� � 2,!

(10)

where �2,!is the return of stock i for month t, �� is the risk-free rate of return for month t, �!Vb�\,

SMB and HML are the three Fama-French factors and UMD is the momentum factor for

respective month. �� u!*� is the beginning of month investor sentiment index. This is

the standard four-factor model augmented with a fifth factor which is the monthly investor

sentiment. The coefficient of �� u!*� is the measure of sentiment loading of stock

return for month t. Following Fama and French (1993), I estimate the model using a five-year

window rolled forward every 6 months to obtain sentiment beta estimate �E�]\,2 for individual

19

stocks at each 6 month period. I use the 6 month interval instead of quarter or month to match

the measures of fragility of liquidity. The 6 month interval allows for time variation in the

measures and reduces the overlaps of observations in the regression compared to the quarter or

month interval. I construct the sentiment betas for both the Baker and Wurgler (2006) sentiment

index and the Orthogonalized University of Michigan Consumer Confidence Index. Table 6

reports the average betas. The average degree of stock sentiment loading is 0.006 on the Baker

and Wurgler Investor Sentiment Index and 0.002 on the Orthogonalized Consumer Confidence

Sentiment.

To examine whether stocks that are more subject to shifts in investor sentiments are also

more fragile in liquidity, that is more vulnerable to mutual fund outflows, I regress the fragility

of liquidity of each stock in June and December at each year on the sentiment beta and control

for other factor loadings.

��Ai�hk2,! � � � �� E�]\,2,! � �� Vb�\,2,! � �� dV�,2,! � �� EV�,2,! � �� VN,2,! (11)

Where ��Ai�hk2,! is the ��2 from baseline VAR model with exogenous factors. �E�]\,2,!, �Vb�\,2,!, �dV�,2,! , �EV�,2,! and ��VN,2,! are the betas estimated from equation (10). I cluster

standard errors by firm and year to deal with the time series or cross-section correlation.


The results in table 7 provide cross-sectional evidence for sentiment-induced liquidity

impact of mutual fund outflows. The regression coefficient of fragility on sentiment beta is 6.652

(t-statistic =2.34) for the Baker and Wurgler sentiment measure and 14.918(t-statistic =2.33) for

the Orthogonalized Consumer Confidence measure. The finding that �EV� is also positively

related to fragility is not surprising since small stocks have larger �EV�. Interestingly, fragility is

negatively associated with market beta. Combined with the sorting results in table 5 that volatile

stock is more fragile, the finding here suggests that it is idiosyncratic volatility that drives the

fragility in liquidity. Overall, these results suggest that for the set of stocks for which sentiment

is most likely to operate, the liquidity is most fragile.

20

V. Contrarian Profit and Investor Sentiment

Kaniel, Saar and Titman (2008) document that contrarian tendency of individuals leads them to

act as liquidity providers to institutions that require immediacy. From models of risk-averse

liquidity provision such as Grossman and Miller (1988) and Campbell, Grossman, and Wang

(1993) that investors who require immediacy (e.g., institutions) must offer price concessions to

induce other risk-averse investors, in this case individuals, to take the other side of their trades.

However, these irrational market makers as modeled in Baker and Stein (2004) are not formally

required to continuously provide market-making services; their supply of liquidity could easily

be withdrawn when they are pessimistic about the stock market. And the large returns demanded

by the uninformed traders enhance price fluctuations, creating more risk in the positions

liquidated than in those assets and increasing the premium demanded by other liquidity providers.

Therefore, it would be interesting to investigate to what extent the expected returns from

liquidity provision in equity markets rise, if at all, during times of negative sentiment. To

construct a proxy for the returns from liquidity provision, I examine the extent of price reversals

using the contrarian trading strategies that long on the loser securities and short on the winner

securities.

I follow the contrarian strategy developed in Avramov, Chordia, and Goyal (2006) and

applied by Hameed, Kang and Viswanathan(2010). Specifically, I construct the Wednesday to

Tuesday weekly returns for all NYSE/Amex stocks in my sample for the period 1991 to 2009.

Next, I sort the stocks in week t into positive and negative return portfolios. For each week t,

returns on stock i (Ri,t) that are higher (lower) than the median return in the positive (negative)

return portfolio are classified as winner (loser) securities. I use stock i’s turnover in week t

(Turni,t) to measure the amount of trading. The contrarian portfolio weight of stock i in week t+1

within the winner and loser portfolios is given by

�X,2! � O�2,!*��#�$2,!*�U/ ∑ �2,!*��#�$2,!*�]X2p� (12)

where Np denotes the number of securities in the loser or winner portfolios in week t. The

contrarian profits for the loser and winner portfolios for week t+k are:

21

�X,!a" � ∑ �2,X,!a��2,!a"]X2p� (13)

Next I take the difference in profits from the loser and winner portfolios to obtain the zero-

investment profits.

I investigate the effect of investor sentiment by conditioning the contrarian profits on the

investor sentiment in the month of the portfolio formation week. Specifically, I examine

contrarian profits in positive sentiment states and negative sentiment states.


Table 8, Panel A reports a significant contrarian profit of 0.56% in week t+1 (t-

statistic=2.98) for the full sample period. The contrarian profit becomes less significant as we

move to t+2 and become negative as we move to t+3. The magnitude and significance of the

contrarian profit is close to the findings in Hameed, Kang and Viswanathan (2010). Since the

contrarian profits and price reversals appear to last for at most two weeks, I limit the subsequent

analyses to the first one or two weeks after portfolio formation. Panel B of Table 10 shows that

week t+1 profits in the negative sentiment month increase noticeably to 0.88% using the Baker

and Wurgler sentiment measure and 0.74% using the Orthogonalized Consumer Confidence

Index, compared to profits of 0.30% and 0.51% in the positive sentiment period.

Hameed, Kang and Viswanathan (2010) show that returns to supplying liquidity increase

following periods of large drop in market return. The period of negative sentiment might also be

the period of down market. To examine whether the high contrarian profit is merely the results of

down market, I further condition the contrarian profit on both market return and sentiment. I

define down (up) market as the cumulative market returns over the previous four weeks less

(greater) than zero. Consistent with Hameed, Kang and Viswanathan (2010), contrarian profit is

much higher in the down market then the up market, however, the effect of sentiment still exists.

Panel C shows that the largest contrarian profit of 1.09% (1.13%) is registered in the period

when the Baker and Wurgler sentiment (Orthogonalized Consumer Confidence Index ) is

22

negative and in the down market, compared to the profit of 0.67% (0.66%) when sentiment is

positive in the same down market. In the up market, contrarian profit is 0.48% (0.21%) in the

negative sentiment regime and -0.20% (0.18%) in the positive sentiment regime.

VI. Conclusion

This paper investigates the impact of investor sentiment on the interaction between the tightening

of funding constraints through mutual fund outflows and their impact on stock market liquidity.

Using a VAR system with OutFlow, illiquidity, and return as endogenous variables, I first

document the mutual reinforcing effect of mutual fund outflows and stock market liquidity. I

then show that when the investor sentiment is negative, liquidity can be fragile, that is a small

mutual fund outflow can lead to a large decline in market liquidity of the assets held by the funds.

The feedback effect of market liquidity on mutual fund outflows is also enhanced when

sentiment wanes. The interaction between mutual outflows and illiquidity is stronger for small

cap stocks, high volatility stocks, stocks with low institutional or mutual fund ownership, and

stocks with less analyst coverage and high negative earnings surprise. In general these stocks

belong to the Hard-to-Value and Difficult-to-Arbitrage category as stated in Baker and Wurgler

(2006), and these stocks are more affected by shifts in investor sentiment. Direct tests on stocks’

sensitivity to sentiment and the fragility of liquidity show that stocks more sensitive to sentiment

are more fragile in liquidity. Overall, my analysis suggests that negative sentiment amplifies the

effects of capital outflows on stock market liquidity, both in the cross-section and inter-

temporally.

Finally, I use the idea that short-term stock price reversals following heavy trading reflect

compensation for supplying liquidity and examine whether the cost of liquidity provision varies

with shifts in investor sentiment. I find that, indeed, the cost of providing liquidity is higher in

periods with negative sentiment. For example, contrarian trading strategies based on return

reversals produce economically significant returns (0.88 % per week) during period of negative

sentiment. The findings still hold after controlling for stock market return. Taken together, my

results support a supply effect on liquidity of investor sentiment as advocated by Baker and Stein

(2004).

23

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27

Figure. 1 Baker and Wurgler Sentiment Index vs Orthogonalized Consumer Confidence

Index. The monthly Baker and Wurgler (2006) Investor sentiment index is the first principal component of the six measures: closed-end fund discount, the NYSE share turnover, the number of IPOs, the average first-day return of IPOs, the equity share in new issues, and the dividend premium. To remove business cycle information, Baker and Wurgler (2006) first regress each of the six measures on a set of macroeconomics variables and use the residuals to build the sentiment index. The orthogonalized Consumer Confidence Index is the residual from the regression of the University of Michigan Consumer Confidence Sentiment on a set of macroeconomics variables. Both measures are standardized to have mean 0 and standard deviation 1. The sample period is from 1991-2007 for the Baker and Wurgler (2006) Investor sentiment index and 1991 -2009 for the University of Michigan Consumer Confidence Sentiment.

-3

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Baker and Wurgler Sentiment Index

28

Figure. 2 Time series of stock level mutual fund OutFlow and InFlow. Stock level OutFlow

and InFlow are the equal-weighted average OutFlow and InFlow of all stocks held by mutual

funds at the end of each month. OutFlow and InFlow are as constructed in section II. C.

Figure. 3 Time series of fragility of liquidity from Baseline VAR model

The fragility of liquidity is the equal-weighted average coefficients ��2 from the baseline VAR model with exogenous factors.

0

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29

Figure.4 Persistence of Fragility of Liquidity Rankings

This figure shows the average fragility of liquidity quintiles in the subsequent 1 to 10 years for

the quintiles of stocks. The fragility of liquidity is the coefficients ��2 from the baseline VAR model with exogenous factors. .

0

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quintile 1: Low

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30

Table 1: Summary Statistics This table reports summary statistics for the sample of mutual funds and stocks used in this paper. Panel A reports the summary statistics of Mutual Funds. The number of distinct mutual funds in the sample is 5533. TNA is the total net asset. Net return is the monthly mutual fund return after fund expenses. Panel B reports the summary statistics of the stock sample. The number of stocks

is 4429. Return is the monthly stock return, �&&hk2,! is the log transformation of monthly Amihud

illiquidity measure times 106, �#/�&'( is as constructed in section II. C. The sample period is from 1991 to 2009. Variable Mean Median StdDev P5 P95

Panel A: Funds

Total Net Assets ($ million) 914.26 121.10 4571.64 3.30 3286.23

Net Return (% per month) 0.65 0.92 5.38 -8.23 8.32

Avg. flow/TNA (% per month) 1.67 -0.02 12.65 -5.79 13.82

Panel B: Stocks

Return (% per month) 0.85 0.35 14.05 -21.31 23.91

OutFlow (%) 0.08 0.04 0.12 0.00 0.33

InFlow (%) 0.12 0.06 0.25 0.00 0.41

Illiq 0.819 0.040 3.428 0.0003 4.134

31

Table 2 Baseline VAR Estimation

The table shows the unrestricted estimates for the first-order VAR model.

} �2,!�#/�&'(2,!�&&hk2,! ~ � }�2��2��2�~ � }��2 ��2 ��2��2 ��2 ��2��2 ��2 ��2 ~ } �2,!*��#/�&'(2,!*��&&hk2,! ~ � � v2�v2�2�v2�2�

�

I estimate the VAR model using the 5-year window rolled forward every 6 months. �2,! is the

monthly stock return, �&&hk2,! is the log transformation of monthly Amihud illiquidity measure

times 106, �#/�&'(2,! is constructed as

�#/�&'(2,! � � [��!" ) ��!*�" +1 � �!"- ) .��!"[ 4 O�#$%�&'(!" Y 0U��!*�" 4 g'&%h$i2,!"��'#/2,!"

Where ��!" and �!" are the total net asset and monthly return of mutual fund k, respectively. .��!" is the increase in total net assets due to mergers . g'&%h$i2,!" is the most recent reported

number of shares of stock i hold by mutual fund k and ��'#/2,! is a stock ‘s number of shares

outstanding. O�#$%�&'(!" Y 0U is a dummy variable with the value of one when

�#$%�&'(!" � ��!" ) ��!*�" +1 � �!"- ) .��!" Y 0 and zero otherwise.

Panel A and Panel B report the cross section average ((t-statistics)) of time series mean and the percentage of significant coefficient estimates at the 5% level (one-tailed). T-statistics (in parentheses) corresponding to the standard error of the mean. In Panel B, the TED spread, market average returns and market average illiquidity are added as exogenous factors. The sample period is from 1991 to 2009. Significance at the 1%, 5%, and 10% level is indicated by ***, **, and*, respectively.

32

Panel A Baseline VAR model

Return OutFlow Illiquidity R2

Return Equation

Mean of Estimated Coefficients -0.036*** -0.044*** 3.320*** 0.10

(t-statistics) (-27.30) (-10.16) (42.67)

% positive (negative) (61%) (56%) 88%

% positive (negative) significant (18%) (13%) 34%

OutFlow Equation

Mean of Estimated Coefficients -0.009*** 0.645*** 3.311*** 0.27

(t-statistics) (-11.14) (329.31) (36.85)

% positive (negative) (52%) 99% 96%

% positive (negative) significant (16%) 97% 43%

Illiquidity Equation

Mean of Estimated Coefficients -0.093*** 1.177*** 0.789*** 0.46

(t-statistics) (-27.39) (41.11) (676.38)

% positive (negative) (73%) 93% 100%

% positive (negative) significant (32%) 52% 100%

Panel B Baseline VAR model with exogenous factors

Return OutFlow Illiquidity

TED

Spread

Market

Return

Market

Illiquidity R

2

Return Equation

Mean of Estimated Coefficients -0.094*** -0.063*** 5.478*** -0.001 0.311*** 0.002*** 19

(t-statistics) (-63.31) (-5.26) (27.75) (-0.87) (45.47) (8.19)

% positive (negative) (74%) (55%) 74% (53%) 70% 56%

% positive (negative) significant (24%) (13%) 27% (21%) 27% 18%

OutFlow Equation

Mean of Estimated Coefficients -0.012*** 0.393*** 2.295*** 0.057*** -0.010*** 0.000*** 32

(t-statistics) (-14.65) (169.60) (22.70) (96.97) (-3.68) (6.46)

% positive (negative) (56%) 95% 65% 92% (55%) 60%

% positive (negative) significant (13%) 81% 34% 58% (13%) 28%


Mean of Estimated Coefficients -0.163*** 0.763*** 0.521*** 0.444*** -0.522*** 0.087*** 52

(t-statistics) (-5.77) (3.90) (213.04) (23.56) (-5.89) (25.78)

% positive (negative) (68%) 81% 98% 79% (73%) 85%

% positive (negative) significant (23%) 42% 91% 48% (30%) 55%

33

Table 3 VAR Estimation with Sentiment index

In this table, I interact the three endogenous variables with the sentiment index.

� � � � � �!*� � � �si�s$/!*� �!*� Where Y= {R, OutFlow, Illiq}. The TED spread, market average returns and market average illiquidity are added as exogenous factors. The tables report the cross section average ((t-statistics)) of time series mean and the percentage of significant coefficient estimates at the 5% level (one-tailed). T-statistics (in parentheses) corresponding to the standard error of the mean. In panel A, �si�s$/!*� is the Baker and Wurgler (2006) sentiment index multiplied by -1. In

Panel B, �si�s$/!*� is the Orthogonalized University of Michigan Consumer Confidence Index multiplied by -1. Both measures are standardized to have mean 0 and standard deviation 1. The sample period is from 1991-2007 in Panel A and 1991 -2009 in Panel B.

Significance at the 1%, 5%, and 10% level is indicated by ***, **, and*, respectively.

34

Panel A Interaction with Baker and Wurgler Investor Sentiment Index


Return*

Sentiment

OutFlow *

Sentiment

Illiquidity*

Sentiment TED

Market

Return

Market

Illiquidity R2

Return Equation

Mean of Estimated Coefficients -0.172*** -0.208*** 4.760*** 0.118*** 0.120 -1.565*** 0.006*** 0.270*** 0.001*** 0.26

(t-statistics) (-16.36) (-3.97) (16.63) (8.05) (1.63) (-4.33) (6.18) (46.15) (6.55)

% positive (negative) 64% 52% 58% 57% 51% 52% 51% 68% 54%

% positive (negative) significant 14% 14% 18% 9% 13% 14% 17% 25% 16%

OutFlow Equation

Mean of Estimated Coefficients -0.005 0.467*** 1.819*** 0.003 -0.156*** 1.289*** 0.065*** -0.011*** 0.001*** 0.37

(t-statistics) (-1.09) (36.00) (12.62) (0.54) (-8.38) (7.39) (93.35) (-5.25) (18.37)




Mean of Estimated Coefficients -0.079** -0.681*** 0.488*** -0.112** 1.138*** 0.038** 0.254*** -0.594*** 0.050*** 0.55

(t-statistics) (-2.02) (-3.74) (41.96) (-2.08) (4.41) (-2.39) (38.32) (-31.63) (42.73)



Panel B Interaction with Orthogonalized University of Michigan Consumer Confidence Sentiment


Return*

Sentiment

OutFlow *

Sentiment

Illiquidity*

Sentiment TED

Market

Return

Market

Illiquidity R2

Return Equation

Mean of Estimated Coefficients -0.046*** -0.107*** 4.499*** -0.188*** 0.370*** 0.316 0.000 0.298*** 0.002*** 0.26

(t-statistics) (-12.81) (-6.94) (27.98) (-20.11) (8.05) (1.01) (0.04) (51.73) (12.91)



OutFlow Equation

Mean of Estimated Coefficients -0.017*** 0.550*** 3.238*** 0.034*** -0.504*** 2.425*** 0.059*** -0.069*** 0.002*** 0.38

(t-statistics) (-9.43) (107.56) (19.82) (7.34) (-37.49) (10.39) (97.45) (-23.23) (24.22)




Mean of Estimated Coefficients -0.093*** -0.356*** 0.499*** -0.103*** 1.296*** 0.038*** 0.247*** -0.508*** 0.045*** 0.57

(t-statistics) (-7.48) (-5.98) (109.01) (-3.15) (8.05) (3.55) (39.56) (-27.54) (42.58)



35

Table 4 Inflow, Illiquidity and Sentiment

In this table, I estimate the VAR specifications in table2 and table3, replacing �#/�&'(2,! with �$�&'(2,!. �$�&'(2,! is constructed

as

�$�&'(2,! � ∑ [\]^LM*\]^L_`M +�abLM-*Vc]LM[4NO�TU\]^L_`M 4 dFIR2QeK,LMEfFP!K,L"

Where ��!" and �!" are the total net asset and monthly return of mutual fund k, respectively. .��!" is the increase in total net

assets due to mergers . g'&%h$i2,!" is the most recent reported number of shares of stock i hold by mutual fund k and ��'#/2,! is a

stock ‘s number of shares outstanding. O�#$%�&'(!" j 0U is a dummy variable with the value of one when �#$%�&'(!" � ��!" )��!*�" +1 � �!"- ) .��!" j 0 and zero otherwise.

Panel A reports the baseline VAR estimation. In Panel B, I interact the three endogenous variables with Baker and Wurgler (2006) sentiment index multiplied by -1. In Panel C, I interact the three endogenous variables with the Orthogonalized University of Michigan Consumer Confidence Index multiplied by -1. Both measures are standardized to have mean 0 and standard deviation 1. The sample period is from 1991-2007 in Panel B and 1991 -2009 in Panel A and Panel C. T-statistics (in parentheses) corresponding to the standard error of the mean. Significance at the 1%, 5%, and 10% level is indicated by ***, **, and*, respectively.

36

Panel A Baseline VAR model with exogenous factors

Equation Return InFlow Illiquidity TED Spread

Market

Return

Market

Illiquidity R

2

Return -0.068*** -0.027*** 2.221*** -0.004*** 0.356*** 0.001*** 23

(t-statistics) (-39.28) (-7.36) (22.31) (-4.84) (44.54) (12.65)

InFlow 0.041*** 0.550*** 1.668 0.052*** 0.079*** 0.004*** 32

(t-statistics) (23.53) (184.18) (1.39) (51.35) (13.77) (37.56)

Illiquidity -0.181*** 0.061** 0.727*** 0.158*** -0.782*** 0.040*** 60

(t-statistics) (-13.73) (2.34) (271.11) (15.64) (-14.32) (17.61)

Panel B Interaction with Baker and Wurgler Investor Sentiment Index

Equation Return InFlow Illiquidity

Return*

Sentiment

InFlow *

Sentiment

Illiquidity*

Sentiment TED

Market

Return

Market

Illiquidity R2

Return -0.126*** -0.382*** 5.492*** 0.089*** 0.485*** -5.854*** 0.010*** 0.266*** 0.001*** 29

(t-statistics) (-7.94) (-6.20) (9.50) (3.92) (5.53) (-7.98) (5.20) (21.22) (2.71)

InFlow 0.029* 0.102*** 6.291* 0.028 0.531*** -7.733*** 0.083*** -0.065*** 0.006*** 38

(t-statistics) (1.71) (4.12) (1.82) (1.13) (15.14) (-11.29) (40.97) (-7.43) (28.30)

Illiquidity -0.300** -0.185 0.519*** 0.074 0.526 0.105*** 0.208*** -1.155*** 0.065*** 59

(t-statistics) (-2.24) (-0.51) (26.22) (0.38) (0.93) (3.86) (10.54) (-11.86) (12.86)

Panel C Interaction with Orthogonalized University of Michigan Consumer Confidence Sentiment

Equation Return InFlow Illiquidity

Return*

Sentiment

InFlow *

Sentiment

Illiquidity*

Sentiment TED

Market

Return

Market

Illiquidity R2

Return -0.081*** -0.001 1.398*** -0.131*** -0.067*** 0.962*** -0.003*** 0.336*** 0.000*** 28

(t-statistics) (-49.19) (-0.32) (23.97) (-36.79) (-10.67) (10.79) (-3.64) (50.16) (5.73)

InFlow 0.047*** 0.472*** 1.845*** 0.040*** 0.324*** -1.806*** 0.048*** 0.110*** 0.003*** 37

(t-statistics) (33.08) (180.13) (25.87) (13.58) (63.05) (-19.72) (59.64) (23.80) (38.58)

Illiquidity -0.146*** 0.023*** 0.626*** -0.087*** -0.038** 0.321*** 0.108*** -0.563*** 0.015*** 64

(t-statistics) (-27.61) (4.68) (216.20) (-9.11) (-2.51) (64.99) (26.12) (-26.34) (27.11)

37

Table 5 Characteristics of Stocks with Fragile Liquidity

This table shows the characteristics of stocks for fragility-sorted portfolios. The fragility of

liquidity is the coefficients ��2 from the baseline VAR model with exogenous factors. Number of Analyst is the number of analysts making a forecast for the firm‘s earnings, obtained from the I/B/E/S Summary File. Earning Surprise is the difference between realized quarterly EPS and the median forecast of quarterly EPS from I/B/E/S Summary File , divided by the stock price at the end of the final month of the fiscal quarter for which earnings is being forecast. Stocks are sorted into portfolios based on June or December fragility. T-statistics (in parentheses) corresponding to the standard error of the mean. The sample period is from 1991 to 2009. Significance at the 1%, 5%, and 10% level is indicated by ***, **, and*, respectively.

Fragility Quintile:

Low 2nd Quintile Middle 4th Quintile High High - Low

Fragility -0.0471 0.0047 0.0267 0.1686 5.4336 5.4807***

(-4.16) (5.96) (5.23) (5.37) (10.41) (10.4)

Book-to-market 0.4794 0.5109 0.5691 0.6164 0.7547 0.2753***

(66.64) (47.8) (48.94) (38.88) (30.94) (13.2)

Volatility 0.0265 0.0257 0.0284 0.0311 0.0331 0.0067***

(34.06) (29.16) (32.69) (36.26) (40.49) (21.94)

Institutional Ownership 0.6118 0.6383 0.5761 0.4803 0.3313 -0.2805***

(31.94) (34.2) (28.62) (30.43) (48.29) (-18.91)

Number of institutions 180.5079 142.7291 90.5702 57.2474 28.7812 -151.7267***

(42.7) (35.42) (21.65) (20.34) (25.27) (-35.61)

Mutual Fund ownership 0.1255 0.1266 0.1113 0.0892 0.0669 -0.0586***

(16.56) (15.25) (14.1) (18.22) (27.68) (-9.44)

Size ($ bill) 4.2738 2.2036 0.8937 0.4387 0.1913 -4.0825***

(19.72) (29.91) (27.58) (30.14) (28.7) (-18.84)

Number of Analyst 6.2977 5.1797 3.6179 2.6030 1.8036 -4.4941***

(62.17) (90.64) (44.5) (39.72) (63.89) (-38)

Earning Surprise 0.0003 0.0003 0.0000 -0.0002 -0.0008 -0.0011***

(4.32) (4.68) (0.14) (-1.62) (-6.04) (-11.56)

38

Table 6: Sentiment Beta

This table reports the equal weighted cross sectional means of coefficients from the following regression,

�2,! ) �� 2 � �Vb�\,2�!Vb�\ � �dV�,2g.�! � �EV�,2�.t! � ��VN,2�. ! � �E�]\,2 �� u!*� � 2,!

�!Vb�\ , SMBt and HMLt are the Fama-French factors, UMDt is the momentum factor, Rf is the risk free rate and �� u!*� is the investor sentiment measure at the beginning of the month. Following Fama and French (1993), all models are estimated using a five-year window rolled forward every 6 months. T-statistics (in parentheses) corresponding to the standard error of the mean. Sample period 1991-2009. The symbols *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels.

Baker and Wurgler Investor

Sentiment Index

Orthogonalized Consumer

Confidence Sentiment �E�]\ 0.006*** 0.002***

(6.97) (4.38) �Vb�\ 0.953*** 0.984***

(85.65) (95.54) �EV� 0.698*** 0.698***

(50.62) (53.94) �dV� 0.374*** 0.330***

(23.49) (22.62) ��VN -0.155*** -0.158***

(-14.43) (-16.25)

Number of Stocks 4238 4429

Average R2 27% 29%

39

Table 7: Sentiment Beta and the Fragility of Liquidity

This table reports the following pool regression coefficients with t-statistics (in parentheses) of the fragility of liquidity on sentiment beta and other factor loadings. ��Ai�hk2,! � � � �� E�]\,2,! � �� Vb�\,2,! � �� dV�,2,! � �� EV�,2,! � �� VN,2,!

The ��Ai�hk2,! is the coefficients ��2 from the baseline VAR model with exogenous factors. �E�]\,2,!, �Vb�\,2,!, �dV�,2,! , �EV�,2,! and ��VN,2,! are the betas estimated in table6. T-statistics are

calculated using clustered (by firm and time) standard errors. Sample period 1991-2009. The symbols *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels.


Sentiment Index


Confidence Sentiment �E�]\ 6.652** 14.918**

(2.34) (2.33) �Vb�\ -0.265 -0.505**

(-1.56) (-2.51) �EV� 0.545*** 0.519***

(2.76) (2.68) �dV� -0.065 -0.107

(-0.66) (-1.02) ��VN 0.156 0.240

(0.90) (1.35)

Constant 0.615*** 1.015***

(2.58) (3.93)

Observations 39642 39642

R2 0.01 0.01

Clustered by firm Yes Yes

Clustered by year Yes Yes

40

Table 8 Contrarian Profits and Investor Sentiment

Weekly stock returns are sorted into winner (loser) portfolios if the returns are above (below) the median of all positive (negative) returns in week t. Contrarian portfolio weight for stock i in week t is given by: �X,2! � O�2,!*��#�$2,!*�U/ � �2,!*��#�$2,!*�]X

2p�

where �2,! and �#�$2,! are stock i’s return and turnover in week t.

The contrarian profits for the loser and winner portfolios for week t+k are:

�X,!a" � � �2,X,!a��2,!a"]X2p�

Panel A reports the unconditional contrarian profits for week t+k, for k=1,2,3, and 4. Panel B reports the contrarian profits conditional on investor sentiment. Negative (positive) refers to sentiment index of the portfolio formation week being below (above zero). Panel C reports the contrarian profits for week t+1 conditional on investor sentiment and the market return. Down (Up) market is defined as the cumulative market returns over the previous four weeks less (greater) than zero. Newey-West autocorrelation-corrected t-statistics are given in parentheses. Sample period 1991-2009. The symbols *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels.

Panel A Unconditional Contrarian Profits

Portfolio Week

t+1 t+2 t+3 t+4

Loser 1.12% 0.46% 0.40% 0.34%

Winner 0.56% 0.29% 0.47% 0.40%

Loser minus Winner 0.56% 0.17% -0.07% -0.07%

(t-statistics) 3.34 1.58 -0.65 -0.64

Panel B Contrarian Profits Conditional on Investor Sentiment

Portfolio Week

t+1 t+2 t+1 t+2


Sentiment Index


Confidence Sentiment

Negative Positive Negative Positive Negative Positive Negative Positive

Loser 1.38% 0.93% 0.70% 0.15% 1.34% 1.03% 0.70% 0.24%

Winner 0.50% 0.64% 0.46% 0.05% 0.60% 0.53% 0.50% 0.07%

Loser minus Winner 0.88% 0.30% 0.24% 0.10% 0.74% 0.51% 0.20% 0.16%

(t-statistics) 3.94 1.11 1.74 0.59 2.83 2.22 1.25 1.06

Panel C Contrarian Profits Conditional on Investor Sentiment and Market Returns

Week t+1

Portfolio Baker and Wurgler Investor

Sentiment Index


Confidence Sentiment

Negative Positive Negative Positive Negative Positive Negative Positive

Down market Up market Down market Up market

Loser 1.34% 1.19% 1.46% 0.57% 1.49% 1.05% 1.13% 1.04%

Winner 0.37% 0.54% 0.63% 0.72% 0.37% 0.53% 0.78% 0.54%

Loser minus Winner 1.09% 0.67% 0.48% -0.20% 1.13% 0.66% 0.21% 0.18%

(t-statistics) 4.14 1.92 1.94 -0.66 3.76 2.12 0.78 0.65

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