Essays on Liquidity in Finance and Real Estate Markets

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A dissertation submitted to the

Graduate School

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

in the Department of Finance and Real Estate

of the Carl H. Lindner College of Business

Qingqing Chang

B.S., Renmin University of China, 2006 M.S., Renmin University of China, 2008

July 2013

Committee Chair: Shaun A. Bond, Ph.D.

Abstract

This dissertation studies liquidity and its relationship with stock returns and real estate markets. Liquidity has wide ranging effects on financial markets and the financial crisis highlighted the important role played by liquidity in finance and real estate markets. The objective of this dissertation research is to examine the characteristics of liquidity in different financial markets and to study the effect of innovations in liquidity on stock return volatility. First, using high-frequency trading data on publicly-traded real estate investment trusts (REITs) and trading data on commercial real estate assets, we document the transmission of a liquidity shock from public to private markets. Furthermore we examine the relationship between liquidity in real estate markets (both public and private markets) and macroeconomic variables. We also show how the transmission mechanism differs between public and private markets. Second, using revisions to equity analyst consensus forecasts to measure cash-flow news directly, we are able to study the relationship between innovations in liquidity and stock-return volatility under the return- decomposition framework. We contend that both cash-flow news and expected return news correlate with liquidity shocks, and the cash-flow news component is a nontrivial channel through which liquidity correlates with stock returns. This dissertation research aims to fill in the gaps in the existing empirical literature on liquidity and sheds light on the important relationship between liquidity and stock returns.

iii

Acknowledgments

Sincere thanks to my advisor, Shaun A. Bond, for his hard work and support, both on the dissertation and throughout my graduation experience. I also wish to thank Steve

Slezak, Brian Hatch, Nicolas Williams and other faculty members for their kind words and many thoughtful suggestions. I am grateful to the Department of Finance and Real

Estate at University of Cincinnati for scholarship, and teaching experiences as well as scholarly support.

In addition to the institutional support I have received while working on this dissertation, I want to thank my graduate student peers, who provided the friendship needed to keep working when the work was very trying. My thanks to Qing Bai, Avis

Devine, Ran Lu, and Haim Kassa.

Last, but certainly not least, my thanks to my family: my parents, and my husband,

Justin Krebbs. Their belief in my abilities is long-standing, and they have provided both the important foundational and the much-needed ongoing support for all the work I do.

My gratitude to them is sincere and deep.

Table of Contents

Essay 1: Liquidity Dynamics across Public and Private Markets ...... 1 Abstract ...... 1 1 Introduction ...... 1 2 Literature ...... 4 2.1 Liquidity in public real estate markets ...... 4

2.2 Liquidity in private real estate markets ...... 5

3 Data and liquidity measures ...... 6 3.1 Data ...... 6

3.2 Liquidity measures ...... 8

4 Methodology ...... 12 4.1 Factor decomposition of liquidity ...... 12

4.2 Granger causality and the testing method ...... 15

5 Results ...... 16 5.1 Common factors of liquidity measures ...... 16

5.2 Lead-lag relations between liquidity measures of REITs ...... 19

5.3 REITs and the direct real estate market ...... 20

5.4 Liquidity measures and macroeconomic variables ...... 22

6 Conclusion ...... 26 References ...... 29 Tables and figures ...... 31

Essay 2: Liquidity Risk and Stock Returns: a Return Decomposition Approach .....45 Abstract ...... 45 1 Introduction ...... 45 2 Empirical Framework ...... 53

2.1 Decomposing returns and regressions of returns on liquidity proxies ...... 53

2.2 Empirical Measurement ...... 56

2.2.1 Expected returns...... 56

2.2.2 Cash-flow news ...... 57

2.2.3 Expected-return news...... 61

2.2.4 Liquidity measures ...... 61

3 Samples and Descriptive Statistics ...... 63 4 Empirical results ...... 65 4.1 Decomposition Results ...... 65

4.2 Reinterpreting regressions of returns on liquidity measures ...... 67

4.3 Analyst forecast ...... 69

4.4 Conditional analysis ...... 71

5 Conclusion ...... 74 References ...... 76 Tables and figures ...... 81

Essay 1: Liquidity Dynamics across Public and Private Markets

Abstract

In this paper we investigate cross-asset liquidity between equity markets and REITs and between REITs and private real estate markets. While many studies have investigated REIT liquidity, and there is an emerging interest in liquidity in the private real estate markets, there appears to be little knowledge of the dynamics of cross-market liquidity. We find lower levels of liquidity for REITs compared to a set of control firms matched on size and book to market ratios. Commonality in liquidity is also lower for REITs than the controls and the overall market. However, we do find an important difference in share turnover for REITs, which appears to have a higher level of commonality than found in other studies. We suggest that this may be due to the financial crisis. Additionally we find evidence of similar time-series variation in liquidity for public and private real estate markets. We also find significant directional causality for most liquidity proxies from the public to private real estate markets. Finally our results show that there is strong contemporaneous correlation between both public and private real estate market liquidity and the term spread and real investment and consumption spending. REIT liquidity measures based on intraday data also appear to contain important information not found in measures constructed from daily returns.

1 Introduction

The financial crisis highlighted the important role played by liquidity in finance and real estate markets. This has stimulated a range of research focusing on the dynamics and cross-section commonality of liquidity, see for instance, Spiegel (2008), Korajczyk

1 and Sadka (2008), and Naes et al (2011). In this paper we examine liquidity measures and transmission across public and private real estate markets. In particular, using data on publicly traded real estate investment trusts (REITs) and trading data on commercial real estate, we document the transmission of a liquidity shock from public to private markets.

Furthermore we examine the relationship between liquidity in real estate markets (both public and private markets) to macroeconomic variances and show how the transmission mechanism differs between public and private markets.

Using data on commercial real estate markets provides an appealing laboratory in which to consider cross-asset commonality and transmission in liquidity. In this case the underlying asset, commercial real estate, forms the main asset holding of publicly traded

REITs and is the source of constant performance monitoring by a number of professional organization1. In terms of most real assets markets, commercial real estate has the most detailed and extensive, validated set of performance data of any alternative asset class.

In terms of the dynamics of the liquidity process, we construct several recognized proxies for liquidity, based on quote and trade prices, and daily trading data, for REITs, a sample of control firms (matched for market capitalization and the book to market ratio), and the overall market. Several papers have examined liquidity proxies using daily trading data, see for instance, Marcato and Ward (2007), Brounen et al (2009), and

Cannon and Cole (2011). However, unlike these studies we include liquidity measures based on intraday quote and trade prices for REITs.

1 Including the National Council of Real Estate Investment Fiduciaries (NCREIF), whose data is used in this study.

To preview our results, we find that REITs generally have a lower level of liquidity than either the controls or the overall market. After documenting the characteristics and dynamics of these series, we then consider the transmission of a liquidity shock between these series. Using Granger Causality tests, we find an intriguing result, even though the Amihud liquidity proxy for the market tends to lead REIT liquidity (Amihud 2002), turnover in REITs does appear to lead overall market turnover.

We discuss possible reasons for this in Section IV.

A further innovation in our study is the use of liquidity measures obtained from the direct real estate market. To date very few studies have considered liquidity measures in the direct real estate market and there is little understanding of the dynamic properties of this series of interest (see Clayton et al 2008 for a related article). Using data from the

MIT Transactions-Based (TBI) Index (see Fisher, et al 2007), we examine liquidity measure based on an Amihud-type measure. Recently Bond and Slezak (2010) have used the latter measure as a liquidity proxy in a portfolio optimization exercise and the results of the present study would appear to support the use of this measure as a meaningful proxy for liquidity. We document the dynamic relationship between these measures and show some difference in the transmission mechanism between each measure and liquidity measures in the public markets. Furthermore, we find evidence of a strong connection between macroeconomic factors and liquidity in the private real estate market.

Our study extends the work of Marcato and Ward (2007) and Brounen et al (2009) in three ways. Firstly, our sample covers the recent financial crisis and given the significance of liquidity in the crisis, provides important information to researchers and investors on the behavior of liquidity in crisis periods in these markets. Second, while our

3 paper examines only US markets, it incorporates measures of liquidity from the public markets as well as private real estate markets. Most of the literature to date has primarily focused on REIT liquidity. Finally, our study investigates the relationships between macroeconomic factors and liquidity in real estate markets.

The outline of our paper is as follows. The next section reviews the relevant literature. Following that we describe the data and liquidity measures used in our study in

Section III. Section IV outlines our approach to the factor decomposition of the liquidity measures and Section V discusses our results. The paper concludes in Section VI.

2 Literature

2.1 Liquidity in public real estate markets

REIT liquidity has been the focus of a large stream of research. Bhasin, Cole and

Kiely (1997) and Clayton and MacKinnon (2000) have previously studied REIT liquidity with a particular emphasis on within day trades. Both authors note the important changes in REIT liquidity post 1993. However in both cases, the sample period studied was confined to the 1990s. Ling et al (2011) finds an important connection between the availability of mortgage financing and real estate market liquidity.

Recent papers by Marcato and Ward (2007) and Brounen et al (2009) extend the research beyond US markets, and analyze REIT liquidity in an international setting. Even though these studies have little emphasis on cross-market liquidity, they are helpful in

4 understanding the determinants of individual company liquidity. However, these studies do not consider linkages between liquidity in the public and private markets.

2.2 Liquidity in private real estate markets

One approach to measuring liquidity risk in private commercial real estate markets is that of Lin and Vandell (2007), Bond et al. (2007), and Cheng, Lin and Liu

(2010). These papers measure the volatility in asset returns over the (uncertain) time to sale (time on market) as use this as a measure of liquidity risk. When the volatility of the time to sale is taken into consideration, the ex-ante volatility of real estate returns can be much greater than an ex-post measure of volatility calculated from historical real estate returns. However, while this line of research clearly has significant merit, it is subject to the limitation that it can be difficult to implement because of data availability. For instance, it is very difficult to get reliable and timely data on time-on-market for commercial real estate assets.

Another liquidity proxy that has been suggested for the commercial real estate market is a measure based on the difference between an index of imputed seller reservation prices and an estimate of the level of buyer’s reservation prices (See Fisher,

Geltner and Pollakowski 2007, and Fisher et al. 2003). A significant advantage of this measure is that because it is a by-product of producing a transactions-based real estate index, it is available at a quarterly frequency, and it is available over an extensive period of time (from 1984 for the all property measure or from 1994 at the sector level). This measure was used in Bond and Slezak (2010) to capture immediate liquidation costs in a

5 multi-asset portfolio optimization context. Their results show considerable promise for this measure as a practical proxy of liquidity in commercial real estate markets.

To our knowledge the only other study that uses liquidity measures from the TBI index is that of Buckles (2008). Rather than use the liquidity spread variable from the

TBI, Buckles estimates a liquidity index from a cointegrating regression between the constant liquidity index and the supply index. He then presents a time series analysis of the resulting series.

3 Data and liquidity measures

3.1 Data

The data used for the analysis come from four sources: the CRSP/Ziman REIT

Database; the CRSP daily/monthly stock returns; the TAQ database; and the transactions- based index (TBI) by MIT center for Real Estate. Our analysis begins with all

NYSE/AMEX/NASDAQ firms in the Ziman REIT database with available daily data since 1980. Between January 1980 and December 2010 there are over 500 REIT firm with daily trading information.

Stocks are filtered in our sample based on the following criteria. For the daily and intraday data: (1) We use only NYSE stocks to avoid any possibility of the results being influenced by differences in trading protocols. (Chordia, Roll, and Subrahmanyam, 2001;

Korajczyk and Sadka, 2008). (2) If a firm changed listing from NASDAQ to NYSE during the year, it was dropped from our sample for that year. There are no firms that

6 changed listing from NYSE to NASDAQ in our sample. (3) To avoid the influence of overly high-priced stocks, stocks whose prices are below $1 and above $1000 are excluded. (4) We excluded firms with less than 24 monthly observations.

For the intraday data: (1) Use only use best bid or offer (BBO)-eligible primary market (NYSE) quotes. (2) Trades out of sequence, trades recorded before the opening or after the closing time, and trades with special settlement conditions are eliminated. (3)

We discard negative bid-ask spreads and transaction prices. (4) To avoid after hours liquidity effects, the first trade after the opening time is ignored. (5) In addition, only quotes that satisfied the following filter conditions are retained: quotes in which the bid- ask spread is positive and below $5; quotes in which the bid-ask spread divided by the midpoint of the quoted bid and ask is less than 10% if the midpoint is greater than or equal to $50; and quotes in which the quoted spread is less than 25% for midpoints less than $50.

Our major results based on a sample from September 1993 to December 2010, include 283 REITs firms with both available daily and intraday data. Our data begins in

September 1993 because the nature of the REIT market changed substantially after the announcement of Revenue Reconciliation Act of 1993 in August 1993. We also consider a long sample from January 1983 to December 2010, that contains 292 REITs firms.

To compare REITs shares with ordinary common shares (CRSP share codes 10 and 11), we also construct a control group and a market sample. Fama and French (1992) argue that common stock returns are related to firm size and book-to-market ratios.

Barber and Lyon (1997) document that constructing control firms by size and book-to-

7 market generates well-specified test statistics in most sample situation considered. As in

Barber and Lyon, we match a REITs sample firm with a control firm with the closest size and book-to-market ratio2. Specifically, we chose a control firm with smallest absolute differences in size and book-to-market ratio; if there are ties, we keep the closest match in size. The market sample includes all ordinary common shares filtered by the criteria mentioned earlier.

3.2 Liquidity measures

For each stock we define the following liquidity measures:

(1) Amihud –– the daily average of absolute value of return divided by volume for asset i in month t:

| | ∑ , (1)

where is the return on asset i on day j of month t, is the dollar volume (number of shares multiplied by the transaction price) traded in asset i on day j of month t, and is the number of trading days in month t. This measure is based the measure proposed in

| | Amihud (2002). If is observed less than 15 days for asset i in month t, of asset

i is deleted from the sample for the month. We also scale by the ratio of market capitalization of the CRSP Ziman REIT Index at t-1 and at a reference date (first month of the sample).

(2) Turnover –– the ratio of monthly volume and shares outstanding:

2 Size and book-to-market are constructed as in Fama and French (1992, 1993).

∑

, (2)

where is shares outstanding of asset i at the end of month t.

(3) Qspread – the quoted percentage spread is measured for each trade as the

3 ratio of the quoted bid-ask spread and the bid-ask midpoint . Monthly estimates are a simple average through the month:

∑ , (3)

where ( )⁄ , and are the ask and bid quotes prevailing at the time of the jth trade of asset i in month t, and is the number of eligible trades of asset i in month t.

(4) Espread – the effective percentage half-spread is measured for each trade as the absolute value of the difference between the transaction price and the quote midpoint:

| | ∑ , (4)

where is the transaction price for the jth trade of asset i in month t.

The next four liquidity measures are price effects on trades estimated using intraday data, distinguishing between the permanent and transitory effects. Permanent effects are believed to be related to the private information revealed through the trading

3 The midpoint of the quotes as of five seconds prior to the trade is used as suggest by Lee and Ready (1991) because of a delay in the time that bid and offer are quoted. Specifically, for the estimation, any quote posted less than five seconds prior to a trade is ignored, and the first quote posted at least five seconds prior to the trade is retained.

9 process, and the transitory effects are the compensation to the market makers’ costs of making a market, such as inventory and order processing (Ho and Macris, 1984; Glosten and Harris, 1988; Madhavan and Smidt, 1991).

The estimation procedures of measuring the components of price impact are summarized as follow. The method is an extension of the theory work in Glosten and

Harris (1998), developed in Sadka (2006) and applied in Korajczyk and Sadka (2008).

Let denote the market maker’s expected value of the security, conditional on the information set available at time t (t represents the event time of a trade)

[ ̃ ] (5)

where is the order flow, is a binary indicator variable that receives a value of (+1) for a buyer-initiated trade and (-1) for a seller-initiated trade, and is a public information signal. Prices above the midpoint of the quoted bid and ask are considered buyer-initiated; prices below the midpoint are considered seller-initiated. Trades whose price equals the midpoint are discarded from the sample (Lee and Ready, 1991).

To estimate the permanent price effects, Sadka (2006) follow the formulation proposed by Glosten and Harris (1988) and assume that takes a linear form such that

[ ] (6) where and are the fixed and variable permanent price impact costs, respectively. This equation describes the innovation in the conditional expectation of the security value through new information, both private ( and public ( . Note that information induces a permanent impact on expected value.

To account for predictability in the order flow that is well documented in the literature, Sadka (2006) adjust Eq. (6) to Eq. (7), assumed that market makers revise the conditional expectation of the security value only according to the unanticipated order flow, not the entire order flow at time t.

[ [ ]] [ [ ]] (7)

Denote the unexpected sign of a trade as , where [ ], and unexpected signed volume of trade , where [ ]. Substituting the above formulations in Eq. (7) and taking the first difference, we have:

(8)

The observed transaction price can be written as

̅ [ ̅ ] (9)

̅ ̅ and are temporary effects by the construction of Eq. (9), as they affect only and are not carried on to . Taking the first differences of and substituting

from Eq. (8) we have

̅ ̅ ( (10)

Therefore, the components are obtained by the regression (11), estimated per firm per month using OLS with corrections for serial correlation in the error term:

̅̅̅̅ ̅̅̅ ̅ ̅ ( ) , (11)

11 where is a binary indicator variable of the jth trade of asset i in month t that receives a value of (+1) for a buyer-initiated trade and (-1) for a seller-initiated trade, is the order flow of the jth trade of asset i in month t, is the unexpected signed volume of trade measured as the fitted error term from a five-lag autocorrelation regression of the order flow , is the unexpected direction of trade calculated while imposing normality of the error , where [ ], and is the first difference operator 4. Thus, the price component liquidity measures we research in this paper are:

(5) is the permanent variable component (PV) of price impact since it measures how much the valuation of the asset changes given a shock to signed trading volume, .

̅̅̅̅ (6) is the transitory variable component (TV) of price impact since the effect of

̅̅̅̅ signed volume for this trade, , has an effect of on the price of trade j,

̅̅̅̅ and effect of on the price of trade , and no effect on subsequent prices.

(7) is the permanent fixed component (PF) of price impact.

(8) ̅̅̅ ̅ ̅ is the transitory fixed component (TF) of price impact.

4 Methodology

4.1 Factor decomposition of liquidity

Following Korajczyk and Sadka (2008), we examine a factor decomposition of each liquidity measure and return in this section.

4 see Sadka (2006) for more details

To avoid overweighting some liquidity measures over others due to their different scale, we first standardize our liquidity measures. Define as the matrix of

observations on the ith liquidity measure ( . Define ̂ as the time-series mean,

and ̂ as standard deviation of the cross-sectional average of liquidity measure i, estimated from the sample up to time . The standardized liquidity measure is

( ̂ )⁄ ̂ , where is the observations of the ith standardized liquidity measure of the matrix .

Assume that the data generating process for is an approximate factor model:

, (3) where is a vector of factor sensitivities to the common liquidity shocks, is a

matrix of shocks to liquidity measure i that are common across the set of n assets, and is an matrix of asset-specific shocks to liquidity measure i. In other words,

are the systematic (undiversifiable) shocks that affect most of the assets, while are idiosyncratic (diversifiable) shocks that have weak link across the assets.

To estimate the factor model, Korajczyk and Sadka (2008) use Asymptotic

Principal Components (APC) analysis developed by Connor and Korajczyk (1986).

Specifically, in an approximate factor-model setting for a balanced panel (complete data), since is unobervable, we use a proxy for consisting by the k largest eigenvectors of

. (4)

Connor and Korajczyk (1986) show that this proxy gives asymptotically identical estimates (as ) to those obtained if we were able to use the unobservable .

Furthermore, because is a matrix, the computational burden of the principal components (eigenvectors) of this matrix is independent of the cross-sectional sample size, n. This implies that this method can be used for very large cross-sectional samples, since for most panel data the time-series matrix has a much smaller dimension than the corresponding cross-sectional crossproduct matrix used by standard factor analysis.

To accommodate missing data, we use the technique developed in Connor and

Korajczyk (1987). Specifically, we estimate each element of by averaging over the observed data. Let be the data for liquidity measure i with missing data replaced by

zeros. Define as a matrix for which is equal to one if is observed and is

zero if is missing. Define

( ) , (5) ( )

where is the unbalanced panel equivalent of in which the ( element is defined as the cross-sectional averages over the observed data only5. The estimates of latent factors, , are obtained by calculating the eigenvectors for the k largest eigenvectors of

We extract three principal components for each liquidity measures, and estimate the time-series regression for each stock’s liquidity on the three extracted factors to

5 While in a balanced panel is guaranteed to be positive semi-definite, is not. However, similar to

Korajczyk and Sadka (2008), we have not find cases in which is not positive definite in large cross- sections sample.

14 demonstrate the degree of commonality across assets for each liquidity measure. The regression model is

̂ ̂ , (6)

where ̂ is the vector of factor estimates for month t.

4.2 Granger causality and the testing method

To exam the relations among liquidity measures, and the relations between liquidity measures and macroeconomic variables, we conduct the Granger Causality test under a linear vector auto regression (VAR) framework.6

To describe the definition of Granger causality and the testing methodology

(Granger, 1969), consider the case of two stationary time series. Denote ( as the conditional probability distribution of given the bivariate information set consisting of an -length lagged vector of ( ( ) and

an -length lagged vector of ( ( ). Given lags

and , the time series does not strictly Granger cause if:

( ( ,

The definition of causality used above is based entirely on the predictability of one time series. Specifically, if contains information in past terms that helps to forecast

6 In this paper we do not consider the case of nonlinearity in the causality relationship as in the case of Hiemstra and Jones (1994).

and if this information is not contained in other series used in the predictor, then is said to Granger cause .

To test Granger causality, we employ the widely used vector auto regression

(VAR) framework:

∑ ∑ , ∑ ∑ ,

where the error term and are uncorrelated white-noise.

The null and the alternative hypotheses are as below:

∑ or does not Granger cause

∑ or does Granger cause

The standard joint test ( -test) of exclusion restrictions is used to determine whether lagged can significantly forecast current . We reject the null hypothesis that

does not Granger casue if ∑ are jointly significantly different from zero. The above method and testing framework can be generalized to the many variables situation as well.

5 Results

5.1 Common factors of liquidity measures

Table 1.1 reports the average and the average adjusted- of time-series regressions using one, two, and three common factors. Results are reported for two sample period:

1993:09 – 2010:12 as well as 1983:01 – 2010:12. Results for the three different groups,

REITs firms and control firms as well as the market are also reported.

[Insert Table 1.1 here]

The results obtained clearly indicate a commonality across assets for most liquidity measures. However, the magnitude of the commonality was different among each of the different groups. For example, the of the Amihud measure for REITs was found to be half of that of the control firms, and only one-third of the Market. For REITs, the of the Amihud measure was much smaller than the of Turnover measure. The values of the Amihud measures for the REITs firms range from 6.64% to 22.8%, while the of the Turnover measure of REITs range from 26.74% to 37.81%. The of Amihud measure of market is consistent with the results of Korajczyk and Sadka (2008), while the

of the Turnover measure of market is nearly three times larger than that of the results documented in Korajczyk and Sadka(2008).

The difference found could likely be the result of the different time periods we used in our sample, which indicates that the Turnover measure’s commonality has been increasing over the past ten years. The of Amihud and Turnover measures for control firms are similar for the period of 1993:09 – 2010:12. The most surprising result is that the Turnover liquidity measure for REITs has the strongest commonality among all three groups. It is also interesting that of Turnover for REITs is significantly larger than that of Amihud for REITs. This is inconsistent with the results of Korajczyk and Sadka

(2008), who show that the of Turnover measure for the market is sizably smaller

17 among other measures. This difference could be due to the unique characteristics of

REITs Firms.

[Insert Figure 1.1 here]

Figure 1.1 shows the time-series variations of the Amihud and turnover measure for REITs, Control Firms and Market for periods 1993:09-2010:12. Both measures are calculated as equally weighted averages across stocks. The first graph shows that the

Amihud measure of REITs is similar to that of control firms from 1996 to 2000, while it is consistently higher over the remaining time periods. Note that the Amihud measure reflects illiquidity, so a high value reflects a high price impact of trade, that is, low liquidity. This fact indicates that, controlling for size and book-to-market ratio, the REITs firms are less liquid than non-REIT firms. However, by controlling for size and book-to- market, we rule out the possibility that the illiquidity of REITs firm is due to the fact that most of the REITs firms are small growth firms, and can conclude that the low liquidity of REITs firms result from their uniquely firm characteristics. The control group’s performance moves closely to that of market after 2003. The turnover measures of three groups tell the same story with the Amihud measure.

As for liquidity measures calculated from intraday data, Qspread, Espread, PV,

PF, TV, and TF, except Qspread, the of the rest liquidity measures for REITs firms are considerably smaller than those reported in Korajczyk and Sadka (2008) for the whole market. For example, the of TF for REITs firms are 13.51%, less than 1/3 of the of TF for the market (47.6%, see table 1 in Korajczyk and Sadka(2008)). This result indicates that, to some extent, the liquidity of REITs firms share less commonality

18 with each other for a short period (intraday) compared to the liquidity of all the firms in the market.

[Insert Figure 1.2 here]

Figure 1.2 shows the time-series variations of Qspread, Espread, PV, PF, TV and

TF for REITs firms for periods 1993:01-2010:10. The first graph of bid-ask spread variables shows that the liquidity of REITs firms is increasing over time, consistent with the results for the Amihud and Turnover measures. However, an important difference compared to the Amihud and Turnover measures, is the clear spike during 2008-2009, indicating that REITs firms became very illiquidity during the financial crisis. The second and the third graphs describe the price impact components. Permanent variables and transitory variables vary in opposite directions for most of the time in our sample period, and they all show evident spikes during financial crisis, suggesting that the liquidity measures derived from intraday data are more sensitive to financial crisis or economic downturns compared to the Amihud and Turnover measures derived from daily data.

5.2 Lead-lag relations between liquidity measures of REITs

[Insert Table 1.2 here]

To explore the relations between liquidity measures obtained both from inter- and intraday data, we conduct Granger causality tests between pairs of liquidity measures of

REITs firms. For each pair we first test the null hypothesis that Column (1) does not

Granger cause Column (2), and then Column (3) does not Granger cause Column (4). We

19 perform the test by using a vector auto regression (VAR) framework. The results of

Granger causality tests in Panel A of Table 1.2 document strong evidence of one way

Granger causality of twelve pairs of liquidity measures of REITs firms at 1% significant level. First of all, there are significant one way Granger causalities from Amihud_MKT to Amihud, and Qspread to Amihud. Further investigation shows that Amihud_MKT and

Qspread for REITs firms have a bi-directional effect on each other (Amihud_MKT lead

Qspread at 1% level, while Qspread also lead Amihud_MKT at 5% level).

Second, Turnover Granger causes TV, while both Espread and TF Granger cause

Turnover (the same with Amihud_MKT and Qspread, Espread and TF have significant mutual effect on each other). However, there is no lead relation from Espread to TV, but a one-way Granger causality from TV to Espread.

Last but not the least, as expected Amihud, Qspread also lead Espread, PF, and

TF, while there is no evidence suggesting reverse causality from the rest seven liquidity measures for REITs firms to Qspread, indicating that bid-ask spread contains information that have influence on the following stock prices and especially the fixed components in prices.

5.3 REITs and the direct real estate market

Next we compare the liquidity measures of REITs firms to the liquidity measures of the actual real estate market. We use a liquidity measure, Spread_TBI, from the transactions-based index (TBI) developed by MIT center for real estate. Construction of this measure is well discussed in Fisher et al. (2003, 2007). Further discussion on the use of this series as a liquidity measure is given in Bond and Slezak (2010). Using well-

20 established econometric techniques, two indices are created; the first represents the midpoint of the means of the buyer and seller reservation distributions (which is referred to as the TBI), and the second is the mean of the buyers distribution (referred to as the constant-liquidity index).7 The difference between these two indices can be thought of as being analogous to a bid–ask spread for real estate and is the measure used in this paper.

[Insert Figure 1.3 here]

Figure 1.3 shows that Amihud measures of REITs, and Spread of TBI share similar patterns, while the liquidity measure of REITs is more volatile. Turnover measures of REITs, on the other hand, move in the opposite direction with Amihud and

Spread_TBI, since Turnover measures ‘liquidity’ and Amihud and Spread_TBI measures

‘illiquidity’. Because the results indicate similar patterns, we investigate the possibility of causality between liquidity measures of REITs firms and the actual real estate market.

We perform the test by using a vector auto regression (VAR) framework. We performed the test on the sample period from 1987:02 to 2010:04.

In panel B of Table 1.2, there is significant evidence of one-way Granger causality from Turnover, Qspread, and Espread of REITs firms to Spread_TBI at 1% level. In terms of transitory price impact variables, there is a two-way Granger causality relationship between TV and Spread_TBI, and TF and Spread_TBI. This evidence suggests that the fluctuation of REITs firms’ stock prices contain information on the direction of liquidity for the actual real estate market.

7 Spread = (Demand index – Supply index)/( (Demand index + Supply index)/2).

Panel C repeats the analysis in Panel A for a period relating to the financial crisis.

Using only monthly data from the series derived from REIT and stock market data, there is evidence to suggest to REIT liquidity measures led the liquidity measures for the overall market during the crisis (measured as July 2007 to June 2010). This result holds for both the Amihud and turnover measures, as well as for Qspread and Espread. This is an intriguing result and may be due to the role that real estate played in the financial crisis.

5.4 Liquidity measures and macroeconomic variables

[Insert Table 1.3 here]

Table 1.3 shows contemporaneous correlations between liquidity measures, market variables and macroeconomic variables of the U.S. We employ real GDP (GDPR), the unemployment rate (UE), real consumption (CONSR), real investment (INV), money supply (M2 and NONM18), and following a recent paper by Ling et al (2011) we also include a measure of the tightening standards for commercial real estate loans

(TIGHTEN)9. We also use Excess market return (MKT), Term Spread (TERM), Credit spread (Cred), volatility of S&P 500 (VIX), and spread in returns between value and growth stocks (HML) to proxy for financial market variation.

SPREAD_TBI are significantly positively correlated with two out of five financial market variables, TERM, and CRED, indicating that actual market liquidity

8 NONM1 is non-M1 component of M2. 9 The GDPR is real gross domestic product, CONSR is real personal consumption expenditures, INV is real private fix investments, and UE is unemployment rate for full time workers. All series are seasonally adjusted. GDPR, CONSR, and INV are from the Federal Reserve Bank of St. Louis, and UE is from the U.S. Bureau of Labor Statistics.

22 links tightly to market interest rate structures. Note that the TURNOVER of REITs firms and Spread_TBI are both negatively correlated to GDP growth. So when GDP growth increases, the liquidity of REITs firms deteriorates but the liquidity in the actual real estate market increases. In other words, the same causes that improve the liquidity in actual real estate market also contribute to GDP growth. The correlation between the INV growth and TURNOVER, ESPREAD, or SPREAD_TBI tells a similar story with those liquidity measures’ correlations with GDP growth.

Panel B in the table shows the correlations leading up to the financial crisis.

During this period, Credit Spreads are significantly inversely correlated with REIT liquidity measures. However, during the financial crisis, this connection is not significant.

However, the credit tightening variable is found to positively correlated with turnover and inversely related to the Amihud measure of illiquidity.

[Insert Table 1.4 here]

To investigate the lead-lag relations between liquidity measures and macroeconomic and market variables, we conduct a similar Granger causality test and the results are reported in Table 1.4. First of all, there is a significant one way Granger causality from AMIHUD to HML, indicating that the risk correlated to HML could be lead by the liquidity risk carried by AMIHUD liquidity measure. Only one macro variables, CRED, out of thirteen lead AMIHUD at 10% level.

Similarly, there is a significant one way Granger causality from TURNOVER to dUE, and it is the only one liquidity measure out of nine has noticeable leading effect on the change of unemployment rate. Moreover, two out of six market variables significantly

Granger cause TURNOVER at 1% level (TURNOVER_MKT, MKT, and TERM), and five out of all thirteen variables significantly Granger cause TURNOVER at the 10% level (VIX, HML, dINV, dUE, and CRED). Comparing the results of AMIHUD with

TURNOVER, it is clearly that the latter are heavily affected by macro and market variables. Also note that from Figure 1.3 we can see that the AMIHUD measure leads the movement of the TURNOVER measures.

Second, the results of ESPREAD are very similar to the results of TURNOVER: more than half of the thirteen variables significantly Granger cause both liquidity measures, and both liquidity measure only have a few effect on the thirteen variables. dINV leads ESPREAD at the 1% significance level, suggesting that the change of private investment has significantly effect on the change of ESPREAD liquidity measure. HML also has a significant Granger causal effect on ESPREAD at 1% level. dM2 and

ESPREAD, dCONSR and ESPREAD, and dTIGHTEN and ESPREAD have a mutual effect on each other. Contrary to ESPREAD, QSPREAD does not Granger cause any of the thirteen macro and market variables, and only two variables have significant effect on

QSPREAD: HML at 1% level, and dINV at 5% level.

Third, none of the four price impact components are Granger caused by any macro variables, but all of them Granger cause several macro variables. For example, there is a one-way Granger causality from PF to dTIGHTEN, but not the other way around. In addition, two permanent price impact component, PV, and PF, have the one way lead relations with dM2, suggesting that the permanent effect in price could lead the changes of money supply.

Last but not the least, only one of the macro variables leads SPREAD_TBI significantly at 1% level, indicating that the movement of money market has significant effect on private real estate market. There is a significant one way Granger causality from

SPREAD_TBI to dM2, VIX, AMIHUD_MKT, and TERM at the 10% level.

In results not reported, we also investigated the impact of the financial crisis on these tests. Using a dummy variable for the time of the crisis, we recalculated the

Granger causality tests. Espread and Qspread showed a strong lag effect from most macroeconomic variables. The lead effect for the Amihud variable on the HML variable disappears. However, the turnover variable continues to be lead by many macroeconomics series.

To summarize, for the private real estate market, the money market variable

(dNONM1) is the only variable among thirteen macro and market variables that has significant effect on liquidity measure SPREAD_TBI. While, for public real estate market, the effects of macro and market variables on the liquidity measures are mainly concentrated on the liquidity measures constructed from daily data but no effect on the liquidity measures constructed from intraday data. This is not surprising as the liquidity measures calculated from intraday data are designed to capture information through the intraday trading process more quickly than the macro or market variables calculated from daily or quarterly data. Moreover, contrary to the results in Ling et al (2011), we do not find the significant lead-lag relation between the tightening standards for commercial real estate loans (dTIGHTEN) and TURNOVER liquidity measure. Among the eight liquidity measures, dTIGHTEN and ESPREAD have mutual effect on each other at 10% significant level, and the transitory fixed component (TF) and the permanent fixed

25 component (PF) significantly Granger cause dTIGHTEN. The effect is strongest for the permanent fixed component of price impact, suggesting that the fixed component of price impact has evident effect on the tightening standards for commercial real estate loans.

This result confirms the findings documented in Schnabl (2011) that there exists a negative lead-lag relation between liquidity shocks and banks lending.

Our results show important connections between these markets. These results are highly relevant to real estate investors who might consider holding REITs in addition to private market real estate to improve portfolio liquidity. The empirical results also have implications for risk measurement for institutional investors and might suggest that information from public markets or macroeconomic variables could be used to improve risk exposure estimates for these investors. This paper has not investigated whether trading strategies could be developed to take advantage of timing differences across public and private markets. Such strategies may be unlikely to be profitable given the large transaction costs of trading direct real estate.

6 Conclusion

Our study has investigated a number of features of cross-market liquidity between public and private commercial real estate markets. To our knowledge this has been the first study to consider liquidity connections between these two markets. Furthermore it is one of the first to investigate liquidity in commercial real estate markets following the financial crisis.

Our initial set of results focuses on the REIT market and compares liquidity for

REITs to a set of controls matched for size and book to market, as well as overall equity market liquidity. We note that controlling for size and book to market, REIT liquidity is lower than for non-REIT firms. While our results show clear commonality in liquidity among REITs, as well the control firms, using the Amihud liquidity measure shows that there is less commonality in the REITs compared to the controls. Indeed, based on the R2 measure, the commonality in REITs is less than half that of the controls and only a third of that of the overall market.

Like Brounen et al (2009), we do note important differences between the liquidity measures. For instance, in terms of the measures of commonality reported for turnover, for REITs we find this to be significantly higher than for the controls and the market.

These results also appear to be at odds with the findings of Korajczyk and Sadka (2008), who generally find lower levels of commonality in liquidity based on turnover measures.

While this results requires further investigation it may be due in part to the financial crisis and the way in which real estate related firms were particularly affected by the nature of the crisis.

Furthermore, we found important information contained in liquidity measures constructed using market microstructure variables that has not been previously identified.

Firstly, the extreme liquidity freeze that took place during the financial crisis is much more evident when intraday data is used than daily data. Also, there is evidence that the liquidity variables based on intraday data lead other liquidity measures for REITs.

In the second set of findings reported, we investigate cross-market liquidity between public and private real estate markets. We find generally similar time-variation in the liquidity measures for both real estate markets. Due to the similar time-series variation, we test for any directional causality between the markets and find that generally the causality runs from the public markets to the private markets. However, we do note the finding of bi-directional causality between the TBI spread measure of liquidity and the Amihud measure for REITs.

Our final set of results investigated a connection between macroeconomic factors and real estate market liquidity. We find a strong association between real estate liquidity and the term spread, and between real estate liquidity and changes in real investment and consumption expenditure, as well as with the unemployment rate. Other strong associations were found between liquidity and changes in GDP. An interesting difference noted between the public and private markets, was that credit spreads did not appear to be associated with liquidity in the private real estate market, but it was associated with liquidity in the REIT market.

References

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Bond, Shuan A. and Steve L. Slezak. 2010. “The Optimal Portfolio Weight for Real Esate with Liquidity Risk and Uncertainty Aversion.” Working Paper, University of Cincinnati.

Brounen, D., P. Eichholtz, and D. Ling. 2009. “The liquidity of property shares: an international comparison.” Real Estate Economics 37:413-445.

Buckles, Brian W. 2008. “Liquidity Dynamics in Commercial Real Estate.” Journal of Real Estate Portfolio Management 14:307-324.

Cannon, Susanne and Rebel Cole. 2011. “Changes in REIT liquidity 1988-2007: Evidence from daliy data.” The Journal of Real Estate Finance and Economics 43:258-280.

Cheng, P., Z. Lin, and Y. Liu. 2010. “Illiquidity, Transaction Cost, and Optimal Holding Period for Real Estate: Theory and Application.” Journal of Housing Economics 19:109-118. chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam. 2001. “Market liquidity and trading activity.” The Journal of Finance 56:501-530.

Clayton, Jim and Greg MacKinnon. 2000. “Measuring and Explaining Changes in REIT Liquidity: Moving Beyond the Bid-Ask Spread.” Real Estate Economics 28:89-115.

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Connor, Gregory and Robert A. Korajczyk. 1987. “Estimating pervasive economic factors with missing observations.” Working paper no. 34. Department of Finance, Northwestern Universtiy.

Fama, Eugene F. and Kenneth R. French. 1992. “The cross-section of expected stock returns.” Journal of Finance 47 427-465.

Fama, Eugene F. and Kenneth R. French. 1993. “Common risk factors in the returns on stocks and bonds.” Journal of Financial economics 33:3-56.

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Fisher, J., D. Geltner, and H. Pollakowski. 2007. “A quarterly transactions-based index (TBI) of institutional real estate investment performance and movements in supply and demand.” Journal of Real Estate Finance and Economics 34:5-33.

Korajczyk, Robert A. and Ronnie Sadka. 2008. “Pricing the commonality across alternative measures of liquidity.” Journal of Financial Economics 87:45-72.

Lin, Z. and K. Vandell. 2007. “Illiquidity and Pricing Biases in the Real Estate Market.” Real Estate Economics 35:291-330.

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Fig. 1.1

Amihud and Turnover are the two liquidity measures. The Amihud (2002) measure is defined as the monthly average of daily absolute value of return divided by dollar volume; Turnover is defined as the ratio of monthly volume and shares outstanding. Both measures are calculated as equally weighted averages across stocks. _REITs is liquidity measures of REITs firms, _control is control group constructed by matching closest size and book-to-market with REITs firms, and _market is liquidity measure of the whole market.

Amihud: 1993:09 - 2010:12 25

200709 200811 199309 199404 199411 199506 199601 199608 199703 199710 199805 199812 199907 200002 200009 200104 200111 200206 200301 200308 200403 200410 200505 200512 200607 200702 200804 200906 201001 201008

Amihud_REITs Amihud_control Amihud_market

Turnover: 1993:09 - 2010:12 12

Turnover_REITs Turnover_control Turnover_market

Fig. 1.2

Qspread, Espread, PV, PF, TV, and TF are the six liquidity measures calculated with intraday data of REITs firms. Qspread is measured as the ratio of the quoted big-ask spread and the bid-ask midpoint; Espread is measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price impact components, PV, PF, TV, TF, are calculated as in Sadka (2006).

Bid-Ask Spread 0.03

0.025

0.02

0.015

0.01

0.005

200110 200708 199301 199308 199403 199410 199505 199512 199607 199702 199709 199804 199811 199906 200001 200008 200103 200205 200212 200307 200402 200409 200504 200511 200606 200701 200803 200810 200905 200912 201007

Espread Qspread

Price Variable Impact 0.00015

0.0001

0.00005

200109 200501 199309 199405 199501 199509 199605 199701 199709 199805 199901 199909 200005 200101 200205 200301 200309 200405 200509 200605 200701 200709 200805 200901 200909 201005 -0.00005 199301

-0.0001

-0.00015

Permanent Variable Transitory Variable

Price Fixed Impact 0.2

0.15

0.1

0.05

199403 199410 200810 200905 199308 199505 199512 199607 199702 199709 199804 199811 199906 200001 200008 200103 200110 200205 200212 200307 200402 200409 200504 200511 200606 200701 200708 200803 200912 201007 -0.05 199301

-0.1

Permanenant Fixed Transitory Fixed

Fig. 1.3

Amihud, Turnover and Spread_TBI are the three liquidity measures of REITs firms. The Amihud measure is defined as the monthly average of daily absolute value of return divided by dollar volume; Turnover is defined as the ratio of monthly volume and shares outstanding. Both measures are calculated as equally weighted averages across stocks. Spread_TBI are constructed from the transactions-based index (TBI) developed by MIT center for real estate. Spread_TBI = (Demand index – Supply index)/( (Demand index + Supply index)/2).

1.2 3.5

1 3

2.5 0.8 2 0.6 1.5 0.4 1 0.2 0.5 0 0

-0.2 -0.5

199902 198702 198801 198804 198903 199002 199101 199104 199203 199302 199401 199404 199503 199602 199701 199704 199803 200001 200004 200103 200202 200301 200304 200403 200502 200601 200604 200703 200802 200901

-0.4 -1

Amihud Spread_TBI Turnover

Table 1.1

This table reports the average and the average adjusted- of time-series regressions using one, two, and three common factors. Within-measure common factors are extracted from both liquidity measures by APC method, and then for each variable and each stock, we regress each of the liquidity measure on its common factors. The Amihud (2002) measure is defined as the monthly average of daily absolute value of return divided by dollar volume; Turnover is defined as the ratio of monthly volume and shares outstanding; Qspread is measured as the ratio of the quoted big-ask spread and the bid-ask midpoint; Espread is measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price impact components, PV, PF, TV, TF, are calculated as in Sadka (2006). Before common factor and regression analysis, for each stock, each liquidity measure is normalized every month by its mean and standard deviation calculated up to the prior month.

REITs Control Firms Market

Factor Factor Factor Factor Factor Factor Factor Factor Factor Variable Statistic 1 2 3 1 2 3 1 2 3 Panel A. 1993:09 - 2010:12

Amihud 6.64 13.57 22.88 11.29 18.42 21.76 19.31 34.66 39.05 Adj. 5.38 11.19 19.66 10.10 16.23 18.56 18.23 32.79 36.42

Turnover 26.74 34.95 37.81 13.50 20.32 29.57 19.97 27.23 37.00 Adj. 25.67 33.01 35.00 12.32 18.10 26.58 18.89 25.24 34.35

Qspread 15.93 35.96 48.29 ------Adj. 14.37 33.38 44.89 ------

Espread 10.08 14.84 28.06 ------Adj. 8.50 11.86 24.02 ------

PV(λ) 1.86 3.44 6.09 ------Adj. 0.01 -0.30 0.46 ------

PF(Ψ) 3.78 8.38 13.05 ------Adj. 2.04 5.05 8.22 ------

TV(λ) 1.74 3.73 5.33 ------Adj. -0.11 0.01 -0.39 ------

TF(Ψ) 4.84 9.00 13.51 ------Adj. 3.11 5.61 8.57 ------

Panel B. 1983:01 - 2010 :12

Amihud 8.60 13.88 18.57 7.06 14.04 19.63 15.76 27.19 36.50 Adj. 7.43 11.65 15.38 5.93 11.98 16.73 14.80 25.48 34.16

Turnover 23.58 31.94 36.24 12.76 17.65 25.16 17.95 24.29 32.19 Adj. 22.55 30.07 33.55 11.68 15.60 22.34 16.95 22.43 29.64

Table 1.2

The table shows Granger causality tests between liquidity measures derived from REITs firms and liquidity measures derived from the transactions-based index (TBI). For each measure, we first test the null hypothesis that the variables in Column (1) does not Granger cause the variables in Column (2), and then variables in Column (3) does not Granger cause variables in Column (4). The -statistics and p-value (in parentheses) are reported for each test.

Panel A: Monthly liquidity measures from 1993:09 to 2010:12 p- p- Null Hypothesis Null Hypothesis value value (1) (2) (3) (4)

Amihud Amihud_mkt 1.754 0.781 Amihud_mkt Amihud 27.930 0.000 Turnover Turnover_mkt 13.302 0.021 Turnover_mkt Turnover 5.579 0.349 Amihud Qspread 2.417 0.491 Qspread Amihud 26.211 0.000 Amihud Espread 12.601 0.126 Espread Amihud 7.865 0.447 Amihud PV 2.397 0.302 PV Amihud 0.625 0.732 Amihud PF 3.613 0.823 PF Amihud 5.475 0.602 Amihud TV 2.675 0.263 TV Amihud 3.147 0.207 Amihud TF 4.535 0.716 TF Amihud 2.702 0.911 Turnover Qspread 5.884 0.318 Qspread Turnover 14.786 0.011 Turnover Espread 5.665 0.129 Espread Turnover 11.722 0.008 Turnover PV 2.553 0.466 PV Turnover 2.544 0.467 Turnover PF 8.746 0.033 PF Turnover 0.788 0.852 Turnover TV 53.898 0.000 TV Turnover 16.374 0.498 Turnover TF 3.299 0.348 TF Turnover 18.958 0.000 Qspread Espread 49.722 0.000 Qspread Espread 4.406 0.819 Qspread PV 1.017 0.313 PV Qspread 0.734 0.392 Qspread PF 19.783 0.000 PF Qspread 1.326 0.250 Qspread TV 3.721 0.054 TV Qspread 0.148 0.701 Qspread TF 26.741 0.000 TF Qspread 4.413 0.731 Espread PV 3.612 0.307 PV Espread 0.758 0.859 Espread PF 26.586 0.000 PF Espread 11.389 0.010 Espread TV 19.111 0.322 TV Espread 51.709 0.000 Espread TF 78.627 0.000 TF Espread 91.971 0.000 PV PF 6.539 0.478 PF PV 6.608 0.471 PV TV 0.399 0.528 TV PV 2.683 0.101 PV TF 18.805 0.009 TF PV 3.991 0.781 PF TV 18.006 0.207 TV PF 75.542 0.000

Panel B: Quarterly liquidity measures from 1993:01 to 2009:03

Null Hypothesis p-value Null Hypothesis p-value (1) (2) (3) (4)

Amihud Spread_TBI 9.594 0.048 Spread_TBI Amihud 7.482 0.113

Turnover Spread_TBI 17.925 0.001 Spread_TBI Turnover 1.723 0.787

Qspread Spread_TBI 13.151 0.004 Spread_TBI Qspread 5.251 0.154

Espread Spread_TBI 21.876 0.009 Spread_TBI Espread 11.334 0.254

PV Spread_TBI 0.082 0.774 Spread_TBI PV 2.431 0.119

PF Spread_TBI 3.933 0.269 Spread_TBI PF 4.952 0.175

TV Spread_TBI 37.097 0.002 Spread_TBI TV 30.580 0.015

TF Spread_TBI 27.379 0.072 Spread_TBI TF 144.416 0.000

Table 1.3

This table shows the correlation coefficients between liquidity measures and market and macroeconomic variables of United States. The p-values are reported parentheses. Amihud, Turnover, Qspread, Espread, PV, PF, TV, and TF are constructed with intra- or interday data sets of REITs stocks. The Amihud measure is defined as the monthly average of daily absolute value of return divided by dollar volume; Turnover is defined as the ratio of monthly volume and shares outstanding. Qspread is measured as the ratio of the quoted big-ask spread and the bid-ask midpoint; Espread is measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price impact components, PV, PF, TV, TF, are calculated as in Sadka (2006). Both measures are calculated as equally weighted averages across stocks. Spread_TBI are constructed from the transactions-based index (TBI) developed by MIT center for real estate. Spread_TBI = (Demand index – Supply index)/( (Demand index + Supply index)/2). TERM is term spread, CRED is credit spread, MKT is excess market return, dGDPR is real GDP growth, dINV is growth in investment, dUE is growth in the unemployment rate, and dCONSR is real consumption growth. dM2 is growth in the money supply M2 that includes M1 in addition to all time-related deposits, savings deposits, and non- institutional money-market funds. dNONM1 is the growth in the non-M1 component of M2. VIX is the volatility of S&P 500. HML is the spread in returns between value and growth stocks. dTIGHTEN is the net percentage of domestic respondents tightening standards for commercial real estate loans10.

10 For further information of this variable, please refer to the Board of Governors of the Federal Reserve System's Senior Loan Officer Opinion Survey on Bank Lending Practices release. http://www.federalreserve.gov/boarddocs/SnLoanSurvey/.

SPREAD AMIHUD TURNOVER QSPREAD ESPREAD PV PF TV TF _TBI TERM 0.165 0.025 0.024 0.099 0.310 -0.145 -0.116 0.041 0.431 0.182 0.843 0.849 0.426 0.011 0.243 0.349 0.745 0.000

CRED 0.188 -0.018 0.107 0.344 0.279 -0.167 0.007 -0.102 0.446 0.128 0.884 0.388 0.004 0.022 0.177 0.958 0.413 0.000

MKT -0.080 -0.147 0.008 -0.090 0.097 -0.117 -0.218 0.085 -0.155 0.522 0.235 0.950 0.471 0.433 0.348 0.076 0.494 0.210

dGDPR 0.034 -0.387 0.102 -0.230 -0.050 0.022 0.044 -0.108 -0.556 0.784 0.001 0.410 0.061 0.689 0.860 0.722 0.385 0.000

dINV 0.060 -0.359 0.082 -0.316 -0.106 0.026 0.130 -0.163 -0.598 0.630 0.003 0.507 0.009 0.393 0.834 0.295 0.189 0.000

dCONSR 0.164 -0.503 0.226 -0.122 -0.049 0.079 0.108 -0.143 -0.591 0.184 0.000 0.066 0.326 0.693 0.525 0.386 0.248 0.000

dUE -0.095 0.327 -0.056 0.334 0.188 -0.060 -0.252 0.179 0.629 0.447 0.007 0.654 0.006 0.128 0.628 0.040 0.147 0.000

dM2 -0.208 0.164 -0.155 -0.079 0.001 -0.048 0.106 -0.261 -0.056 0.091 0.184 0.210 0.524 0.994 0.698 0.393 0.033 0.650

dNONM1 -0.294 0.044 -0.117 -0.124 -0.128 -0.002 0.144 -0.229 -0.313 0.016 0.722 0.345 0.317 0.301 0.989 0.244 0.062 0.010

VIX -0.061 0.019 0.103 0.330 0.127 0.137 -0.153 0.053 0.247 0.626 0.877 0.406 0.006 0.306 0.267 0.217 0.672 0.044

HML 0.166 -0.030 0.078 -0.023 0.075 -0.259 -0.040 -0.095 0.002 0.181 0.807 0.531 0.857 0.547 0.034 0.750 0.443 0.990 dTIGHTEN 0.021 0.020 0.008 0.001 -0.012 0.134 0.208 -0.014 -0.053 0.866 0.870 0.951 0.991 0.926 0.279 0.092 0.908 0.671

Table 1.4

The table shows Granger causality tests between liquidity measures macro variables. For each measure, we first test the null hypothesis that if each of liquidity measures does not Granger cause macro variables, and then whether each of the macro variables does not Granger cause any liquidity measures. The -statistics and p-value (in parentheses) are reported for each test.

Null Hypothesis Null Hypothesis

dM2 4.805 0.308 dM2 0.604 0.963 dNONM1 7.630 0.106 dNONM1 1.767 0.778 VIX 2.718 0.606 VIX 4.646 0.326 HML 5.101 0.277 HML 17.069 0.002 AMIHUD_MKT 11.997 0.017 AMIHUD_MKT 2.094 0.718 dGDPR 1.602 0.808 dGDPR 5.122 0.275 dINV AMIHUD 7.581 0.108 AMIHUD dINV 5.437 0.245 dCONSR 0.302 0.990 dCONSR 6.542 0.162 dUE 5.837 0.212 dUE 2.058 0.725 MKT 0.693 0.952 MKT 1.907 0.753 TERM 1.575 0.813 TERM 1.730 0.785 CRED 8.283 0.082 CRED 5.978 0.201 dTIGHTEN 1.942 0.747 dTIGHTEN 3.795 0.435

Null Hypothesis Null Hypothesis

dM2 6.553 0.162 dM2 7.514 0.111 dNONM1 3.518 0.475 dNONM1 4.853 0.303 VIX 9.991 0.041 VIX 1.318 0.858 HML 12.368 0.015 HML 6.102 0.192 TURNOVER_MKT 21.409 0.000 TURNOVER_MKT 5.904 0.207 dGDPR 2.744 0.602 dGDPR 2.823 0.588 TURNOVE dINV 8.980 0.062 TURNOVER dINV 3.354 0.500 R dCONSR 5.194 0.268 dCONSR 1.521 0.823 15.27 dUE 10.363 0.035 dUE 0.004 6 MKT 21.469 0.000 MKT 4.717 0.318 TERM 21.113 0.000 TERM 3.040 0.551 CRED 8.092 0.088 CRED 2.505 0.644 dTIGHTEN 7.318 0.120 dTIGHTEN 4.694 0.320

dM2 20.614 0.000 dM2 8.051 0.090 dNONM1 13.054 0.011 dNONM1 4.352 0.360 VIX 3.812 0.432 VIX 1.865 0.761 HML 31.777 0.000 HML 1.849 0.764 dGDPR 4.526 0.340 dGDPR 2.297 0.681 dINV 13.992 0.007 dINV 0.542 0.969 ESPREAD ESPREAD dCONSR 17.768 0.001 dCONSR 9.153 0.057 dUE 12.979 0.011 dUE 2.099 0.718 MKT 9.730 0.045 MKT 3.530 0.473 TERM 6.569 0.161 TERM 1.893 0.756 CRED 3.225 0.521 CRED 6.344 0.175 dTIGHTEN 8.846 0.065 dTIGHTEN 7.817 0.099

Null Hypothesis Null Hypothesis

dM2 6.636 0.156 DM2 5.009 0.286 dNONM1 5.215 0.266 DNONM1 2.493 0.646 VIX 7.425 0.115 VIX 0.940 0.919 HML 20.034 0.001 HML 1.774 0.777 dGDPR 5.003 0.287 DGDPR 0.876 0.928 dINV 12.387 0.015 DINV 1.171 0.883 QSPREAD QSPREAD dCONSR 5.292 0.259 DCONSR 4.931 0.295 dUE 3.679 0.451 DUE 2.177 0.703 MKT 6.012 0.198 MKT 0.639 0.959 TERM 6.834 0.145 TERM 1.735 0.784 CRED 1.996 0.737 CRED 4.146 0.387 dTIGHTEN 2.129 0.712 DTIGHTEN 7.485 0.112

dM2 1.945 0.746 dM2 8.382 0.079

dNONM1 0.042 1.000 dNONM1 18.605 0.001

VIX 3.209 0.523 VIX 3.073 0.546

HML 3.392 0.495 HML 2.198 0.700

dGDPR 2.578 0.631 dGDPR 3.562 0.469

dINV 3.368 0.498 dINV 7.410 0.116 PV PV dCONSR 1.446 0.836 dCONSR 8.308 0.081

dUE 2.448 0.654 dUE 1.074 0.898

MKT 2.296 0.682 MKT 2.521 0.641

TERM 0.511 0.972 TERM 0.874 0.928

CRED 1.693 0.792 CRED 4.826 0.306 dTIGHTEN 0.592 0.964 dTIGHTEN 1.092 0.896

Null Hypothesis Null Hypothesis

dM2 3.290 0.511 dM2 10.01 0.040

dNONM1 2.727 0.605 dNONM1 6.874 0.143

VIX 1.151 0.886 VIX 6.834 0.145

HML 0.994 0.911 HML 1.105 0.894

dGDPR 1.714 0.788 dGDPR 1.379 0.848

dINV 0.436 0.979 dINV 0.202 0.995 PF PF dCONSR 0.936 0.919 dCONSR 4.626 0.328

dUE 1.142 0.888 dUE 1.647 0.800

MKT 0.433 0.980 MKT 8.268 0.082

TERM 0.763 0.943 TERM 4.739 0.315

CRED 0.458 0.978 CRED 13.36 0.010 dTIGHTEN 0.826 0.935 dTIGHTEN 13.88 0.008

dM2 2.132 0.712 dM2 8.504 0.075

dNONM1 1.381 0.848 dNONM1 6.211 0.184

VIX 2.236 0.693 VIX 3.644 0.456

HML 1.020 0.907 HML 1.259 0.868

dGDPR 1.997 0.736 dGDPR 3.808 0.433

dINV 2.992 0.559 dINV 5.990 0.200 TV TV dCONSR 2.004 0.735 dCONSR 9.296 0.054

dUE 0.546 0.969 dUE 6.867 0.143

MKT 1.012 0.908 MKT 5.392 0.249

TERM 0.793 0.939 TERM 0.434 0.980

CRED 1.891 0.756 CRED 6.652 0.156

dTIGHTEN 1.725 0.786 dTIGHTEN 4.038 0.401

Null Hypothesis Null Hypothesis

dM2 6.067 0.194 dM2 3.931 0.415

dNONM1 6.168 0.187 dNONM1 2.823 0.588

VIX 6.511 0.164 VIX 0.560 0.967

HML 11.392 0.023 HML 2.092 0.719

dGDPR 0.474 0.976 dGDPR 0.816 0.936

dINV 3.063 0.547 dINV 1.471 0.832 TF TF dCONSR 3.835 0.429 dCONSR 6.820 0.146

dUE 2.054 0.726 dUE 6.891 0.142

MKT 0.898 0.925 MKT 1.693 0.792

TERM 1.410 0.842 TERM 1.666 0.797

CRED 4.215 0.378 CRED 2.493 0.646 dTIGHTEN 6.542 0.162 dTIGHTEN 8.868 0.065

dM2 4.319 0.365 dM2 8.230 0.084

dNONM1 13.610 0.009 dNONM1 1.003 0.909

VIX 1.540 0.820 VIX 8.451 0.076

HML 6.546 0.162 HML 0.705 0.951

AMIHUD_MKT 6.380 0.173 AMIHUD_MKT 12.274 0.015

dGDPR 6.687 0.153 dGDPR 4.075 0.396 SPREAD SPREAD dINV 4.138 0.388 dINV 0.616 0.961 _TBI _TBI dCONSR 0.555 0.968 dCONSR 4.137 0.388

dUE 3.765 0.439 dUE 1.192 0.879

MKT 3.471 0.482 MKT 6.209 0.184

TERM 5.080 0.279 TERM 8.161 0.086

CRED 5.290 0.259 CRED 5.208 0.267

dTIGHTEN 4.072 0.396 dTIGHTEN 5.937 0.204

Essay 2:

Liquidity Risk and Stock Returns: a Return Decomposition Approach

Abstract We study the effect of innovations in liquidity on stock-return volatility under the return-decomposition framework. Using revisions to equity analyst consensus forecasts to measure cash-flow news directly, we contend that both cash-flow news and expected return news correlate with liquidity shocks, and the cash-flow news component is a nontrivial channel through which liquidity correlates with stock returns. Specifically, we find a positive (decrease) liquidity shock for firms that have positive (negative) cash-flow news and expected-return news. Furthermore, since the correlation between liquidity proxies and stock returns also arise from the association of liquidity proxies with the three stock return components, the from a regression of returns on liquidity proxies may understate or overstate the importance of liquidity as a source of stock-return variance. Finally, liquidity proxies tend to explain stock returns better during negative market liquidity shocks, but this additional explanatory power comes mostly from the increased correlation between liquidity proxies and cash-flow news, while the correlation between liquidity proxies and unexplained stock return variations does not change with market liquidity conditions.

1 Introduction

In this paper, we study the effects of innovations in liquidity on stock-return volatility under the return-decomposition framework. Using revisions to equity analyst consensus forecasts to measure the cash-flow news directly, we contend that both cash- flow news and expected return news correlate with liquidity shocks, and the cash-flow news component is a nontrivial channel through which liquidity correlates with stock returns. Specifically, we find a positive (negative) liquidity shock for firms that have positive (negative) cash-flow news and expected-return news. Furthermore, since the

45 correlation between liquidity proxies and stock returns also arise from the association of liquidity proxies with the three stock return components, the from a regression of returns on liquidity proxies may understate or overstate the importance of liquidity as a source of stock-return variance.

We address the following research questions. First, what is the relationship between liquidity shocks and the three stock return components – one-period expected returns, cash-flow news, and expected-return news? And which relationship is more important for innovations in liquidity to affect stock return volatility? It is possible that innovations in liquidity affect stock returns through one-period expected returns, cash- flow news, expected-return news, or any combinations of the three components.

Moreover, the explanatory power of the liquidity proxies may arise from the correlation of liquidity proxies with one-period expected returns, cash-flow news, and/or expected- return news. If cash-flow news is responsible for the high explanatory power of the regression, these s should not be interpreted as evidence that liquidity is driving returns.

Similar, if the relationship between liquidity proxies and cash-flow news is offset by the relationship between liquidity proxies and expected-return news and/or one-period expected returns, it is possible for liquidity proxies to explain any of the three stock return components but not returns. Second, are the relationships between liquidity shocks and stock return components stable over time and across different stock characteristics?

Given that firm size is frequently used as a proxy for liquidity, the relationships between liquidity shocks and stock return components could be another form of the size effect.

Third, does the state of market conditions cause the effect of innovations in liquidity on stock-return volatility to vary? If it does, does this effect come from the time-variation of

46 the correlation of innovations in liquidity with a specific stock-return component or all of them? There are reasons to believe that liquidity effects are time varying and dependent on market liquidity. Liquid stocks generally outperform illiquid stocks during negative market liquidity shocks (Goyenko and Sarkissian, 2008; Acharya and Pedersen, 2005;

Jensen and Moorman, 2010). But there is little evidence on whether or not the correlation of innovations in liquidity and stock return components vary with the state of market conditions.

The relationship between innovations in liquidity and expected-return news has been studied extensively and is well understood (inter alia, Amihud, 2002; Pastor and

Stambaugh, 2003; Acharya and Pedersen, 2005; Sadka, 2006). Because liquidity varies over time, investors face uncertainty about future transactions costs that they will incur when they need to sell an asset in the future. Since liquidity affects the level of prices, liquidity fluctuations can affect the asset price volatility itself. For both of these reasons, liquidity fluctuations constitute a new type of risk that might link to the fundamental expected-return news. Acharya and Pedersen (2005) argue that the persistence of liquidity implies that liquidity predicts future returns and negatively co-moves with contemporaneous returns. Intuitively, as stated in Amihud (2002), high illiquidity today predicts high expected illiquidity next period, implying a high required return, which is achieved by lowering current prices. This intuition relies on the assumption that liquidity shocks correlate with expected-return news and affects stock returns by the channel of the expected-return-news component of stock returns, and that liquidity and cash-flow news are not too correlated or uncorrelated.

However, there is evidence to suggest that changes in liquidity could also be related to the cash-flow news component of stock returns due to changes in adverse selection. The theoretical literature on the role of adverse selection in capital markets predicts that market makers and other less informed market participants reduce liquidity in response to greater adverse selection (Copeland and Galai, 1983; Kyle, 1985; Glosten and Milgrom, 1985, Admati and Pfleiderer, 1988).

When a firm’s cash-flow news reveals firm level information, it leads to a change in the perception of the firm’s fundamental value uncertainty. Greater uncertainty regarding a firm’s fundamental value provides opportunities for informed market participants to engage in adverse trades against less informed participants (Sadka and

Scherbina, 2006). Therefore, less informed participants are likely to protect themselves through actions that reduce liquidity. In the extreme case, liquidity may be so low that no trades occur (Glosten and Milgrom, 1985).

Most recently, Brunnermeier and Pedersen (2009) develop a model to link an asset’s market liquidity to a trader’s funding liquidity. Speculative traders provide market liquidity but face funding constrains because they have limited amounts of capital and rely on funding liquidity to purchase stock. Market declines and decreases in funding liquidity reduce traders’ capital and increase margins, leading traders to withdraw liquidity, particularly from ‘capital intensive’ (high margin) securities. As traders shift out of high margin stocks, market liquidity in those stocks dries up. As a results, stocks with greater uncertainty about fundamental value experience greater volatility in liquidity.

This model also implies a link from cash-flow news to liquidity risk because cash-flow news changes an investor’s perception of the fundamental value of the asset, and margin

48 requirements in the model are a function of the ability to determine the fundamental value of the asset. Empirically, Ng (2007) finds a decrease (increase) in illiquidity for firms that announce positive (negative) earnings surprises.

The evidence documented above suggests that liquidity could affect stock returns by covarying with either cash-flow news or expected-return news or both. However, to our knowledge, there has been little or no research focused on the links between the components of stock returns and liquidity, and little is known with regard to the channel through which liquidity correlates with stock returns.

We begin by examining the correlation between innovations in liquidity and the three stock return components for the sample period of 1982 through 2011. First, we confirm the positive and significant correlation between innovations in liquidity and cash-flow news. The Spearman correlation between innovations in the Amihud and cash- flow news is 0.037, and the Spearman correlation between innovations in Turnover and unexplained stock-return volatility is 0.059. Second, regression results reveal that the innovations in Amihud and Turnover are able to track cash-flow news with a coefficient of -0.236 and of 5.8 percent and a coefficient of 1.123 and of 5.5 percent, respectively. This indicates that after extracting the one-period expected return, expected- return news and cash-flow news from stock returns, liquidity still plays an important role in explaining stock-return volatility.

We next test the cross-sectional relationship between innovations in liquidity and stock-return components. We measure the significance of the stock return components on various regressions of stock returns on liquidity proxies. We measure expected returns

49 using the Fama and French (1993) three-factor model and measure the cash flow news directly using revisions of equity analyst consensus forecasts following the procedure described in Da andWarachka (2009). We back out discount rate news as the residual, or the difference between return innovations (return minus an expected return measure) and cash-flow news. This means the empirically identified expected return news component will also incorporate any temporary deviations from fundamental value due to liquidity shocks, such liquidity shocks (which fall outside the Campbell and Shiller (1988) framework) will show up in returns but cannot be explained by changes in future cash- flow expectation and therefore (by definition) will be included in the component labeled

“expected return news”. Once the three return components are extracted, we regress them individually on the liquidity proxies. These four regressions expose what drives the regression coefficients in the original returns-on-liquidity-proxies specification.

Our empirical results show that, for the sample period from 1982 to 2011, estimating the total-return regression equation yields a regression coefficient of 0.568 (t =

14.79) and of 1.5 percent for innovations in Amihud, and a regression coefficient of

0.249 (t = 7.56) and of 2.5 percent for innovations in Turnover, suggesting that a stock return will be high when its liquidity shock is positive (i.e., expected future liquidity increases). Furthermore, the innovations in Amihud tracks cash-flow news with a coefficient of 0.108 (t=7.2) and of 0.1 percent, the negative of expected return news with a coefficient of -0.404 (t=-13.17) and of 0.4 percent, and the level of expected returns with coefficient of 0.056 (t=5.16) and of 0.4 percent. Using either Turnover or different specifications of the pricing model result in generally similar patterns. Since the liquidity proxies are positively correlated with cash-flow news and negatively correlated

50 with expected-return news, the association of the liquidity proxies with cash-flow and expected return news partially cancel each other, leaving the original specification with a low coefficient and .

All the analysis up to this point has been unconditional. However, there are strong reasons to believe that liquidity effects are time varying and dependent on market conditions. Liquid stocks generally outperform illiquid stocks during negative market liquidity shocks (Goyenko and Sarkissian, 2008; Acharya and Pedersen, 2005; Jensen and Moorman, 2011). Therefore, the normally positive liquidity premium is expected to reverse during periods of high market illiquidity (Brunnermeier and Petersen, 2009). It is possible that the innovations in liquidity affect stock return components differently during periods of large negative aggregate liquidity shocks. We therefore introduce an indicator variable to control for periods of high unexpected aggregate illiquidity, and another indicator variable to control for firm size which is a natural proxy for liquidity in the analysis, and examine the relationships between innovations in liquidity and stock return components. The results show that, during periods of large negative aggregate liquidity shocks (bottom 20% of aggregate liquidity shocks), the innovations in Amihud track stock-return volatility with a of 18 percent, while during periods of large negative aggregate liquidity shocks (top 20% of aggregate liquidity shocks), innovations in Amihud track stock-return volatility with a of 4.9 percent. Similarly, the innovations in Turnover track stock return volatility with a of approximately 7.6 percent. While during periods of large positive aggregate liquidity shocks (top 20% of aggregate liquidity shocks), innovations in Turnover track stock-return volatility with a of only

2.2 percent. This additional explanatory power of innovations in liquidity during ‘bad’

51 market conditions comes mostly from the increased correlation between Amihud and cash-flow news and expected-return news ( of 1% vs. of 0.1%, and of 0.6% vs.

of 0.2%, respectively). The results are similar to Turnover innovations.

In addition, the performance of small firms and large firms is quite different during negative aggregate illiquidity shocks, but does not show much difference during positive aggregate illiquidity shocks. Turnover for small firms (bottom 10% of firm size) tend to covary with stock returns more than Turnover for large firms and the difference between small firm and large firms mainly come from the higher correlation between

Turnover for small firms with cash-flow news: a one standard deviation decrease in

Turnover for small firms predicts a decrease in cash-flow news of 61.7 basis points more than large firms. Interestingly, Amihud for small firms (bottom 10% of firm size) tends to covary with stock returns slightly less than Amihud for large firms, and this effect is particularly strong during the positive market illiquidity shocks. Our results for the stock return components regressions suggest that the different performance between small firms and large firms mainly comes from the weaker correlation between Amihud for small firms with expected-return news and the unexplained part of stock returns variances: a one standard deviation increase in Amihud for small firms predicts a decrease in expected-return news of 7.5 basis points less than large firms, and a decrease in unexplained stock returns of 10.6 basis points less than large firms.

This paper makes several contributions to the liquidity and asset pricing literature.

First, we find that innovations in liquidity track the cash-flow news component of stock returns in an economically meaningful way, contributing to a better understanding of the relationship between liquidity and stock returns. Second, liquidity proxies are also

52 significantly correlated with one-period expected returns, expected-return news and cash- flow news. However, the relationship between liquidity proxies and expected return news is offset by the relationship between liquidity proxies and cash-flow news and one-period expected return news. As a result, the from a regression of returns on liquidity proxies may understate the importance of liquidity as a source of return variance. Finally, liquidity proxies tend to explain stock returns better during a negative market liquidity shock, but this additional explanatory power comes mostly from the increased correlation between liquidity proxies and cash-flow news, while the correlation between liquidity proxies and unexplained stock return variations does not change with market liquidity conditions.

In what follows, Section II briefly discusses the empirical framework for decomposing the stock return and the regression coefficient of returns on liquidity proxies. Section III describes the data, and Section IV provides the empirical results.

Section V concludes.

2 Empirical Framework

2.1 Decomposing returns and regressions of returns on liquidity proxies

The liquidity-returns relationship can be characterized as the relationship between liquidity and the different components of stock returns. In this context, the Campbell

(1991) return decomposition is useful for illustration. Campbell decomposes returns into three components as follow:

[ ] ( [∑ ] ( [∑ ]

[ ] (1)

where denotes stock returns (in logs) at time , denotes dividend growth (in logs) at time , is a deflator (the inverse of 1 plus the dividend yield), and ( is the expectation operator. Thus the components of returns are one-period expected returns

( [ ] , changes in expected cash flows (cash-flow news, ), and changes in expected returns (expected-return news, ).

The cashflow component in Eq. (1) equals an investors gain from holding a stock.

However, this payoff represents an outflow of funds from the firm’s perspective.

Conversely, earnings are related to one another through the clean-surplus accounting identity

where , , and denote a firm’s book value, earnings, and cash-flow, respectively, with in Eq. (1) being the log of . The log return on book equity is defined as

( )

Vuolteenaho (2002) log-linearizes the clean-surplus identity to replace the

terms in Eq. (1) with log returns on book equity, which implies the cashflow component in Eq. (1) becomes

( [∑ ]

Using the above return decomposition, a regression of returns on liquidity proxies can be decomposed into three component regressions, one corresponding to conditional one-period expected return, cash-flow news and expected-return news each. Consider a typical regression of returns on liquidity proxies,

(2)

where LIQ denotes the liquidity proxy, and denotes the information set at the end of the period. Using Campbell’s (1991) return decomposition (equation (1)), the original regression can be split into three component regressions,

(3)

Since the explanatory variables in each of the three component regressions are the same as in the original regression (2), we can think of the original regression (2) as the sum of the three component regressions11:

( ) ( ) (4)

From (3) and (4), it is clear that the liquidity can explain stock returns for many reasons. The can explain the level of one-period expected returns, cash-flow news, expected-return news, or any combination of the three. If , , and/or

, it is possible for liquidity proxies to explain stock returns because their

11 This approach is similar in spirit to Hecht and Vuolteenaho (2005)

55 correlation with the level of one-period expected returns, cash-flow news, and/or expected-return news, and a regression of returns on liquidity proxies may overstate or understate the importance of liquidity as a source of return variance.

2.2 Empirical Measurement

The component regressions (3) requires the measurement of expected returns

( [ ]), cash-flow news ( ), and expected return news ( ). Once the different components are constructed, the component regression (3) can easily be implemented.

2.2.1 Expected returns

In order to compute conditional expected stock returns, we need to use a pricing model. To be consistent with the methodology used to risk-adjust returns in our empirical results, we estimate the conditional expected return using the Fama-French (1993) three- factor model12:

[ ] [ ] [ ] [ ] [ ]

To avoid any look-ahead bias, the factor betas are estimated using monthly returns in the previous five-year rolling window (with a minimum of 36 months of observations) while the factor risk premium is set equal to the average factor return in our sampling period.

2.2.2 Cash-flow news

12 We note that our empirical results do not appear to hinge on the choice of pricing model, (e.g., CAPM or augmented Five-factor Fama-French model).

A popular way to implement Campbell and Shiller's (1988) return decomposition in equation (1) is to use a vector autoregression (VAR). Campbell and Vuolteenaho (2004) implement a VAR at the market level, while Vuolteenaho (2002) and Campbell, Polk, and Vuolteenaho (2010) implement it at the firm level. The VAR approach is economically appealing and allows for time-varying discount rates. Empirically, however,

Chen and Zhao (2009) argue that the VAR approach might be sensitive to the choices of state variables. In addition, accounting variables that are required to implement the VAR at firm level are updated quarterly at best.

Instead, we follow Easton and Monahan (2005), Da and Warachka (2009) and Da,

Liu and Schaumburg (2011) and measure cash-flow news using revisions in equity analyst earnings forecasts. Crucially, the use of analyst earnings forecasts allows us to measure cash-flow news at monthly frequencies in real time, which enable a sufficient amount of data to implement an AR(2) process for the liquidity measures. Furthermore, computing monthly revisions mitigates any analyst forecast biases that persist over this short horizon.

We obtain the analyst consensus earnings forecasts from the Institutional Brokers

Estimate System (I/B/E/S) summary unadjusted file. I/B/E/S produces these consensus earnings forecasts each month, typically on the third Thursday of the month. To better match returns to earnings forecast revisions, for most parts of our analysis, we examine the I/B/E/S-month ranging from the current I/B/E/S consensus forecast issuance date

(third Thursday this month) to the next consensus forecast issuance date (third Thursday next month), although we do confirm that using the simple calendar month produces very similar results. We initially include all unadjusted consensus earnings forecasts between

January 1982 and March 2009. Unadjusted I/B/E/S forecasts are not adjusted by share splits after their issuance date.

We keep consensus earnings forecasts for the current and subsequent fiscal year

( , ), along with its long-term growth forecast ( ). The earnings forecasts are denominated in dollars per share, and the t subscript denotes when a forecast is employed.

The long-term growth forecast represents an annualized percentage growth rate. This forecast has no fixed maturity date but pertains to the next three to five years.

We compute cash-flow news following Da, Liu and Schaumburg (2011) by taking advantage of multiple earnings forecasts for different maturities.

Let denote the expectation of future earnings ( ); here the additional subscript refers to an expectation at time t. A three-stage growth model that parallels the formulation in Frankel and Lee (1998) as well as Pastor, Sinha, and Swaminathan (2008) infers these earnings expectations from analyst forecasts. In the first stage, expected earnings are computed directly from analyst forecasts until year 5 as follows:13

(

13 If is missing, we set . If is missing, we set . If is also missing, we set ( . If , we set ( . We exclude stocks / month observations if is missing. 58

( (5)

Given that exceeds 30% for certain stocks, it is unrealistic to assume that such high earnings growth will continue indefinitely. Therefore, we assume that expected earnings growth converges (linearly) to an industrial wide steady-state growth rate from year 6 to year 10 in the second stage.

Expected earnings in the second stage are estimated as:

[ ( ] (6)

for . The steady-state growth rate is computed as the cross-sectional average of .

We also assume the cash-flow payout is equal to a fixed portion ( ) of the ending-period book value. Under this assumption, the clean surplus accounting identity implies that the evolution of expected book value is ( )(

. The parameter is set to the average industrial payout rate. The average payout rate for all the firms in our sample is around 50%.

In the third stage, expected earnings growth converges to , which implies

expected accounting returns converge to beyond year 10. After ten years, the

annualized discount factor also means that the remaining cash flows exert little influence on the earnings beta estimates.

14 The expected log accounting return is estimated at time t as:

( )

( ) {

where the expectations are defined in equations (5) and (6).

Consequently, the three-stage growth model implies:

∑ ∑ ( )

Vuolteenaho (2002) shows that the cash-flow news are the difference between cash flow expectations over consecutive months; that is:15

∑ ∑

Although earnings forecasts pertain to annual intervals, their revisions are computed over monthly horizons, which helps to mitigate analyst forecast biases that persist over this short horizon.

2.2.3 Expected-return news

14 Consistent with our notational convention, denotes the expectation of at time t. The ( approximation [ ( ] ( ignores a convexity term that is mitigated by computing ( the necessary innovationss. 15 If there is an earnings announcement during month , we make the necessary adjustments because the forecasting horizon is shifted by one year after the announcement. For example, the first term would include the actual announced earnings.

Since we do not have an empirically observable direct measure of expected return news, we define the expected return news as the residual:

( (7)

As the expected-return news are backed out, we want to emphasize that they are really residuals and should be better interpreted as non-cash-flow news. Any unexpected stock returns that are not explained by the cash-flow news will be contained in our expected return news component. For example, liquidity shocks may cause price impacts that are not justified by cash flow news. Another example is mispricing due to investor sentiment. In fact, investor sentiment, according to Baker and Wurgler (2007), is broadly defined as “a belief about future cash-flows and investment risks that is not justified by the facts at hand". Finally, to the extent that cash-flow news may be measured with error, the same error will show up in our expected-return news (with the opposite sign).

2.2.4 Liquidity measures

In our analysis, we use 1) the Amihud (2002) measure of liquidity, which is founded on the basic intuition about a security’s price impact (i.e. Kyle’s ), and can be easily computed from the market daily price and volume data; and 2) the turnover measure of trading activity in individual stocks, which is defined as the number of shares traded on a given day dividend by the total number of shares outstanding.

Following Amihud (2002), the liquidity of stock i in year t is defined as:16

16 Because Amihud liquidity measures the illiquidity while the turnover measure liquidity, to illustration purpose, we convert the Amihud liquidity to measure liquidity instead of illiquidity cost.

∑ (18)

where and are, respectively, the return and dollar volume (in millions) on day d

in month t, and is the number of valid observation days in month t for stock i.

We also follow Acharya and Pedersen (2005) to normalize the liquidity measure as follow:

( (19)

where is the ratio of the capitalizations of the market portfolio at the end of year t-1 and of the market portfolio at the end of December 1981.17 The normalized liquidity

measure has an average of 0.26% and a standard deviation of 1.60% over our sample period from 1983 to 2011.

Our turnover measure for stock i in month t can be expressed as follows:

∑

(20)

where is the trading volume of asset i on day j of month t, and is shares outstanding of asset i at the end of month t.

Since turnover measure is non-stationary (Lo and Wang, 2000), we normalize the resulting series with the cross-sectional mean and standard deviation. A similar approach is taken by Korajczyk and Sadka (2008).

17 For a discussion of how this function normalizes the distribution of the Amihud measure, see Acharya and Pedersen (2005)

To predict the liquidity for stock i, we run the following AR(2) regression:

( ( ( (21) where LIQ could be either Amihud or Turnover, and the same date is used for the market

index ( in all three terms so that the regression is measuring the uncertainty only in

18 liquidity, not changes in . The residual, , of the regression in (21) is interpreted as the liquidity risk for stock i:

( (22)

The average for the AR(2) specification for the Amihud illiquidity measure is

22%. The resulting innovations in liquidity has an average standard deviation of 0.278%.

3 Sample and Descriptive Statistics

Our sample of analyst earnings forecast is obtained from the Institutional Broker’s

Estimate System (I/B/E/S) Summary unadjusted file. I/B/E/S produces these consensus earnings forecasts each month, typically on the third Thursday of the month. We initially include all unadjusted consensus earnings forecasts from 1982 to 2011.

We retain 783,416 firm-month observations, with each observation including a firm’s earnings in the previous ( ), consensus earnings forecasts for the current and subsequent year ( , ), along with its long-term growth forecast ( ). The earning

18 Our results are robust to the specification of liquidity risk, and including other stock-market variables available at time t-1 does not improve significantly the explanatory power of the regression. (see also, Acharya and Pedersen (2005) and Pastor and Stambaugh(2003))

63 forecasts are denominated in dollars per share, with the t subscript denoting when a forecast is employed. The long-term growth forecast represents an annualized percentage growth rate. This forecast has no fixed maturity date but pertains to the next three to five years. Quarterly forecasts are not utilized because of seasonality effects. A minimum analyst converge filter of at least three analysts for each forecast maturity is imposed. Our conclusions are also robust to defining the consensus forecast as the median forecast.

The resulting dataset is then merged with Compustat and CRSP whenever price and /or accounting variable are needed. Observations with negative book values are eliminated when constructing the book-to-market ratios. Share splits are also accounted for using the split factor in CRSP. For delisting, we use CRSP delisting returns whenever possible. Otherwise, we assign a return of -0.3 to firms delisted for performance related reasons (delisting code is 500 or in [520, 584]).

To get book equity, we subtract from shareholders’ equity the preferred stock value, where we use redemption value (Data 56), liquidating value (Data 10), or carrying value (Data 130), in that order, as available. If all of the redemption, liquidating, or par value are missing from COMPUSTAT, then we treat the book-equity value as missing for that year. Finally, if not missing, we add in balance sheet deferred taxes (Data 35) to this book-equity value, and subtract off the postretirement benefit asset adjustment (item

330) .19

[Insert Table 2.1 here]

19 Book equity is measured following the definition from Daniel and Titman (JF, 2006).

Table 2.1 provides a brief overview of the statistical characteristics of the major variables of interest. On average, there are approximately 2,000 stocks in each month’s sample, comprising around 70% of the entire US stock universe in terms of market capitalization, according to Table 1. Hence, our sample is representative of the broader universe of US stocks. NYSE, Amex, and Nasdaq account for 61.5%, 2.7%, and 35.8 of these stocks, respectively. Finally, our sample contains relatively large stocks whose average market capitalization is about 2.2 billion dollars. Stocks in our sample also receive high analyst coverage, with an average of eight analyst reports per month.

For industry classification, we use the two-digit IBES SIGC code, which classifies all stocks into 11 industries: finance, health care, consumer non-durable, consumer services, consumer durables, energy, transportation, technology, basic industries, capital goods, and public utilities.

4 Empirical results

4.1 Decomposition Results

[Insert Table 2.2 here]

Table 2.2 provides descriptive statistics for unexpected return ( ( ), expected-returns news ( ), cash-flow news ( ), and innovations in liquidity measures

( and ). The mean of is slight negative (-0.5%), indicating that on average the cash-flow news is bad in our sample period. The mean of is slightly positive (0.2%).

The median of the unexpected return, ( , is also negative (-0.2%), consistent with the negative median cash-flow news. Finally, the median of the innovations in

Amihud (0.6%) is significantly positive, indicating that on average changes to liquidity improve liquidity at the firm level. Note that the Amihud we used in our research measures are revised to be comparable with Turnover and it measures liquidity. However, as Turnover measures liquidity, its slightly negative median (-0.6%) indicate that on average changes to trading activity have moderate negative effect on liquidity.

[Insert Table 2.3 here]

The variance decomposition are shown in Table 2.3, and contrary to prior literature, cash-flow news directly measured by revisions of equity analyst consensus forecasts is not the main driver of firm-level stock returns in our monthly sample period.

This is not surprising considering that expected return news is broadly defined in our sample and could include any liquidity shocks. The standard deviation of expected-return news (broadly defined, including liquidity shocks) and cash-flow news are 19 percent and

16 percent.

[Insert Table 2.4 here]

Table 2.4 shows the Spearman and Pearson correlation among the news items and innovations in liquidity measures. Innovations in the Amihud measures, , are positively and significantly correlated with (e.g. Spearman correlation = 0.058) and

(e.g. Spearman correlation = 0.037). is also positively and significantly correlated with unexpected returns, ( (e.g. Spearman correlation = 0.098), consistent with the positive correlation between liquidity and cash-flow news.

The correlations between the innovations in Turnover and news items are considerably larger than those of innovations in Amihud. is positively and 66 significantly correlated with (e.g. Spearman correlation = 0.064) and (e.g.

Spearman correlation = 0.059). In addition, consistent with prior literature, and and

is negatively and significantly correlated with each other (e.g. Spearman correlation

= -0.8). The correlations between and unexpected returns is consistent with the predictions of Eq. (1), but the correlations between and unexpected returns is not.

Specifically, the model predicts that the association of unexpected returns with ( ) is positive (negative). Considering the liquidity shocks ( , ) are also positively correlated with unexpected returns, the positive correlation between and unexpected returns could very well come from the liquidity component included in the broadly defined expected-return news.

4.2 Reinterpreting regressions of returns on liquidity measures

We regress ̃ and its three estimated components (one-period expected return, cash-flow news, negative of expected-return news, and unexplained residual) individually on innovations in liquidity measures similar in spirit to Hecht and Vuolteenaho (2005),

Fama (1990) and Schwert (1990):

(23)

[Insert Table 2.5 here]

As shown in the first row of Table 2.5 Panel A, the innovations in Amihud and

Turnover explain 1.5 percent and 2.5 percent (adjusted , period 1963-2011) of the monthly cross-sectional total return variation, respectively. Similar to prior literature, we find that both the innovations in Amihud and the innovations in Turnover have a positive and significant coefficient in our regression. Overall, positive changes in liquidity correlate with positive stock returns.

In addition, the innovations in Amihud are negatively and significantly related to all stock return components, while the innovations in Turnover is positively and significantly related to all stock return components, indicating that the regressions of returns on liquidity proxies may overstate the importance of liquidity as a source of return variance. The innovations in Amihud and Turnover explain 10 percent and 7 percent of the cross-sectional variation of estimated expected returns, respectively. The innovations in Amihud explains 7 percent of the estimated cash-flow-news series, while the innovations in Turnover explains only 3.5 percent of the estimated cash-flow-news series.

The innovations in Amihud and Turnover explain about the same amount of the estimated expected-return news series (2.1% and 2.2%, respectively).

4.3 Analyst forecast bias

There is sufficient evidence indicating that analyst forecast could be biased (e.g.

Gu and Wu, 2003; Ljungqvist, Malloy, and Marston, 2009). We are interested in the analyst forecast revisions instead of analyst forecast levels in this study, but it is possible that forecast biases may affect the revisions. To alleviate this concern, we construct three

68 measures of analyst forecasts that can help address the bias issue. These measures are similar to those used by Chen and Zhao (2012), and Chava and Purnanadam (2010).

Forecast according to optimism: Rather than using the consensus analyst forecast, we can use the lowest (most pessimistic) forecasts or the highest (most optimistic) forecasts. In this way, even if there is a bias when the consensus forecast are used, the bias might not be as strong if the lowest or the highest forecasts are alternatively used.

Forecast adjusted by external financing: It has been documented that analyst forecasts can be overly optimistic for firms for which there is large investment banking demand (Rajan and Servaes, 1997; Bradshaw, Richardson, and Sloan, 2006). Bradshaw,

Richardson, and Sloan (2006) measure investment banking business as the amount of cash raised through external financing. We thus rank all firms, year by year, according to amounts of net external financing (equity and debt issuance) and calculate the percentile

ranking, , for each firm i. The external-financing-adjusted forecast is calculated as

( (24)

where is the lowest forecast, and is the highest forecast. The idea is to rely more on the pessimistic estimate if a firm has more investment banking business in a particular year, in an effort to correct for the potential bias.

Forecast adjusted by recent forecast error: Analyst forecast errors tend to be persistent (Mendenhall, 1991; Abarbanell and Bernard, 1992). Therefore, current earnings forecasts are more likely to be optimistic (or Pessimistic) if they were optimistic

(pessimistic) during the recent past. We thus rank all firms, year by year, according to consensus earnings forecast error (FE) during the most recent fiscal year and calculate the

percentile ranking, , for each firm i. The forecast error (FE) is defined as forecast minus the actual scaled by the price at the beginning of the fiscal year. The recent- forecast-error-adjusted forecast is calculated as

( (25)

where is the lowest forecast, and is the highest forecast. The idea is to rely more on the pessimistic estimate if a firm has been associated with optimistic earnings forecasts in the recent past.

Panels A and B of Table 2.6 report the main results using the lowest and highest analyst forecasts. Note that these decomposition coefficients are reflecting extreme views from the cross-section of analysts; the “true” decomposition coefficients will be less extreme. Panel C of Table 7 reports the main results after correcting for the potential bias related to external financing (EF), and Panel D of Table 7 reports the main results after correcting for the potencial bias using the recent forecast errors (FE). The results are fairly stable. Using all bias adjustments, the innovations in Amihud and Turnover are negatively and significantly related to expected-return news, and are positively and significantly related to cash-flow news, indicating that the regressions of returns on liquidity proxies may overstate the importance of liquidity as a source of return variance.

The innovations in Amihud explains 0.1 percent of the estimated cash-flow-news series, while the innovations in Turnover explains 0.3 percent of the estimated cash-flow-news

70 series. The innovations in Amihud and Turnover explain about 0.4% of the estimated expected-return news series in most cases.

Again, both cash-flow news and expected-return news are significantly correlated with liquidity shocks, and the relationship between liquidity proxies and cash-flow news is offset by the relationship between liquidity proxies and expected-return news. We therefore conclude that analyst forecast biases are unlikely to be the main driver of our results.

4.4 Conditional analysis

All the analyses up to this point have been unconditional. However, there are strong reasons to believe that liquidity is time varying and dependent on market liquidity.

The contemporaneous response of equity prices to changes in aggregate liquidity

(Amihud, 2002) is dependent on a stock’s liquidity. Liquid stocks tend to perform well during negative market liquidity shocks (Goyenko and Sarkissian, 2008) compared to their illiquid counterparts (Acharya and Pedersen, 2005; Jensen and Moorman, 2011).

Therefore, the expected liquidity premium can weaken or even reverse (liquidity discount) during periods of high market liquidity (Brunnermeier and Pedersen, 2009). Similarly, for the liquidity risk premium, stocks with high positive liquidity betas will see large contemporaneous negative returns during liquidity crises while stocks with low or negative betas will see zero or positive abnormal returns (Vayanos, 2004). The expectation is that, during such liquidity crises, the liquidity risk premium will invert

(Acharya, Amihud and Bharath, 2010).

We therefore create a high illiquidity regime indicator variable equal to one for small stocks with size in the lowest decile, which is a natural measure of liquidity. We look at two different period of high and low market illiquidity defined as the aggregate

Amihud innovations in the highest and lowest quintile of our sample period.20 Figure 2.1 shows a graph of the innovations in aggregate Amihud illiquidity with a horizontal line at

0.051, representing the 80th percentile of innovations. The solid black line represents the innovations in equal weighted market normalized log Amihud illiquidity measure, assuming an AR(2) process,21 between 1996 and 2011. The dark shaded areas represent years within the top 20% of the market Amihud illiquidity innovations and the light gray shaded regions represent years which have been classified by the NBER as in recession.

The generated regime variable moves very closely with NBER recessions, suggesting that it is sufficiently accurate to serve as a conditioning variable.

[Insert Table 7 here]

The results show that once we control for the effect of high illiquidity periods, innovations in liquidity has a more substantial impact on stock returns. During periods of large negative aggregate liquidity shocks (bottom 20% of aggregate liquidity shocks), the innovations in Amihud track the stock return volatility with an of approximately 4.9 percent, while during the periods of large positive aggregate illiquidity shocks (top 20% of aggregate liquidity shocks), the innovations in Amihud track the stock return volatility with an of 1.5 percent. Similar, innovations in Turnover tracks stock return volatility with an of approximately 7.6 percent, while during periods of large positive aggregate

20 We have also conducted these analyses with the high liquidity regime defined as the top decile of aggregate Amihud innovationss, and have found similar results. 21 An AR(2) process is sufficient to make Aggregate Amihud Stationary.

72 liquidity shocks, innovations in Turnover track stock return volatility with an of only

2.2 percent. This additional explanatory power of Amihud innovations comes mostly from the increased correlation between Amihud innovations and cash-flow news ( of 1 % vs. of 0.1%), while the correlation between Amihud innovations and expected-return news stays relatively stable with different market liquidity conditions ( of 0.4% vs. of 0.2%). The results are similar to Turnover innovations.

The performances of small firms and large firms are quite different during large negative aggregate liquidity shocks, but do not show much difference during large positive aggregate liquidity shocks. Turnover for small firms (bottom 10% of firm size) tend to covary with stock returns more than Turnover for large firms. A one standard deviation decrease in Turnover predicts a decrease in stock returns of 879 basis points for small firms and only 228 basis points for large firms. Looking at the results for stock return components, we find that the difference between small firms and large firms mainly come from the higher correlation between Turnover for small firms with the unexplained part of stock returns: a one standard deviation decrease in Turnover for small firms predicts a decrease in unexplained stock returns of 410 basis points more than large firms.

Interestingly, Amihud for small firms (bottom 10% of firm size) tend to covary with stock returns slightly less than Amihud for large firms and this effect is particularly strong during large negative aggregate liquidity shocks. A one standard deviation increase in Amihud predicts a decrease in stock returns of 45.8 basis points for small firms and

64.9 basis points for large firms. This is surprising because prior literature suggests that liquid stocks tend to perform well during negative market liquidity shocks (Goyenko and

Sarkissian, 2008) compared to their illiquid counterparts (Acharya and Pedersen, 2005;

Jensen and Moorman, 2011), and small firms are generally considered to be illiquid stocks. Our results for the stock return components regressions suggest that the different performance between small firms and large firms mainly come from the weaker correlation between Amihud for small firms with expected-return news and the unexplained part of stock returns variances: a one standard deviation increase in Amihud for small firms predicts a decrease in expected-return news of 7.5 basis points less than large firms, and a decrease in unexplained stock returns of 10.6 basis points less than large firms.

5 Conclusion

In this paper, we examine the impact of innovations in liquidity on stock return volatility by examining the relationships between the three stock return components and liquidity shocks. This analysis is important both for understanding the components of stock return volatility and gaining insight into the relationships between innovations in liquidity and stock return components.

First, the correlation between liquidity proxies and stock returns arise from the association of liquidity proxies with the three stock return components which is particularly strong for expected-return news. Hence, the from a regression of returns on liquidity proxies may understate the importance of liquidity as a source of stock return variance. For the sample period from 1982 to 2011, estimating the total-return regression equation yields a regression coefficient of 0.568 (t = 14.79) and an of 1.5 percent for

74 innovations in Amihud, and a regression coefficient of 0.249 (t = 11.85) and of 2.5 percent for innovations in Turnover. The innovations in Amihud tracks the cash-flow news with a coefficient of 0.108 (t=7.2) and of 0.1 percent, while the innovations in

Turnover tracks cash-flow news with a coefficient of 0.118 (t=15.4) and of 0.3 percent.

Last but not the least, liquidity proxies tend to explain stock returns better during times of large negative market liquidity shocks, but this additional explanatory power comes mostly from the increased correlation between liquidity proxies and cash-flow news, while the correlation between liquidity proxies and other stock return components does not change with market liquidity conditions. In addition, the performance of small firms and large firms are quite different during negative aggregate illiquidity shocks, however, we do not find much difference during periods of positive aggregate illiquidity shocks. Turnover for small firms tends to covary with stock returns more than Turnover for large firms, and the difference between small firms and large firms mainly come from the higher correlation between Turnover for small firms’ cash-flow news. Interestingly,

Amihud for small firms tends to covary with stock returns slightly less than Amihud for large firms, and this effect is particularly strong during periods of positive market illiquidity shocks.

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Figure 2.1: Innovations in Market Amihud Illiquidity

The solid black line represents the innovations in equal weighted market normalized log Amihud illiquidity measure, assuming an AR(2) process, between 1996 and 2011. The light gray shaded areas represent years classified as in recession by the National Bureau of Economic Research. The dark shaded areas represent years with top 20% of the market Amihud illiquidity innovations. The Horizontal line across the y-axis is the value of the 80th percentile of normalized log market Amihud innovations, and all months with values above are classified as high illiquidity periods.

Table 2.1 Sample Characteristics

The table shows the characteristics of the stock sample from the Institutional Brokers Estimate System (IBES) Summary unadjusted file used in our empirical analysis. The full sample period is from January 1982 through December 2011. The stock-level characteristics are: mean and median size (in $mil), mean and median book-to-market ratio (BM), and mean and median number of analyst earnings reports per month. To avoid the bias caused by outliers, we winsorize the BM values at the 99th percentile each month. Our sample is compared to CRSP database on the number of stocks included and the average size. Percent of market capitalization measures the total market value of all stocks in our sample relative to total market value of all stocks in CRSP. The full sample period is also divided into three subsample period: January 1982 through December 1989, January 1990 through December 1999, and January 2000 through 2011.

Number of 360 (Jan 1982 - 120 (Jan 1982 - 120 (Jan 1992 120 (Jan 2002 - Months Dec 2011) Dec 1991) - Dec 2001) Dec 2011)

Mean size 2238.35 932.62 1817.72 3665.08

Median Size 545.02 308.54 446.36 999.13

Mean BM 0.94 0.76 0.89 1.12

Median BM 0.55 0.66 0.51 0.52

Mean Analyst 8.17 9.05 8.06 7.86 Coverage

Median Analyst 5.70 6.33 5.41 5.24 Coverage

Average number 2178.87 1648.48 2609.96 2278.16 of stocks

Percent of market 66.75% 62.70% 52.65% 73.40% capitalization

Average number 7046.45 6505.60 8183.94 6486.97 of stocks in CRSP

Mean size of 1318.06 393.80 1141.67 2438.85 CRSP stocks

Median size of 923.88 387.99 923.88 2513.48 CRSP stocks

Table 2.2 Descriptive Statistics

This table shows the sample statistics of stock decomposition and liquidity shocks. r-E(r) is unexpected return, E(r) is the one-period expected returns, Ncf is cash-flow news, and Nr is expected-returns news. Na and Ntv is liquidity shocks. The number of firm-year observation is 784,392.

Variable Mean StdDev Q1 Median Q3

r-E[r] 0.002 0.113 -0.056 -0.002 0.054

Ncf -0.005 0.156 -0.025 -0.001 0.017

Nr 0.007 0.189 -0.062 0.001 0.069

Na 0.008 0.277 -0.008 0.006 0.049

Ntv 0.001 0.065 -0.023 -0.006 0.015

E[r] 0.007 0.067 -0.022 0.010 0.039

Table 2.3 Covariance Matrix

This table shows the covariance matrix between the news items as defined in Sect. 3.1.

( ( 0.0128 0.0008 0.0120 0.0032 0.0010

0.0245 -0.0236 0.0008 0.0005

0.0356 0.0024 0.0005

0.0765 -0.0022

0.0042

Table 2.4 Correlation Coefficients

This table shows the correlation between the news items as defined in Sect. 3.1. Spearman (Pearson) correlation are reported above (below) the diagonal, and the number in the bracket is the p-value under the null hypothesis of .

(

( 1 0.070 0.766 0.098 0.124 (0.000) (0.000) (0.000) (0.000)

0.048 1 -0.450 0.037 0.059 (0.000) (0.000) (0.000) (0.000)

0.561 -0.800 1 0.058 0.064 (0.000) (0.000) (0.000) (0.000)

0.101 0.019 0.045 1 0.310 (0.000) (0.000) (0.000) (0.000)

0.134 0.050 0.039 0.120 1 (0.000) (0.000) (0.000) (0.000)

Table 2.5 Regressions

Amihud and Turnover are calculated as described in Section III. Coefficients reported are from panel regressions of risk adjusted returns or returns components on the innovations in liquidity. Stock returns are decomposed into three components: one-period expected return E(r), cash-flow news , and expected-return news ,. The table shows estimated regression coefficients and adjusted . The second number (in brackets) is a t-statistic computed using the Newey-West standard error.

Panel A: 1982 - 2011 Const. A AdjR2 Const. Turnover AdjR2

R 0.008 0.568 0.015 R 0.008 0.249 0.025 2.71 14.79 2.77 11.85

E[r] 0.007 0.056 0.004 E[r] 0.007 0.028 0.007 2.44 5.16 2.44 6.29

Ncf -0.005 0.108 0.001 Ncf -0.005 0.118 0.003 -1.95 7.2 -1.93 15.4

Nr(-) -0.006 -0.404 0.004 Nr(-) -0.006 -0.150 0.005 -2.01 -13.17 -2.08 -8.72 7.93

Panel B: 1982 - 1991 Const. A AdjR2 Const. Turnover AdjR2

R 0.007 0.571 0.017 R 0.008 0.401 0.034 1.43 7.12 1.5 12.18

E[r] 0.007 0.063 0.005 E[r] 0.007 0.043 0.008 1.42 2.91 1.36 4.77

Ncf -0.007 0.054 0.001 Ncf -0.006 0.134 0.002 -2.04 2.98 -1.77 7.81

Nr(-) -0.007 -0.454 0.004 Nr(-) -0.006 -0.223 0.055 -1.79 -6.38 -1.76 -6.54

Panel C: 1992 - 2001 Const. A AdjR2 Const. Turnover AdjR2

R 0.01 0.446 0.015 R 0.009 0.331 0.035 3.25 12.64 3.1 13.61

E[r] 0.008 0.04 0.003 E[r] 0.008 0.051 0.015 2.26 4.5 2.3 4.87

Ncf -0.002 0.074 0.001 Ncf -0.002 0.13 0.004 -0.53 7.8 -0.48 15.42

Nr(-) -0.004 -0.332 0.004 Nr(-) -0.004 -0.15 0.007 -0.86 -12.31 -0.71 -7.08

Panel D: 2002 - 2011 Const. A AdjR2 Const. Turnover AdjR2

R 0.007 0.673 0.014 R 0.007 0.194 0.021 1.08 11.8 1.17 8.65

E[r] 0.006 0.065 0.004 E[r] 0.006 0.028 0.007 0.86 3.35 0.89 3.34

Ncf -0.007 0.183 0.001 Ncf -0.007 0.09 0.003 -1.23 5.4 -1.22 9.21

Nr(-) -0.008 -0.425 0.003 Nr(-) -0.008 -0.077 0.003 -1.21 -9.43 -1.31 -3.78

Table 2.6 Robustness

Amihud and Turnover are calculated as described in Section III. Coefficients reported are from panel regressions of returns components on the innovations in liquidity. Stock returns are decomposed into three components: one-period expected return E(r), cash-flow news , and expected-return news ,. The table shows estimated regression coefficients and adjusted . The second number (in brackets) is a t-statistic computed using the Newey-West standard error.

Panel A: Using Low Forecast Const. A AdjR2 Const. Turnover AdjR2

Ncf -0.005 0.085 0.001 Ncf -0.005 0.096 0.002 -1.78 5.88 -1.75 11.59

Nr(-) -0.006 -0.421 0.004 Nr(-) -0.006 -0.165 0.005 -1.91 -14.04 -1.97 -10.58

Panel B: Using High Forecast Const. A AdjR2 Const. Turnover AdjR2

Ncf -0.005 0.121 0.001 Ncf -0.005 0.116 0.003 -1.80 7.24 -1.80 11.10

Nr(-) -0.006 -0.384 0.003 Nr(-) -0.006 -0.145 0.004 -1.99 -11.10 -2.07 -7.10

Panel C: Using EF rank Const. A AdjR2 Const. Turnover AdjR2

Ncf -0.005 0.110 0.001 Ncf -0.005 0.121 0.003 -1.99 7.64 -1.97 15.11

Nr(-) -0.006 -0.398 0.004 Nr(-) -0.006 -0.140 0.004 -2.11 -12.64 -2.18 -7.57

Panel D: Using FE rank Const. A AdjR2 Const. Turnover AdjR2

Ncf -0.006 0.081 0.001 Ncf -0.006 0.088 0.003 -2.45 5.00 -2.46 9.61

Nr(-) -0.007 -0.427 0.003 Nr(-) -0.007 -0.173 0.004 -2.51 -11.49 -2.60 -9.94

Table 2.7: Conditional Liquidity and Stock Return Components

Amihud and Turnover are calculated as described in Section III. D is an dummy indicator variable with a value of 1 for the top quintile illiquid years as measured by the innovations in equal-weighted market normalized Amihud liquidity (Acharya and Pedersen, 2005) and 0 otherwise. Coefficients reported are from panel regressions of risk adjusted returns or returns components on the innovations in liquidity, dummy indicator, dummy indicator and innovations in liquidity interaction. Stock returns are decomposed into four components: one-period expected return E(r), cash-flow news , and expected-return news . The table shows estimated regression coefficients and adjusted . The second number (in brackets) is a t-statistic computed using the Newey-West standard error.

Panel A: Amihud Negative Aggregate Liquidity Shock Postive Aggregate Liquidity Shock Const. Na D*Na D AdjR2 Const. Na D*Na D AdjR2

r -0.007 -0.649 0.191 0.057 0.049 r 0.138 -0.882 0.156 -0.101 0.015 (-3.80) (-13.93) (3.62) (2.78) (10.89) (6.54) (-3.25) (0.88) (-6.47) (6.98)

E[r] -0.008 0.001 0.030 0.035 0.004 E[r] 0.010 -0.098 0.090 0.043 0.002 (-4.10) (0.28) (-5.03) (3.64) (5.93) (1.17) (-3.13) (2.25) (9.68) (5.73)

Nr(-) -0.027 -0.122 -0.075 0.027 0.004 Nr(-) 0.023 -0.060 0.155 -0.037 0.002 (-1.96) (-3.53) (3.34) (-3.82) (2.71) (1.25) (0.58) (-0.92) (-2.46) (2.73)

Ncf -0.038 0.236 0.410 0.019 0.010 Ncf 0.056 0.318 0.114 -0.073 0.001 (-2.87) (-12.91) (2.61) (2.13) (5.83) (4.06) (-4.31) (2.29) (-8.87) (4.62)

Panel B: Turnover Positive Aggregate Illiquidity Shock Negative Aggregate Illiquidity Shock Const. Ntv D*Ntv D AdjR2 Const. Ntv D*Ntv D AdjR2

R -0.008 2.284 6.508 0.068 0.076 R 0.186 2.553 4.090 -0.009 0.022 (-4.12) (7.69) (4.71) (-2.24) (9.07) (10.26) (3.38) (2.58) (-0.46) (5.93)

E[r] -0.016 0.084 0.611 0.026 0.004 E[r] 0.016 0.231 0.488 0.047 0.004 (-3.88) (2.05) (1.84) (3.64) (3.74) (1.91) (2.78) (1.29) (7.84) (6.62)

Nr(-) -0.030 -0.366 -0.177 0.049 0.003 Nr(-) 0.023 -0.377 0.604 -0.024 0.002 (-1.94) (5.57) (0.67) (-6.76) (2.98) (1.17) (3.53) (1.34) (-2.30) (2.53)

Ncf -0.043 0.677 0.617 0.061 0.020 Ncf 0.072 0.687 0.603 -0.038 0.009 (-3.42) (9.78) (3.36) (-5.13) (5.34) (7.18) (3.42) (1.80) (-4.66) (3.51)