Master Thesis
The Pricing of Liquidity in Chinese A-share Market
Author: Bingxin Liu Student No.: 11375116
Master program: Finance (Asset Management) Faculty: Amsterdam Business School
Supervisor: dr. J. Ligterink Submission Date: 1st, July, 2017
ACKNOWLEDGMENTS
I would like to thank my supervisor dr. Ligterink for his patient guidance and useful advice during this arduous journey of writing thesis. Also, this study would never been completed if I hadn’t learnt courses such as Advanced Investment and Empirical Methods of Finance. Hence, I want to express my deep gratitude to dr. Eiling and dr. Peters.
Furthermore, I would like to thank my dear friends Dongni Li for her support and suggestions throughout the working process. I couldn’t go this further without my friends.
Finally, I deeply need to thank my parents who pay my tuitions for further study abroad and they are always there to encourage me every time I feel frustrated.
Bingxin Liu
STATEMENT OF ORIGINALITY
This document is written by Student Bingxin Liu who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
ABSTRACT
This thesis examines the liquidity pricing in Chinese A-share market. The author tests the LCAPM on Chinese equity market using the data from January 2006 to December 2016 on Shanghai Stock Exchange. Three different liquidity measures are employed — Amihud, High-Low Spread and PQS— to see if the usage of different illiquidity measures could lead to different findings. The author finds that the results count on the liquidity proxies utilized to a great extent. In general, the robust findings based on High-Low Spread suggest that only liquidity level is priced significantly, while the liquidity risks are not important in explaining stock returns. Besides, these different results derived from different proxies bring a new angle to see pricing of liquidity dimension. The outputs of Amihud may imply that market resiliency doesn’t influence security returns and the results for HLS estimator show that one of the rest dimensions —depth and breadth—may also be not priced. Therefore, the author speculates that different liquidity dimensions affect stock returns differently.
TABLE OF CONTENTS
1 INTRODUCTION ... 6
2 THEORETICAL FRAMEWORK ... 9
2.1 Liquidity and Liquidity Measure ... 9
2.2 Literature Review and Hypothesis Development ... 13
3 METHODOLOGY... 21
3.1 Illiquidity Measure ... 21
3.2 Portfolio Formation ... 23
3.3 Illiquidity Innovations ... 25
3.4 LCAPM and Betas Calculation ... 25
3.5 Cross-Sectional Regression ... 27 4 DATA ... 30 5 RESULTS ... 35 5.1 Innovations in Illiquidity ... 35 5.2 Estimation of Betas ... 38 5.3 Regression Analysis ... 42 6 ROBUSTNESS TEST ... 51 6.1 Size Portfolio... 51
6.2 Controlling for Size ... 55
6.3 Specification Test ... 59
7 CONCLUSIONS ... 61
REFERENCES ... 63
1 INTRODUCTION
Normally, we interpret liquidity as the ability to trade large order within a short time at a low cost whenever the investor is willing to trade (Harris, 2003, p.394) and the investors will demand compensations when they can’t convert the assets into cash easily in the market, which is referred to as liquidity premium. Unlike in the perfect world in textbooks where there is no trading cost, in real world liquidity is a big concern for market participants and not only liquidity level but also liquidity risk affects the expected returns on stocks. For example, investors seem to be reluctant to be engaged in the deals with high transaction cost and that’s why we expect high returns as compensation to investors for taking such risks.
It has been extensively shown that liquidity premium exists in US market however no united conclusion on the other markets was drawn, especially for the premium of liquidity risks. For example,Dalgaard (2009) found no solid proof to answer whether liquidity level and liquidity risks impact the securities in Denmark significantly (1987-2008). Liang and Wei (2012) examined 21 developed markets and reported that only three markets—France, Ireland and Japan—have significant liquidity risks priced. Therefore, we can see that the existence of liquidity premium in other non-US markets is still debating. As the largest developing country, China is a special candidate to test the existence of liquidity premia for several reasons. First, unlike NASDAQ or AMEX which are quote-driven (Foucault, Pagano and Roell, 2013, p31), Chinese stock market is order-driven. There are big differences between the characteristics of market microstructure of the two types of markets (Brockman and Chung, 2002). Doing such research will provide a new angle to see the link between liquidity and stock returns in an order-driven market. Furthermore, it is interesting to explore how liquidity affects stock returns in a market that full of individual investors who are used to trading speculatively without a long investment vision, thus leading to a high turnover rate. All of these traits mentioned above make Chinese stock market a special test ground.
Model (LCAPM) which can incorporate both the liquidity level and the liquidity risks in a single framework. They tested the model using US stock market data and confirmed significant liquidity risk effect on security returns. Another interesting test on this model in other developed and emerging markets was conducted by Lee (2011). He reported the significance of liquidity risks only in the US and developing countries after running several robustness tests. Also he believed that the liquidity risk is priced differently in various countries because of geographic, economic, and political situations. Finally, the latest work of Kim and Lee (2014) also investigated the common shares in the framework of LCAPM on AMEX and NYSE during the period of 1962-2011 but with eight different liquidity proxies. They showed that the results are quite sensitive to the measure used and only half of them confirmed the significant aggregate liquidity risk.
The main goal of this study is to answer whether or not the liquidity level and risks are priced in Chinese A-share (common share) market after the share reform in 2005 and also try to analyze this problem in different liquidity dimensions using 3 different illiquidity measures. This thesis tests the LCAPM on Chinese A-share market using the data from January 2006 to December 2016 of stocks listed at Shanghai Stock Exchange. The most important reason to use the LCAPM model is that this framework combines both liquidity level and three kinds of liquidity risk factors, which is much more comprehensive than any other liquidity-augmented models. The author employs two recently created liquidity proxies—Percent Quoted Spread (PQS) which was introduced by Chung and Zhang(2014) and High-Low Spread developed by Corwin and Schultz(2012)—as well as the most traditional and widespread measure—Amihud (Amihud,2002) in order to investigate if there is any difference in findings among different proxies for liquidity level. All the measures are chosen carefully based on the highest correlation with high-frequency liquidity measures according to findings of Fong, Holden and Trzcinka (2017). Also they are derived from different dimensions of liquidity, thus contributing to a more reliable framework on liquidity pricing. Finally, the author carefully choose the period from January 2006 to December 2016 because there was an influential split share reform in China on
May 9,2005 and it was almost completed at the end of 2005. Before this reform, controls remained firmly in State hands and only about one third of stocks in Chinese stock market are tradable shares. Since there are many other papers having proved that liquidity is improved dramatically after the share reform, this thesis will directly concentrate on the stock market after this split share reform.
This research shows that the results of the analysis and their robustness count on the liquidity measures we used in LCAPM to a great degree. In general, the robust finding based on HLS measure suggests that only liquidity level is priced while liquidity risks don’t affect security returns significantly. Furthermore, the robust HLS-based results may imply that market resiliency is unimportant in explaining stock returns. Also this study for Amihud measure reveals some strong proof for the unimportant effect of one of the rest liquidity dimension—depth and breadth. Nonetheless, this study raises a new conjecture that different liquidity dimensions influence equity returns differently. Hence, this study makes contributions to the previous research in the following ways. First, it investigates Chinese equity market using LCAPM (Acharya and Pedersen, 2005) which was not investigated before rather than LACAPM (Liu, 2006), a model tested by most scholars in China. Second, two recent liquidity proxies— PQS and High-low ratio are included into the LCAPM framework for the first time for emerging market. Third, it gives new insights and motivation on liquidity pricing in specific liquidity dimension instead of liquidity pricing as a whole. Fourth, it also enriches the findings of liquidity pricing from an order-driven market perspective. Finally the sample period is chosen after split share reform with relatively new data. The remainder of this work is organized in such order: Section 2 gives plentiful theoretical framework and literature review about this topic. Section 3 provides every step of the methodology which is employed to investigate Chinese equity market using LCAPM. Section 4 reports a detailed description of data I used. Section 5 presents the empirical results on the liquidity premium in Chinese A-share market. Section 6 discusses the results of robustness tests for main analysis. Finally I conclude in Section7.
2 THEORETICAL FRAMEWORK
2.1 Liquidity and Liquidity Measure
Normally, we interpret liquidity as the ability to trade large order within a short time at a low cost whenever the investor is willing to trade (Harris, 2003, p.394, Cooper, Groth and Avera, 1985). Amihud (2002) describes liquidity as a reflection of the influence of order flow on the price of an asset.
Amihud, Mendelson and Pedersen (2005) conclude that illiquidity stems from four factors: direct transaction costs, inventory risk, informed trading and search costs. Transaction costs including broker’s commissions, trade taxes and other order-processing costs are incurred whenever a trade happens. Dealers play a role of buyers when investors want to liquidate their positions when natural buyers are limited in the current market. Adding these securities to their inventory exposes themselves to the risk of a sudden fall in the price, hence, dealers will ask a compensation for this additional risk. Besides, there is a tension between price discovery and liquidity. If information is announced to market by means of trading pressure rather than a public announcement, liquidity suffers and there would be loss if trading with someone with internal information. Finally, search costs happen when investors find it difficult to cut a deal with another counterparty, but more likely to occur in an OTC market. Therefore, liquidity can be gauged from the above four angles and it seems that every measure of illiquidity has to start from one of these angles.
Speaking of liquidity of a market, one must also mention its three dimensions: depth, breadth and resiliency (Kyle, 1985 and Harris 2003). In a deep market, large deals can be traded without substantially moving the price (the spread doesn’t increase in trade size). Breadth, also referred to as tightness, is reflected by bid-ask spreads in the market (Kyle, 1985). Resiliency, the speed at which liquidity returns to normal after a trade, is another dimension of market liquidity. In this kind of market, brokers can accelerate executions of large orders, leading to lower execution costs and lower
opportunity costs (Foucaut, Pagano and Roell, 2013, p.69). Therefore, understanding different dimensions of liquidity is crucial when we want to measure it.
Before choosing the most suitable liquidity measures for this study, first we need to distinguish between high-frequency and low-frequency measures. Basically, a high-frequency measure is the illiquidity measure calculated utilizing data within a day of each trade, on the contrary low-frequency measure is the illiquidity measure computed utilizing the end of daily data. There is no doubt that the high-frequency proxy must be more precise than the low-frequency one. However it is not hard to imagine that this high-frequency data must be too enormous and sometimes difficult to find. Thus recently more and more scholars propose to use low-frequency liquidity measure.
Normally the both high and low-frequency proxies are divided into two types: percent-cost and cost-per-dollar-volume proxies (Fong, Holden and Trzcinka, 2017). The first one links liquidity cost to a percentage of price or bid-ask spread. The second one captures the price impact per certain number of assets traded. It’s interesting to find that although we categorize market liquidity into three dimensions, yet the proxies created are basically divided into two types. As for their benchmarks, high-frequency liquidity measures, this thesis will mainly discuss Percent Effective Spread (PES) and Lambda since they are employed further to select best low-frequency liquidity measures according to the findings of Fong Holden and Trzcinka (2017). PES is computed using trade price minus bid-ask midpoint before order submission. Lambda is the slope of the following equation, according to the paper of Goyenko, Holden, and Trzcinka (2009):
The thesis chooses the liquidity measures based on an interesting research conducted by Fong, Holden and Trzcinka on comparison between high-frequency benchmark and the most traditional and latest low-frequency liquidity proxies globally during the period 1996-2007 comprehensively. Table 1 presents the best ten liquidity estimators for Chinese equity market based on the findings of Fong, Holden and Trzcinka (2017). Among these different illiquidity measures, Percent Quoted Spread (PQS) (Chung and Zhang, 2014) and High-Low Spread (HLS) (Corwin and Schultz, 2012) are pure spread measures. This kind of measures are often based on ask, bid, high, low and closing prices. The rest of measures on the other hand are derived from the number of zero-return observations of stocks. More specifically, FHT (Fong, Holden and Trzcinka, 2017) have a relatively higher correlation with the benchmarks than other zero-return measures. It increases with the increased frequency of zero returns and volatility of the return distribution. LOT measures were created from the thought that non-zero returns are observed only if the true return is larger than the trading cost. While Zeros or Zeros2 measures are computed using the proportion of days with zero returns. With regard to Roll (Roll, 1984) and Extended Roll (Holden, 2009), they are computed by serial covariance in price changes. Finally, the Effective Tick (Goyenko, Holden, and Trzcinka, 2009) utilizes the idea of price clustering to identify the effective spread and the authors believed that it’s not worthy to spend tremendous efforts to employ high-frequency proxies. Another noteworthy liquidity proxy not presented in Table 1 is Gibbs (Hasbrouck, 2009). Since it is very numerically-intensive and the sample is large, Fong, Holden and Trzcinka (2017) omitted this estimator in analysis for the potential infeasibility. Gibbs estimator stems from daily closing prices, on the condition that the public information shock satisfies N (0,𝜎𝑒2)1
. On the other hand, concerning for the emerging markets, some scholars highlighted that special illiquidity proxy must be applied. For example, Kang and Zhang (2013) examined 20 emerging markets and proposed a new proxy for the inactively traded emerging markets --- AdjILLIQ measure adjusts the old Amihud
1
proxy for low trading frequencies problem. This thesis will not apply this measure because the problem of having too many zero-trading days doesn’t bother Chinese equity market. On the contrary high turn-over and active trading can be spotted instead. Apparently, this measure is not suitable for Chinese share market.
As we can see from Table 1, the most suitable illiquidity proxies for Chinese equity market are PQS and HLS since they exclusively occupied the top positions according to four criteria (listed in Table 1). Amihud still performs well associated with the criteria of Lambda. Thus this thesis uses three low-frequency liquidity proxies— Amihud which was utilized by Acharya and Pedersen (2005) in original paper and high-low ratio as well as PQS on the basis of best monthly low-frequency measures for Chinese equity market. These measures will be discussed further in the methodology part, Section 3.1. The next section will review the literature about liquidity pricing and develop the main hypothesis.
rank PES Lambda Average Cross-Sectional Correlation Portfolio Time-Series Correlaton RMSE Average Cross-Sectional Correlation 1 PQS 0.689 PQS 0.856 PQS 0.0021 High-Low 0.812 2 High-Low 0.261 Effective Tick 0.545 Effective Tick 0.0041 Amihud 0.785 3 FHT 0.099 High-Low 0.42 FHT 0.0044 PQS 0.738 4 Zeros 0.082 FHT 0.323 High-Lo w 0.0066 Extended Roll 0.476 5 Zeros2 0.082 Extended Roll 0.119 Roll 0.0071 FHT 0.451 6 Effective Tick 0.058 Roll 0.097 Extended Roll 0.0102 Effective Tick 0.438 7 Extended Roll 0.027 Zeros -0.037 LOT
Y-split 0.014 LOT Mixed 0.387
8 Roll 0.022 LOT Y-split -0.06 LOT
Mixed 0.0215 Zeros2 0.385 9 LOT Mixed 0.013 LOT Mixed -0.126 Zeros2 0.0467 LOT Y-split 0.207 10 LOT Y-split 0.009 Zeros2 -0.141 Zeros 0.064 Roll 0.104
2.2 Literature Review and Hypothesis Development
With regard to the empirical tests on the relationship between liquidity and share returns, substantial researches since Amihud and Mendelson (1986), have found that liquidity is a significant factor that impacts share prices. They analyzed the influence of the spread on stock pricing and found that the expected returns increases with bid-ask spread. Later Chalmers and Kadlec (1998) using amortized spread, and Brennan, and Subrahmanyam (1996) employing dollar trading volume, also revealed that share return is positively correlated with illiquidity. Amihud (2002) confirmed
similar findings for NYSE stocks from 1964 to 1997 with his original proxy that required share return corresponds to an illiquidity premium in a way. Although the above cited studies are in line with the liquidity premium notion, one should notice that so far, liquidity has been treated as a kind of feature on individual stock level instead of a risk factor of concern to investors. Now we can define our first hypothesis as follows:
H1: The illiquidity level of stocks is positively and linear priced.
Since this liquidity level has been studied extensively with a relatively united conclusion of significant existence, the author supposes that liquidity level is priced in Chinese equity market as well and will test this hypothesis using LCAPM (Acharya and Pedersen, 2005).
A further research topic about the role of liquidity in asset pricing attracts more and more attention since the famous paper written by Páster and Stambaugh (2003) was published. Table 2 below presents a summary of empirical studies on liquidity and asset pricing.
No. Author(Year) Sample Model Tested Proxy 1 Páster and Stambaugh(20 03) USA-AMEX,N YSE Fama-French 3-factor model Own proxy 2 Acharya and Pedersen (2005) USA-AMEX,N
YSE LCAPM Amihud 3 Liu(2006) USA-AMEX,N
YSE,NASDAQ LACAPM Adjusted turn-over
4 Bekaert, Harvey, and Lundblad (2007) 19 Emerging-mark et countries Simple model
Transformation of the percentage of zero daily returns
5
Brockman, Chung, and Perignon (2009)
Global Own model Intra-day effective spread and intra-day dollar depth
6 Lee (2011) Global LCAPM Zeros 7
Karolyi, Lee, and van Dijk (2012)
Global Simple
model Measure obtained from 𝑅
22
8 Liang and Wei (2012) 21 Developed- market countries Model including HML and MKT
Páster and Stambaugh’s measure and Amihud
9 Kim and Lee(2014)
USA-AMEX,N
YSE LCAPM Eight measures
Páster and Stambaugh (2003) unveiled that market-wide liquidity is a significant state variable for asset pricing using US equity market data. Later on Acharya and Pedersen (2005) developed a new framework combining liquidity level and three types of liquidity risks. This model incorporates 4 betas: the standard CAPM beta, and three
liquidity betas including commonality in liquidity, Pastor and Stambaugh (2003) liquidity beta, and liquidity sensitivity to market return. Liu (2006) also proposed his own liquidity-augmented two-factor model. All of them confirmed the liquidity premium due to the effect of covariance between asset returns and market illiquidity (third beta in LCAPM) in U.S. market. As for markets in other countries, Bekaert, Harvey, and Lundblad (2007) confirmed that the risk from the sensitivity of share return to market illiquidity is a crucial factor in explaining share returns on 19 emerging markets3 (1993-2003). However Liang and Wei (2012) conducted a research on 21 developed markets4 (1989-2005) about liquidity pricing and reported significant liquidity risk premium only in 3 countries – France, Ireland, and Japan. It’s worth to mention that this result is contradict to the earlier findings which indicate significant liquidity risk in US equity market. Thus the results of non-US markets are still debating. Note that what these researches mentioned above concentrated on is the systematic liquidity risk (third beta) of LCAPM.
Regarding the commonality in liquidity and liquidity sensitivity to market return (second and fourth beta in LCAPM), there are relatively not many papers studying on them. Also most of papers on the former topic often do not link the importance of commonality in liquidity with share returns. However, Brockman, Chung, and Perignon (2009) examined intraday spread and depth observations in 47 stock exchanges and revealed that most markets across 38 countries have a strong commonality in liquidity. Besides, they also reported that emerging Asian exchanges have a relatively more significant commonality. Analogously, Karolyi, Lee, and van Dijk (2012) found that commonality in liquidity is greater in countries with high market volatility, greater presence of international investors, and more correlated trading activity (developing countries) using data from different countries and periods. Therefore, we expect that for the emerging market in China the second beta of the LCAPM should be priced significantly. Unfortunately the fourth beta hasn’t been
3 Argentina, Brazil, Chile, Colombia, Greece, India, Indonesia, Korea, Malaysia, Mexico, Pakistan, Philippines,
Portugal, Taiwan, Thailand, Turkey, Venezuela, Zimbabwe
4 Australia, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong, Italy, Ireland, Japan, the
Netherlands, New Zealand, Norway, Singapore, Spain, Sweden, Switzerland, the United Kingdom, and the United States
discussed solely in any paper so far, but mostly in the study under LCAPM framework. Now the author would review some papers in the context of this model. Firstly, Acharya and Pedersen (2005) tested their unconditional version of model on AMEX and NYSE during the period 1962-1999 using Amihud measure. They showed that liquidity level and risks are priced significantly with the fourth beta most strong and second one least strong. Note that the four betas in their study are highly correlated, thus leaving potential multicollinearity problem.
Apart from the original paper by Acharya and Pedersen (2005), there is an interesting research conducted by Lee (2011). He conducted analysis using LCAPM on 50 countries5 from 1988 to 2007. The author used Zeros as illiquidity measure but do the research on individual stocks rather than portfolios. It was found that local aggregate liquidity risk impact share returns considerably in the US and emerging markets, however this finding doesn’t hold in other developed markets. Also it is worth noting that the fourth beta is the main force behind this effect in developed markets while the other betas are not important. Besides, the local commonality beta (second beta) was found significant in emerging markets at 99% confidence level and 90% for the US.
However, liquidity risk due to the sensitivity of the return to market-wide illiquidity (third beta), is not important to explain share returns for any market. This result is against the previous finding of Páster and Stambaugh (2003). One thing should be noticed that Lee drew his conclusions by mixing data from different countries of developed or emerging markets. In contrast to stocks in other emerging markets, Chinese equity market has its own characteristics (as we discussed in Section 1) which means it may be inappropriate to indiscriminate Chinese equity market and other emerging markets.
Following the idea of Lee (2011), the author thus define hypothesis H1 and H2 to answer whether aggregate liquidity risk and illiquidity level are positively priced risk factors in Chinese share market.
5 Developed countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong,
Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, Singapore, Spain, Sweden, Switzerland, UK, US. Emerging markets: Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt, Greece, Hungary, India, Indonesia, Israel, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Poland, Portugal, Russia, South Africa, South Korea, Sri Lanka, Taiwan, Thailand, Turkey, Venezuela.
H2: The aggregate liquidity risk of stocks is positively and linear priced.
Hypothesis H2 will be tested to see if there is an overall effect of liquidity on required returns. LCAPM (Acharya and Pedersen, 2005) is a comprehensive model incorporating different kinds of overall effect of liquidity, thus the author employs this model for main research. Since the original full version of LCAPM has intrinsic problem about multicollinearity due to highly correlated betas, this thesis would also follow the methodology of Lee (2011) who defines aggregate liquidity risk as a aggregation of three types of liquidity risks.
In addition, Kim and Lee (2014) also investigated the common shares in the framework of LCAPM on AMEX and NYSE during the period of 1962-2011 but with eight different liquidity proxies6 only including Amihud that we are interested in. Half of the measures show significance while the others gave the opposite results and the fourth beta is significant only for Amihud measure as the Acharya and Pedersen (2005) found. Obviously we can’t deny that empirical outputs are quite sensitive to the liquidity proxy employed in the test. One possible explanation has the following logic. Since different liquidity measures are constructed capturing different liquidity dimensions, we may observe quite different results about pricing of liquidity in equity market. Thus I define:
H3: Different liquidity dimensions affect stock returns differently.
However, we can’t test this hypothesis using low-frequency liquidity measures which captures only one aspect of liquidity dimensions due to the lack of liquidity proxy. This can be tested in the future when the liquidity measure solely represents one of depth, breadth and resiliency is available. Now we can only compare the results of three liquidity measures to see if different measures focusing on different liquidity
6 Amihud’s (2002) measure, Pástor and Stambaugh’s (2003) measure, the zero-return measure, Liu’s (2006)
measure, , the illiquidity measure from Lesmond, Ogden, and Trzcinka (1999; LOT), Roll’s (1984) measure, run length(Das and Hanouna (2010) and turnover.
dimensions have contradicting result and try to test this hypothesis in such direct way. There is also some literature researching about the microstructure of the market but in a context of intraday patterns of liquidity and returns which is not our concern of this study. However there are some papers about liquidity pricing in an order-driven market. First one needs to be aware that there are two kinds of markets based on the feature of frequency of trading: quote-driven market and order-driven market (Malinova and Park, 2012). One of the most important characteristics of a quote-driven market is that market makers who act as an intermediary between buyers and the sellers play irreplaceable roles in it. Prices are set before quantities. The market maker provides liquidity by buying or selling shares at any time regardless of the number of shares. In order to maintain enough liquidity and fair prices, the market makers have to try their best to manage the inventories and also have to trade with another dealer sometimes. Such inter-dealer trades occupy a large proportion of market transactions. Compared to quote-driven markets, the order-driven markets have no market makers involved. Prices and quantities are set altogether. All the orders of investors are submitted directly into an order book through computers and waited to execution. They are matched according to the price and timing priority criteria.
Most markets of developed countries such as the US, the UK, France, and Germany are all price-driven markets. Although more and more security markets begin to incorporate both mechanisms as a hybrid markets, NYSE, NASDAQ, LSE, and MTS etc. are still considered as traditional dealer markets (Foucault, Pagano and Roell, 2013, p.31). There are also some literature concerning about order-driven market. As far as the author acknowledges, Dalgaard (2009) found no solid proof to answer whether liquidity level and liquidity risks impact the securities in Denmark significantly (1987-2008) which is also order-driven. Syamala, Reddy and Goyal (2014) examined and provided satisfactory proof that pricing of commonality in liquidity for both stocks and options exist on NSE (National Stock Exchange) in India. Marshall (2004) added to the existing literature that liquidity level is an important factor of returns on ASX (Australian Stock Exchange), a small pure order-driven
market. Note that unfortunately these findings are not from top-tier journals thus undermining the credibility.
As far as the author knows, there are no researches studying one specific market in the context of LCAPM. This thesis tends to explore the impact of using different liquidity measures in different liquidity dimensions on Chinese stock market and conduct study on a varying portfolio basis. The author carefully chooses the period from January 2006 to December 2016 after the influential split share reform in china that was almost completed at the end of 2005. This thesis mainly focuses on the equity market after share reform. Previous studies utilized diverse methodologies for empirical test. The next Section presents every detail about how the author conducts the research.
3 METHODOLOGY
This study will basically use Fama-MacBeth methodology (Fama and MacBeth, 1973). Despite different modification of this approach, the author employs the one in the book of Cochrane (2005, p245). Roughly speaking, the process is as follows: First, we need to form portfolios for individual stocks to eliminate the white noise. Then the betas are calculated. Finally, the coefficients of LCAPM are obtained using cross-sectional regressions.
3.1 Illiquidity Measure
This thesis utilizes three low-frequency liquidity proxies—High-Low Spead and PQS on the basis of best monthly low-frequency proxies for Chinese equity market according to the findings of Fong, Holden and Trzcinka presented in Table 1 as well as Amihud used by Acharya and Pedersen (2005) in their original paper.
Amihud—This measure is quite popular and widely used in top-tier journals by many
scholars. According to statistics, there are more than 100 papers using this measure in The Journal of Finance, which assures good performance of this measure. The definition of illiquidity using Amihud is calculated as:
(2)
It can be seen from the definition that this proxy captures the price impact of different trading volume. However this is not the best illiquidity measure for Chinese equity market according to the findings of Fong, Holden and Trzcinka (2017). Furthermore, return premium actually is driven mostly by its volume rather than its return-to-volume ratio, leading to some other explanations for this measure. For instance, Baker and Wurgler (2006) linked the explanatory power of this measure to investor sentiment.
high and low prices. The main idea behind this creation is that daily high (low) prices are almost always buy (sell) trades, thus high-low ratio represents both the variance and the bid-ask spread. Moreover, since the spread component is not proportional to the return interval, the bid-ask spread estimator can be extracted as a function of high-low ratios over 2-day intervals. Relative to other measures, the computation of this ratio is more complicated. High-Low Spread is presented in the following equations:
For longer periods like a month, we can take average of the spread estimates of all overlapping 2-day periods within a month.
High-low ratio considers that the expectation of a stock’s true variance over 2-day period is twice as large as the expectation of the variance over one single day. However, actually the observed 2-day variance may be more than twice as large as the variance over one-day period in some cases like a big overnight price change. If this happens, the High-Low Spread estimates we calculate could be negative. The author conducted analysis as Corwin and Schultz (2012), we set all negative 2-day period spreads to zero before taking average for a monthly spread.
PQS——This estimator is brought up by Chung and Zhang (2014). Despite the
simple calculation, PQS has the highest correlation with the benchmarks and the lowest RMSE under three criteria (see Table 1). The illiquidity using PQS is expressed as follows: 𝑃𝑄𝑆𝑡𝑖= 1 𝐷𝑎𝑦𝑠𝑖𝑡∑ 2(𝐴𝑠𝑘𝑡𝑑𝑖 −𝐵𝑖𝑑𝑡𝑑𝑖 ) 𝐴𝑠𝑘𝑡𝑑𝑖 +𝐵𝑖𝑑𝑡𝑑𝑖 𝑑𝑎𝑦𝑠𝑡𝑖 𝑑=1 (6)
Since PQS is derived from bid-ask spread, it doesn’t capture much price impact. However it is pretty simple and straightforward in the respect of calculations. In addition, it still lacks strong explanatory power economically in spite of the good statistical match.
In a word, this study employs three liquidity measures which have the highest correlation with the high-frequency benchmarks based on the findings of Fong, Holden and Trzcinka (2017). Next section we will come to portfolio formation.
3.2 Portfolio Formation
The empirical study will be on a portfolio rather than individual stock basis. The main reason is that testing the model based on individual stocks will obtain too much white noise and amplify the errors in variables in the beta estimation.
All the illiquidity proxies for individual stocks need to be normalized by multiplying market index to remove the inflation effects before portfolio formation. In the paper written by Acharya and Pedersen (2005), they thought that ILLIQ is non-stationary and Amihud only measures the cost of selling rather than actual illiquidity trading cost. Hence, they proposed a solution of normalization as follows:
(7) They normalize the illiquidity measure by truncating it at a maximum of 30% and a minimum of 0.25% and the coefficients of 0.25 and 0.3 are chosen according to findings of Chalmers and Kadlec (1998). The coefficients can make normalized illiquidity have about the same level and variance as does the effective half spread. Nevertheless, here we omit the coefficients but only use the product of market index and ILLIQ because the corresponding coefficients for Chinese A-share market are undetermined in any paper available.
Thus we use this simplified normalization as follows:
𝑐𝑡𝑖 = 𝑖𝑙𝑙𝑖𝑞𝑡𝑖𝑃𝑡−1𝑀 (8) where 𝑐𝑡𝑖 is the illiquidity cost of stock i in month t, while 𝑖𝑙𝑙𝑖𝑞𝑡𝑖 is illiquidity of stock i in month t measured by one of the three estimators—Amihud, High-Low ratio or PQS, 𝑃𝑡−1𝑀 is calculated using the capitalization of overall market of month t-1 over the initial overall market capitalization of January 2006, 𝑃𝑡−1𝑀 = 𝑃𝑡−1𝑀
𝑃𝐽𝑎𝑛2006𝑀 . This step can still help us solve the problem of non-stationarity. By doing so, we can make all the illiquidity proxies stationary.
Now we start forming portfolios. More specifically, we sort all stocks into 25 portfolios for each year y from 2006 to 2016 according to the illiquidity in year y-1, thus Portfolio 1 is the most liquid and Portfolio 25 is the most illiquid. The yearly illiquidity for year y-1 of each share is computed as the mean of its daily illiquidity for Amihud, High-Low ratio and PQS estimators. Hence, we can obtain 25 illiquidity portfolios for each liquidity proxies. Finally the market portfolio is composed of all the stocks included in the illiquidity portfolios. This study employs equally-weighted portfolios rather than value-weighted ones.
In the similar way, as for the size portfolio, 25 portfolios are created by sorting stocks according to their market capitalization at the beginning of the year y, from largest to the smallest. This size portfolios are used to do robustness tests on the results obtained from the illiquidity portfolios and here we omits the other tests based on liquidity variation portfolios since we found that illiquidity level is positively correlated with illiquidity variations across three proxies which means the portfolios sorted by liquidity variation should be quite similar to the illiquidity portfolios.
After the formation of portfolios, we can determine the return for each portfolio as follows:
𝑐𝑡𝑃 = 1
𝑛∑ 𝑐𝑡 𝑖 𝑛
𝑖=1 (10)
where 𝑐𝑡𝑖 𝑖𝑠 the adjusted illiquidity of stock i for portfolio p. The detailed calculation will be discussed in Section 4.
Thus, we have obtained all the portfolios and computed returns and illiquidity for each portfolio so far. In the following Section, we will continue to calculate the innovations in illiquidity and the betas. The description of the next estimations and analysis will be on the basis of portfolios of stocks rather than individual stocks.
3.3 Illiquidity Innovations
This thesis will consider illiquidity innovations on a portfolio basis, namely 𝑐𝑡𝑝− 𝐸𝑡−1(𝑐𝑡
𝑝
) , and the calculation is according to methodology of Acharya and Pedersen (2005). To compute the innovations, the author will apply the autoregressive model with two lags.
But first we need to obtain the un-normalized illiquidity of portfolios as follows:
(11) Then we can calculate the innovations by autoregressive model with 2 lags, namely AR (2) model:
(12)
Thus for now we have estimated all the variables needed in the process of the calculations of betas, which will be conducted in next Section.
3.4 LCAPM and Betas Calculation
Pedersen (2005), the most important reason to use this model is that this framework combines both liquidity level and three kinds of liquidity risk factors, which is much more comprehensive than any other liquidity-augmented models.
This is the LCAPM deriving from the traditional CAPM by adding illiquidity costs to the economy:
In this model, λ is the risk premiums of different liquidity betas, and in the original paper, short-selling is also banned implying an investor must sell the asset at pti-cti . In addition, it’s important to mention that the λ doesn’t have subscript because the full version of LCAPM (equation (14)) is created initially imposing such restriction that λ1 = λ2 = −λ3 = −λ4.
As we can see from the equations (15) to (18), the unconditional LCAPM have four betas. It is quite crucial to understand the economic meanings behind them. First 𝛽1𝑖 is the market beta but after considering innovations in illiquidity costs. The stock return is positively correlated with market beta, 𝛽1𝑖, which ties the return of individual stock to the market return.
market illiquidity, namely, commonality in illiquidity. This covariance exists because an investor will demand a higher return if he holds an illiquid asset when the market gets more illiquid. Therefore, the required return rises with the positive second beta. 𝛽3𝑖, represents the effects associated with the covariance between the share return and market illiquidity, which is referred to as systematic liquidity risk sometimes. This can be translated as the willingness of investors to hold securities with smaller return initially if there is a higher return when market becomes illiquid. Thus, the expected return is negatively related to the positive systematic liquidity risk.
Finally, 𝛽4𝑖 captures the sensitivity of security illiquidity to market return. It manifests that the investors are not reluctant to accept a lower required return for a liquid stock in a downward market. Therefore, the expected return is negatively related to the positive sensitivity of security illiquidity to market return.
In brief, to obtain the betas, this study utilizes the full sample of data from January 2006 to December 2016. The calculations of betas are presented using equations (21)-(24) on a portfolio basis.
3.5 Cross-Sectional Regression
Following the methodology of Acharya and Pedersen (2005), this paper also use “net beta” to eliminate the potential multicollinearity among the betas since the adding or removing beta will change the estimates of the other betas. After imposing the restriction that λ1=λ2= −λ3= −λ4
(19) then following paper by Lee(2011) we also defines the aggregate liquidity beta :
(20) By doing so, we can separate the market risk and liquidity risks , this aggregate liquidity risk is one of our concern in this thesis. This thesis will conduct four main regressions as follows:
where k is treated as a constant to scale E(𝑐𝑡𝑝) for the difference between holding periods and estimation periods or a free parameter, 𝑢𝑡𝑝 𝑖𝑠 the pricing error term and α is the intercept,.
Note that equation (22) is the traditional CAPM adjusted for the innovations in illiquidity costs.
α should not be significant if our sample data fit LCAPM model well. k =1 in the original regressions of Acharya and Pedersen (2005). Since the monthly estimation period differs from the typical investor holding period, they use k to adjust for this gap. k is actually the average monthly turnover across all stocks because holding periods is gauged by period over which all shares are turned over once. However, k is not linearly scalable in the majority situations. Therefore, we consider k either a constant or a free argument. When k is considered as a constant, E(𝑟𝑡𝑝 ) − 𝑘E(𝑐𝑡𝑝 ) will act as the dependent variable. So the question is how long the average holding period of Chinese investor is. The typical investor’s holding period for Chinese investor is 6 months based on the statistics in 2010 from World Federation of Exchanges. In this case, k=1/6≈ 0.167. If so, the regression (19) that presents Fama-MacBeth approach looks reciprocal to:
(25) Note that if we treat k as a constant, it means we already assume liquidity level does influence security returns. In this thesis due to the lack of updated statistics about average Chinese investor holding period and most importantly the willingness to test the significance of liquidity level, the author will consider k as an independent variable. Finally, we come to the cross-sectional analysis. Since Acharya and Pedersen (2005) showed a direct way to obtain the beta values, no time series regression is needed in advance. So first I will run cross-sectional regressions to get the estimates
λ̃𝑡𝑛𝑒𝑡 and ũ𝑡𝑝 for each t. Then take average of them to get estimates λ̃𝑛𝑒𝑡 and ũ𝑝:
(26) While the sampling errors are calculated as follows (Cochrane,2005, p.246):
(27) For each time t, we calculate the R2 of the cross-sectional regression and take the average.
Basically, I will test the statistical significance of the estimated risk premia λ̃𝑛𝑒𝑡using t-statistics and the joint significance of the pricing errors ũ𝑝. All the calculations are implemented in Stata and I will describe the filtering of data in next Section.
4 DATA
The sample is composed of all A-shares (common shares) traded on the Shanghai Stock Exchange from January 01, 2006 to December 31, 2016. In total there are 1211 stocks included and 2,311,867 daily observations of different factors (before any filtration) in the sample. All the daily and monthly data are drawn from CSMAR except for the closing ask and bid prices which are downloaded from Datastream. This means the initial samples to calculate HLS and Amihud before any filtration are the same and distinct from the sample to compute PQS. The trading volumes are gauged in millions of RMB and market capitalization is expressed in millions of RMB too.
The dataset is screened by missing values. Specifically, the daily observations without volume figures are considered as missing observations. There is no missing value of any variable in dataset obtained from CSMAR, however there are plenty of missing values of closing ask and bid price drawn from Datastream (98,586 for closing ask price and 85,368 for closing bid price). Also if the number of trading days within a month for some stock is less than 15, then the observations in this month will be deleted but keep data in other months intact. Finally, the data of stocks with the number of observations less than 100 within a year is also dropped. In order to expand the sample and avoid the survivorship bias, this study employs unfixed sample of stocks. This means the sample used includes all the stocks listed by the end of examined year. By the end of calculating Amihud and High-Low Spread measures, the sample contains the same amount of daily observations (2,250,092). However, in total 271,350 of daily figures are dropped after screening the data for PQS measure, leaving 2,041,274 daily observations.
In this study, we focus on 103,678 valid monthly data for PQS and 112,194 valid stock-month observations for High-Low Spread and Amihud that are involved in forming 25 portfolios. Since we need to form the portfolio in year t based on the illiquidity in year t-1, naturally the eventual sample period to be analyzed is from January 01, 2007 to December 31, 2016. As for monthly stock returns during the
analyzed period, our sample shows a range from -86.46% to 497.68% for Amihud and High-low ratio while vary from -61.88% to 215.31% for PQS.
Moreover, Table 3 presents the descriptive statistics of 25 illiquidity portfolios based on 3 illiquidity measures. We can find that the more liquid (portfolios on the top) the portfolio is, the smaller liquidity variation it shows. Therefore, the portfolios sorted by illiquidity and portfolios sorted by illiquidity variation should be similar, thus this study won’t do robustness test on liquidity variation portfolios but on size portfolios. As for the relationship between the mean excess return and illiquidity, generally speaking, the extreme of portfolios often has a lower excess return. Besides, For Panel A, it’s easy to find that as the illiquidity grew, the market capitalization of the portfolio is decreasing which means the more liquid (portfolios on the top) is the portfolio the more market capitalization it has. However, for Panel B and C, the most illiquid portfolio doesn’t hold the least capitalization.
Regarding the different betas, it is easy to find that the first and second beta are positive while the third and fourth beta are negative. Having known the different meanings of four betas, we are not surprised by this finding. This result reveals that return of individual stocks is positively correlated with market return and the illiquidity level of individual stocks increases with market illiquidity. Furthermore, the returns of individual stocks are lower when the whole market becomes more illiquid and the illiquidity of individual stocks will increase in a downward market. Also, 𝛽1 seems quite larger than the other three betas across three different measures. The author would like to discuss the dynamics of these betas more in the latter Section 5.2.
The liquidity level is time-varying but persistent according to the findings of Acharya and Pedersen (2005) and Páster and Stambough (2003). If liquidity is persistent, then investors can estimate liquidity level of tomorrow based on data today. Liquidity persistency makes the liquidity level a more accurate tool to examine whether illiquid stocks require a higher return premium than liquid stocks. Since a variable is persistent if the correlation between the sequential time frames is bigger than 0, the author checks this autocorrelation of 25 portfolios sorted on illiquidity standards. It turns out that the autocorrelation of portfolios for PQS and High-Low Spread is
0.8974 and 0.8113 respectively but only 0.2083 for Amihud. This finding is intriguing and may indicate one weakness of Amihud measure. In general, the persistence of illiquidity level is visible employing different lags and it is declining with the number of lags. Thus we can draw a conclusion that illiquidity is persistent and time-varying in Chinese A-share market. Besides, after running a Fisher-type unit root test based on Augmented Dickey-Fuller Test, the results assure that both illiquidity cost and return of portfolios are stationary at a confidence level of 99%. This means we are less worried about the spurious regression problem and more confident about further calculations.
In conclusion, different liquidity proxies lead to diverse results, therefore it is expected that the usage of different liquidity measures could give diverse regression outputs as well. The main results of this study will be presented in the following section.
Portfolio No. Excess Return,𝑟𝑡𝑝-𝑟𝑓 Illiquidty,𝑐𝑡 𝑝 Illiquidity StD σ(𝑐𝑡𝑝) 𝛽 1𝑝 𝛽2𝑝 𝛽3𝑝 𝛽4𝑝 𝛽𝑛𝑒𝑡 𝛽𝑖𝑙𝑙𝑖𝑞 Market Capitalization,ln(𝑀𝐶𝑡𝑝) PanelA:Amihud 1 0.0082 0.0019 0.0016 0.6256 0.0013 -0.0610 -0.0054 0.6933 0.0677 5.3096 5 0.0169 0.0097 0.0067 0.8405 0.0064 -0.0763 -0.0277 0.9508 0.1103 2.6209 10 0.0181 0.0176 0.0148 0.8319 0.0114 -0.0799 -0.0469 0.9701 0.1382 2.1021 15 0.0186 0.0257 0.0204 0.8197 0.0191 -0.0831 -0.0686 0.9905 0.1708 1.7405 20 0.0224 0.0375 0.0267 0.8149 0.0270 -0.0827 -0.1060 1.0305 0.2156 1.7358 25 0.0203 0.1258 0.1287 0.7902 0.1237 -0.0820 -0.4456 1.4415 0.6513 1.5738 PanelB:HLS 1 0.0163 0.0393 0.0195 0.7933 0.0059 -0.0109 -0.0178 0.8278 0.0346 4.8942 5 0.0181 0.0468 0.0222 0.9409 0.0083 -0.0164 -0.0166 0.9822 0.0413 2.7008 10 0.0155 0.0487 0.0211 0.9433 0.0081 -0.0187 -0.0218 0.9920 0.0486 2.6316 15 0.0175 0.0509 0.0218 0.9849 0.0086 -0.0198 -0.0208 1.0342 0.0493 2.3247 20 0.0173 0.0530 0.0226 1.0122 0.0088 -0.0193 -0.0199 1.0602 0.0480 2.1096 25 0.0125 0.0550 0.0242 1.0342 0.0090 -0.0215 -0.0218 1.0865 0.0523 2.2140 PanelC:PQS
1 -0.0008 0.0037 0.0011 1.0147 0.0001 -0.0089 -0.0042 1.0279 0.0132 4.0203 5 0.0072 0.0055 0.0014 0.9891 0.0001 -0.0085 -0.0062 1.0040 0.0149 2.9830 10 0.0108 0.0069 0.0017 0.9846 0.0001 -0.0089 -0.0078 1.0014 0.0168 2.4900 15 0.0124 0.0078 0.0020 1.0351 0.0002 -0.0093 -0.0096 1.0541 0.0190 2.2808 20 0.0128 0.0092 0.0025 1.0126 0.0002 -0.0087 -0.0113 1.0328 0.0202 2.0982 25 0.0043 0.0143 0.0049 0.8331 0.0002 -0.0078 -0.0135 0.8546 0.0215 3.2387
5 RESULTS
This section provides the empirical tests results corresponding to the Section 3 methodology part. In this thesis, the author would like to present the results in this order: innovations in illiquidity, estimation of betas, and Fama-MacBeth regressions.
5.1 Innovations in Illiquidity
As we discussed in Section 3.3 before, illiquidity innovations are estimated on a basis of portfolio. Since we use AR (2) model, the final dataset is reduced by two month at the beginning of the sample period. The illiquidity innovations for market portfolio are estimated with the 𝑅2of 69.41% for PQS, 17.58% for Amihud and 78.68% for HLS. It is worth noting that Amihud measure not only has a small autocorrelation of portfolios but also has lower 𝑅2 for illiquidity innovations of portfolios. Perhaps this is one of the weaknesses of Amihud which doesn’t bother the other two new measures. Figure 1 documents the change of these market illiquidity innovations.
-. 0 0 2 0 .0 0 2 .0 0 4 C h a n g e i n I lli q u id it y In n o va ti o n s 2007 m1 2008 m1 2009 m1 2010 m1 2011 m1 2012 m1 2013 m1 2014 m1 2015 m1 2016 m1 month
PQS
Figure 1. Dynamics of Market Illiquidity Innovations, 2007-2016
The illiquidity innovations for market portfolio are estimated as the residuals using autoregressive model with 2 lags from January 2007 to December 2016, namely AR(2)
model: -. 0 5 0 .0 5 .1 .1 5 C h a n g e i n I lli q u id it y In n o va ti o n s 2007 m1 2008 m1 2009 m1 2010 m1 2011 m1 2012 m1 2013 m1 2014 m1 2015 m1 2016 m1 month
Amihud
-. 0 4 -. 0 2 0 .0 2 .0 4 .0 6 C h a n g e i n I lli q u id it y In n o va ti o n s 2007 m1 2008 m1 2009 m1 2010 m1 2011 m1 2012 m1 2013 m1 2014 m1 2015 m1 2016 m1 monthHLS
We find that the market illiquidity innovations for different measures do not share a similar pattern. With regard to the dynamics for Amihud, there is a huge spike at the beginning of 2008. This huge spike is interpreted as liquidity leakage which corresponds to the far-reaching global financial crisis. Chinese equity market suffers from this crisis badly. Another huge spike which is captured by all three liquidity measures would be around the end of 2015 and the beginning of 2016. This must be associated with the rare and notorious Chinese “Great Equity Disaster” starting from June 2015. Nevertheless, the real reasons behind this disaster which has a more influential impact on the share market than global financial crisis are open to different stories. Since this disaster happens only in China, the conspiracy theory is spread by some analysts but the author is prone to the other revolutionary explanations. For example, some scholars believe this crisis happens due to the threat of internet credit system to the traditional bank credit system. No matter what driving force is behind this frustrating liquidity leakage, there is no doubt that this should be the consequence of imperfect mechanism in Chinese stock market. Furthermore, the trial of Circuit Breaker in January 2016 also triggered the crash of the stock prices in A-share market. However, concerning about the result of HLS, it seems strange to find a relatively small change in illiquidity innovations around 2008. Since the consequence of international financial crisis has a profound impact on every aspect of economy in China and thus liquidity of stocks on Shanghai Exchange can’t get away with it. The change in market illiquidity innovations for PQS shows a relatively more fluctuating trend in the vicinity of year 2008, 2011 and 2016. The corresponding incidents for 2008 and 2016 are mentioned above, the event at the end of 2011 might still refer to another bear market period in Chinese share market and fund market attributed to the fluctuating tightening monetary policy such as lifting the deposit reserve ratio to the extreme and the more serious supervising power signal.
In general, the common conclusion which can be drawn from the figure should be that liquidity leakage coincides with the spikes in market illiquidity innovations. This is consistent with the findings of Acharya and Pedersen (2005) too.
5.2 Estimation of Betas
After obtaining the betas calculated using the equations (21)-(24). it is found that 𝛽1 𝑎𝑛𝑑 𝛽2𝑎𝑟𝑒 𝑝𝑜𝑠𝑡𝑖𝑣𝑒 𝑤ℎ𝑖𝑙𝑒 𝛽3 𝑎𝑛𝑑 𝛽4 have negative values, consistent with the findings of Acharya and Pedersen (2005). Figure 2 visualize the dynamics of betas associated with different illiquidity portfolios. From the Figure 2, we find that it seems that betas of HLS and PQS share a more similar pattern and have closer values, while the betas of Amihud is sort of different. It should be noticed that liquidity betas obtained from PQS and HLS presents a relatively smoother dynamics. On the other hand, betas estimated with Amihud show a larger jump or drop for the last portfolios (portfolios with least liquidity), especially for 𝛽2 𝑎𝑛𝑑 𝛽4.
.6 .7 .8 .9 1 1 .1 Be ta 0 5 10 15 20 25 Portfolio No. PQS Amihud HLS
Beta1
0 .1 .2 .3 .4 Be ta 0 5 10 15 20 25 Portfolio No. PQS Amihud HLS
Beta2
-. 0 8 -. 0 6 -. 0 4 -. 0 2 0 Be ta 0 5 10 15 20 25 Portfolio No. PQS Amihud HLSBeta3
Figure 2. Change of Betas across Portfolios Based on Different Illiquidity Measures
All betas are calculated using equations (21)-(24) on the illiquidity portfolio basis.
Trend of 𝛽1 roughly is upward for PQS and HLS, which matches the findings of Acharya and Pedersen (2005). This positive relationship between illiquidity and 𝛽1 captures the phenomenon that the more liquid the portfolio is, the less its stock return is related to overall market return. The logic behind this may be that: the stocks with higher liquidity level can be liquidated more freely and thus the co-movement between stock return and market return is weaker. However, the change of 𝛽1 for Amihud shows more proof for downward trend which is hard to explain its economic meaning.
As for second beta, in general we can observe an upward trend, which can be found from Table 3. The result is also consistent with both Acharya and Pedersen (2005) and Lee (2011). This implies that the more liquid the portfolio is, the less likely that its illiquidity co-move with market illiquidity. The possible explanation could have the following logic: If market becomes more illiquid, market participants tend to be more likely to get rid of old illiquid stocks and trade for more liquid shares, which makes
-. 5 -. 4 -. 3 -. 2 -. 1 0 Be ta 0 5 10 15 20 25 Portfolio No. PQS Amihud HLS
Beta4
liquid stocks even more liquid.
𝛽3 calculated using Amihud and HLS shows a downward trend while the third beta for PQS is relatively stable among different portfolios. This downward dynamics is also confirmed in the paper of Acharya and Pedersen (2005). Besides, the values for PQS and HLS seem much higher than the values associated with Amihud. Since 𝛽3 represents the phenomena when investors are willing to hold liquid assets with lower return if the market becomes more illiquid, it makes sense if we observe a higher 𝛽3 in the more liquid portfolios.
Finally, the fourth beta is actually decreasing with portfolios for PQS, which can be found more easily in the Table 3. 𝛽4for Amihud also presents a downward trend with a larger range of values especially in the most illiquid portfolios. Such trend also matches what Acharya and Pedersen found (2005). The dynamics of 𝛽4for HLS is relatively not that obvious however. Still values of betas with regard to PQS and HLS are quite close and close to 0. 𝛽4 reflects the willingness of investors to hold liquid stocks with lower return in a downward market. Therefore, it makes sense that the more illiquid the portfolio is, the more sensitive it is to market return movements when market return is decreasing.
Table 4 reports the correlation between different betas for three liquidity proxies. We expect that there may be strong multicollinearity of liquidity risks of different measures. This could raise problems when do regressions of the full version of LCAPM. It is not difficult to find that 𝛽1 shows a high correlation with 𝛽3 across three different panels. Besides, 𝛽2 is highly correlated with 𝛽4 in all three panels as well. Furthermore, it’s also interesting to mention that the positive or negative sign of betas for Amihud and HLS are the same, while the corr (𝛽2, 𝛽3) and corr (𝛽1, 𝛽4) for PQS presents an opposite sign. In summary, multicollinearity should be strong and thus undermine the regression results of equations (24), the full format of LCAPM model. That’s why we don’t attach much importance to the discussion of the result of specification 4 (equation (24)) in this work and concentrate on the model with aggregate liquidity risk as in equation (23).
5.3 Regression Analysis
Table 5 shows the outputs for Fama-MacBeth regressions using three illiquidity measures. In this table, we assume k is a free parameter rather than a constant. The first column corresponds to the four equations (21)-(24) accordingly and the fifth specification in Panel A is added considering k=0 with variable 𝛽1 and 𝛽𝑖𝑙𝑙𝑖𝑞.Each panel represents a different measure. Nevertheless, k should have positive value according to the short-sale constraints forced by LCAPM at the beginning.
Constant E(𝑐𝑡𝑝) 𝛽1,𝑝 𝛽2,𝑝 𝛽3,𝑝 𝛽4,𝑝 𝛽𝑛𝑒𝑡,𝑝 𝛽𝑖𝑙𝑙𝑖𝑞,𝑝 R2 PanelA:PQS 1 -0.0669*** 1.0428 0.067*** 0.319 -(3.6600) (1.2839) (3.7577) 2 -0.0327** 0.0401** 0.0993 -(2.3557) (2.4802) 3 -0.0478*** -0.4591 0.0374** 1.1289** 0.3693 -(2.9477) -(0.6341) (2.2474) (1.9737) 4 -0.0527*** -0.5224 0.0624** 63.9369 1.2581 -0.3331 0.4274 -(2.9606) -(0.6306) (2.3030) (0.8970) (0.5434) -(0.3996) 5 -0.0586*** 0.0504*** 0.8795** 0.3229 -(3.6895) (3.2212) (1.9833) PanelB:Amihud 1 0.0029 0.0278 0.0106* 0.2447 (0.2971) (0.4977) (1.7752) 2 -0.0251 0.0497* 0.2026 -(1.3089) (1.8667) 3 -0.0229 0.1012 0.0432* 0.0033 0.4005 -(1.2502) (1.5120) (1.7539) (0.7541) 4 -0.0233 0.1960*** 0.0404* 0.0228*** -0.0354 0.0258** 0.4680
-(1.2491) (2.6974) (1.7804) (2.6243) -(0.2171) (2.1131) PanelC:HLS 1 0.0385*** 1.2612*** -0.0828*** 0.2841 (2.6577) (7.2583) -(5.1800) 2 0.0275* -0.0129 0.1984 (1.6714) -(0.6527) 3 0.0379*** 1.2657*** -0.0805*** -0.1512 0.3160 (2.6887) (6.9984) -(4.8987) -(1.5227) 4 0.0239* 1.2497*** -0.0641*** 0.8999 0.7031** 0.0964 0.3973 (1.6780) (6.9270) -(3.2279) (0.8348) (2.4852) (0.6494)
As for the Panel A, first of all, we can find that all the constants are significant at a confidence level of 95%, which implies that this LCAPM model still is not enough to capture all factors that may affect the pricing of stocks in Chinese A-share market. This is also why the 𝑅2s are not big enough as Acharya and Pedersen (2005) reported for the U.S. market. At the same time, it’s also worth to mention that in specification 2 all the, market betas, 𝛽1 are positively correlated with stock expected returns. This significant coefficient for 𝛽1 means that the covariance of individual stock return and market return is positive and significant, thus if market return risk is higher, the stock price will get higher. Furthermore, 𝛽𝑛𝑒𝑡is statistically significant too with positive coefficient in the first regression. As for aggregate liquidity risk 𝛽𝑖𝑙𝑙𝑖𝑞, it is statistically significant at a confidence level of 95% with the positive coefficient, while liquidity level, E(𝑐𝑡𝑝) seems not important. However, in the third specification, the positive assumption of k is not satisfied, thus the author conduct another
regression 5 with k=0, assuming that the illiquidity level, E(𝑐𝑡𝑝) is not priced significantly. We can still observe a significant signal in the coefficient of 𝛽𝑖𝑙𝑙𝑖𝑞. Finally, in the fourth specification, we find no significant evidence for each liquidity risks separately. However, since the fourth model of LCAPM contains some potential multicollinearity problem, we don’t discuss its result strictly in this study. All in all, we can draw a conclusion from Panel A that aggregate liquidity risk affects share returns in Chinese A-share market. However, it seems that illiquidity level doesn’t significantly affect stock returns under this measure.
Associated with Panel B: Amihud, from the second column it can be seen that the constant is not significant. However the 𝑅2 is still quite low which indicates that the model actually is not quite suitable for pricing the Chinese share market and some other risks are needed to explain the pricing of stock returns. In this panel, note that the illiquidity level, E(𝑐𝑡𝑝), across different specifications are positive which is in line with the assumption. Besides, all the coefficients of market beta, 𝛽1 are also
significant statistically with the positive estimates. This fact is consistent with the results from Panel A, suggesting that market beta indeed affects the stock returns. Furthermore 𝛽𝑛𝑒𝑡 is significant from the second regression, whereas, the aggregate
