Liquidity correlation between the bond and stock market

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Master of International Finance

Master Thesis

Liquidity Correlation Between the Bond and Stock Market

Student:

Dan Zhao

Student ID:

10839461

Supervisor:

P.F.A. Tuijp MPhil

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1. Introduction

In the last financial crisis, liquidity and its related issues have attracted a substantial amount of attention. It has become one of the hot topics in the financial industry and its consequences have offered many corporations and institutions a hard lesson particularly on risk management (Cornett, McNutt, Strahan, and Tehranian, 2011). A number of funds and companies suffered severely from the losses. Many banks received aid from the local governments in order to survive (Brunnermeier, 2008). However, from a research point of view, a crisis is a good opportunity for studying the financial market. This paper utilizes this opportunity and examines the correlation between the bond and stock market in the periods before, during and after the 2008 financial crisis. It aims to improve our understanding of the liquidity interaction between different markets and it is relevant to investors given the well-documented phenomenon of flight to quality and flight to liquidity (Beber, Brandt, and Kavajecz, 2009; Vayanos, 2004).

Liquidity played a crucial role in the 2008 financial crisis. The crisis started in the summer of 2007 when the credit quality of subprime residential mortgages and other types of securitized products started to deteriorate (Brunnermeier, 2009). Due to the large involvement of the housing market it raised concerns about the solvency and liquidity of financial institutions. Banks became unwilling to lend to both corporations and their peers. The main reasons were that they were not certain about their counterparties’ risk and they wanted to protect themselves against any potential unanticipated liquidity needs (Ivashina and Scharfstein, 2010). The lack of short-term liquidity put many corporations and financials into deep difficulties. Investors lost confidence in the market and rushed to safer assets like Treasury bonds (Krishnamurthy, 2010). The crisis diminished gradually after a series of governmental and central bank interventions, help to promote the liquidity and solvency (Ivashina and Scharfstein, 2010).

To many economists, the 2008 financial crisis is the worst crisis since the great depression of the 1930s (Cornett et al., 2011). The stock market was severely shocked by the crisis. In 2008 alone, the US stock market dropped nearly 37%. Trillions of dollars were wiped out shortly. At the same time, the yield of the Treasury bond dropped dramatically due to the strong demand from the investors that seek for security and the

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policy of quantitative easing where the central bank increases its holding of government bonds (Krishnamurthy, 2010). The yield of corporate bonds especially with lower rating was the other way around. The onset of the crisis caused the corporate bond spread widened dramatically. This is largely caused by a decrease of liquidity which in turn lead to an additional premium (Dick-Nielsen, Feldhütter, and Lando, 2012).

There is a substantial amount of literature studying the liquidity of the stock and bond market during the financial crisis. Frank et al. (2008) studied how the liquidity shock was transmitted across US financial markets and found that the interaction between markets increased sharply during the crisis. Rösch and Kaserer (2014) studied the liquidity commonality and flight to quality based on the stock data from the crisis period. They showed that the liquidity commonality varies over time and particularly increases during market downturns. Dick-Nielsen et al. (2012) compared the bond market liquidity before and after the onset of the crisis. They found that the corporate bond liquidity dropped dramatically with the onset of the crisis. The drop was slow and persistent for investment grade bonds while for speculative grade bonds it was stronger and more short-lived.

Chordia, Sarkar and Subrahmanyam (2005) compared between the bond and stock markets by using 10-year treasury notes and NYSE stocks from 1991 to 1998. They did not find a causal relationship between the stock and bond spreads. In other words, liquidity changes in one market do not lead to changes in the other market. Bond and stock market liquidity movements are subject to common influences. However, utilizing data with longer time span (from 1962 to 2003), Goyenko and Ukhov (2009) found a strong bidirectional Granger causality between the liquidity of the two markets. They argued that the discrepancy between the two findings is due to the long horizon of the data selected.

This paper aims to contribute to the above findings and studies the liquidity dynamics of the stock and bond market based on the financial crisis background. We focus on the corporate bond market utilizing US data recorded in Trace (Trade Reporting and Compliance Engine) database from year 2003 to 2014. The relation between the two markets was analyzed in three periods, namely before, during and after the financial crisis to compare the possible changes in their integration. We employed the Amihud (2002)

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ILLIQ measure, which takes the monthly average of the illiquidity level and the daily measure which is also known as the Amivest ratio (Amihud, 2002). We tested the Vector Error Correction (VEC) model and Granger causality based on both measures. The results indicate that before the crisis, the market is led by bonds, where liquidity changes of the stock market follows the bond market in the negative direction, meaning an increase in the bond liquidity decreases the stock liquidity in the following days. However, during the crisis time, the market is changed to be led by stocks. The liquidity movement of the bond market follows the path of the stock market. The liquidity contagion seems to be notable. After the crisis, the correlation altered back to negative. The corporate bond market appears to behave differently under different economic backgrounds. It is a safer investment in normal times concerning the level of liquidity while behaves similarly to stocks in times of the crisis. Dick-Nielsen et al., (2012) also found a widened spread of the corporate bonds with the onset of the crisis. Therefore, flight to quality appears to occur only to Treasury bonds and a few highly rated corporate bonds.

2. Literature review

2.1 Liquidity

Liquidity is defined as how easy an asset can be converted into cash without sacrificing its price. By definition, cash is the most liquid asset. Treasury bills are considered to be very liquid, nearly cash equivalent. Corporate bonds are in general more liquid than listed stocks. A minority stake in a private company is considered to be less liquid (Damodaran, 2005). Based on the CAPM model established by Sharpe (1964) and Lintner (1965), Acharya and Pedersen (2005) presented a liquidity-adjusted capital asset pricing model (LCAPM) by incorporating the liquidity risk into the model. After analyzing US stocks from 1962 to 1999, they concluded that their LCAPM explains the data better than the standard CAPM. Liquidity is priced in the market and it accounts for about 1.1% of the cross-sectional returns. It is shown that investors require a premium based on the level and the risk of the asset liquidity.

Liquidity can be generally classified into market liquidity and funding liquidity. Market liquidity is defined as how easy an asset can be traded at the prevailing market

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without sacrificing its price. Funding liquidity is defined as the ease with which traders or investors can raise capitals in short notice (Sarr and Lybek, 2002). Brunnermeier and Pedersen (2009) modeled the relation between the two types of liquidity. Traders require capital for executing transactions. Typically, they use securities as collateral and borrow against it. The difference between the amount they borrow (collateral value) and the security value is the margin which has to be financed with the trader’s own capital. Short selling works in a similar way. A shortage in funding liquidity tightens traders’ capital and in consequence makes them reluctant to take on positions. This in turn lowers the trading activity and reduces market liquidity.

2.2 Market Liquidity

Market liquidity can be gauged in three aspects, namely tightness, depth and resiliency (Kyle, 1985). Tightness represents the transaction cost. More specifically, the bid-ask spread, which is the difference between the buy and sell price. A larger spread delivers a higher volatility and lowers the liquidity. Depth refers to the existence of abundant orders. It measures the magnitude of price changes given a large transaction. The higher the amount of abundant orders the less impact is resulted to the asset price therefore, leading to a higher liquidity (Kyle, 1985). Resiliency measures the speed with which pricing errors caused by uninformative order flow shocks are corrected in the market (Dong, Kempf, and Yadav, 2007). Among the three aspects, tightness and depth are the most often used indicators in identifying market price of liquidity risk.

2.3 Liquidity Commonality

The term liquidity commonality was introduced by Chordia et al. (2000). By using US stock data listed on NYSE in year 1992, they found that after controlling for individual liquidity determinants, common influences are present affecting securities. The individual quoted spreads, quoted depth and effective spreads co-move with the aggregate market and industry level measures. This existence of a significant common liquidity factor that influences firm-level liquidity is called liquidity commonality (Tarun Chordia et al., 2000).

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Brockman, Chung, and Pérignon (2009) later established the findings of Chordia et al. (2000) from a global prospective. Using 3,838,241 observations from 47 stock exchanges over year 2000 to 2004, they compared the intraday spread and depth and found that the firm-level liquidity changes are significantly affected by the exchange-level changes across most of the world’s stock markets. Stock exchanges from emerging Asian countries showed particularly strong commonality. The sources of the firm’s liquidity commonality are roughly 39% from the local level and 19% from the global level (Brockman et al., 2009).

2.4 Contagion in Financial Markets

Throughout the history of major financial events, it is not unusual that shocks in one market spill over into other markets across asset classes and geographical locations. In 1997, the Asian crisis spread to the other parts of the world and persistent in the following years. The 1998 Russian default resulted in the collapse of Long Term Capital Management, which subsequently hit Brazil and spread to other emerging markets in Latin America (Rösch and Kaserer, 2014). The most recent subprime crisis of 2007, which occurred majorly in the US housing market, evolved into a worldwide financial crisis eventually. This significant increase in cross market linkages particularly after a shock is called contagion (Rösch and Kaserer, 2014). With the increasing speed of globalization, a small shock which initially affect a few institutions or a particular region may spread easily by contagion and affect the larger economy (Allen and Gale, 2000).

Literature identified three possible mechanisms that may cause this cross market contagion (Longstaff, 2010). The first one is based on information transmission. One market receives a negative shock due to adverse economic news decreases its collateral values or cash flows associated with securities from other markets. The second mechanism is based on liquidity. A shock to one financial market decreased the overall liquidity of all financial markets since investors lose on one market experience impaired ability to obtain funding (Longstaff, 2010). The third mechanism is based on the risk premium. A number of studies reported that a severe negative shock in one market may lead to an increase in the risk premium in other markets (Acharya and Pedersen, 2005; Longstaff and Rajan, 2008; Vayanos, 2004). Longstaff (2010) studied the three

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mechanisms using data from the subprime index and concluded that financial contagion was transmitted primarily through liquidity and risk premium channels.

2.5 Flight to Quality and Flight to Liquidity

With the movements of the economic environment, investors need to rebalance their portfolios to maximize their utility. When the uncertainty increases in the financial market, we often observe phenomenon called flight to quality and flight to liquidity. A capital movement towards less risky or high quality assets is called flight to quality; a capital movement towards more liquid assets is called flight to liquidity (Rösch and Kaserer, 2014). By analyzing 2003-2004 euro-area government bond market, Beber, Brandt and Kavajecz (2009) concluded that although credit quality matters for bond valuation, in times of market stress, investors in fact opt for liquidity. However, these two phenomena are inter-related as risky assets also tend to be less liquid.

2.6 Correlation Between the Bond and Stock Market

Using 10-year US treasury notes and stocks listed on NYSE, Chordia, Sarkar and Subrahmanyam (2005) compared the quoted bid-ask spread between the bond and stock markets. They found that the liquidity of the two markets are significantly correlated with each other but no causal relation was present. The liquidity levels of the two markets are driven by common factors. However, Goyenko and Ukhov (2009) argued that they found a strong bidirectional Granger causality between the two markets by using Amihud's (2002) ILLIQ measure for the bond market and quoted spread measure for the bond market. Their results indicate that a negative shock to the stock liquidity increases bond liquidity level and a negative shock to bond liquidity decreases stock liquidity level, which is consistent with flight to quality and flight to liquidity. Goyenko and Ukhov (2009) believed that the discrepancy between the two findings is due to their data selection. Chordia, Sarkar and Subrahmanyam (2005) used data from 1991 to 1998 whereas Goyenko and Ukhov (2009) used data from 1962 to 2003. A long time span of data is needed in order to capture several monetary shocks and to detect the interaction across markets.

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Dick-Nielsen et al. (2012) studied the corporate bond market under the background of financial crisis, utilizing TRACE data ranged from 2005 to 2009. By studying the bond spread, they found that the corporate bond liquidity decreases in times of crisis. For investment grade bond, the decrease was slow and persistent, and for speculative grades, it was stronger and short-lived. They concluded that the flight to quality is only confined to AAA-rated bonds.

3. Data

3.1 Data Selection

TRACE is a trade reporting and compliance engine which records FINRA’s over the counter US corporate bond market data starting from mid-2002. This study utilized the price and trading quantity data available on TRACE to compute the bond market illiquidity level. The daily stock return and trading volume from companies listed on NYSE and AMEX were obtained from CRSP. To capture a better representation of the stock market, we followed De Jong and Driessen's (2006) approach, computed the stock illiquidity level based on the companies included in the S&P 500, S&P Midcap 400 and S&P Smallcap 600 indices.

Data ranging from early 2003 to end 2014 were selected and classified evenly into 3 periods. The crisis period (2007-2010) includes the market downturn data from beginning 2007 to end 2010. Four years before the crisis (2003-2006) and four years afterwards (2011-2014) were taken into consideration in comparison with the crisis period.

The bond data obtained from TRACE was cleaned according to the paper from Dick-Nielsen (2009). Reporting errors including duplicates, reversals and same-day corrections were eliminated from the data. Any negative price or negative trading volume data were also removed. Price changes exceeding 10% were considered as noises therefore also deleted. Very illiquid bond without trading activities for more than 30 days on average were excluded to improve the comparability of the data. Similar to the bond data, stocks with any missing or negative price or negative trading volume were eliminated from the data. Computation was preceded with stocks traded between $5 and $1000 and with at

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least 15 days of return and volume data in a calendar month (Acharya and Pedersen, 2005).

3.2 Amihud Illiquidity Measure

The illiquidity of both the stock and bond markets were determined using the ILLIQ measure described by Amihud (2002). This method avoids the issue of limited bid-ask spread data particularly from the bond market. By computing the ratio of the absolute price change and the absolute trading volume, it captures the impact of order flows on its asset prices. The ILLIQ measure is given by

𝐼𝐿𝐿𝐼𝑄_𝑖,𝑡 = 1 𝐷_𝑡∑ |𝑅_𝑖,𝑡𝑑_| 𝑉_𝑖,𝑡𝑑 𝐷𝑡 𝑑=1 . (1)

ILLIQ_𝑖,𝑡 measures the illiquidity of the asset 𝑖 in month 𝑡, 𝐷_𝑡 donates the number of trading days in time 𝑡, R_𝑖,𝑡𝑑 _{computes the return of asset 𝑖 in time 𝑡 composed of 𝑑 trading}

days, V_𝑖,𝑡𝑑_{represents the dollar trading volume for asset i in time t as a percentage of the}

market capitalization.

The ILLIQ measure put forward by Amihud (2002) is a monthly based measurement. However, the market liquidity is highly dynamic. It is subject to market environment and varies each trading day. Therefore, this paper utilizes Amihud illiquidity measure on a daily basis, using equally-weighted illiquidity average of different assets traded on the same day to represent the illiquidity level of the asset class.

3.3 Descriptive Statistics

Table 1 presents the mean, standard deviation and illiquidity level from both the bond and stock market. Throughout the three time periods from 2003 to 2014, the bond return was at its lowest level in the before crisis period whereas the stock return was at its highest level. During the financial crisis, the stock market experienced severe shocks and the return went to the bottom whereas the bond return went to its highest level. The lowest return seems to coincide with the highest trading volume like bond market in the

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before crisis period and stock market in the crisis period. Not surprisingly, both markets peaked in its illiquidity level during the crisis period.

Table 1. Summary of descriptive statistics for bond and stock market trading information over the year 2003-2014.

The table displays the daily return, trading volume and illiquidity level of the bond and stock data obtained from TRACE and CRSP. The before crisis period is from 2003 to 2006 and contains data of 21581 bonds and 938 stocks. The crisis period is from 2007 to 2010 and contains data of 28265 bonds and 1000 stocks. The after crisis period is from 2011 to 2014 and contains data of 40114 bonds and 984 stocks. The volume is presented in million dollars which in turn served for the illiquidity level computation.

Return Volume (per mil $) Illiquidity

Mean Stdv Mean Stdv Mean Stdv

Bond Before Crisis -0.011% 0.011 242.898 753.156 0.002 0.027

Crisis 0.016% 0.013 200.080 583.681 0.067 13.727

After Crisis 0.002% 0.008 219.650 620.151 0.039 15.480

Stock Before Crisis 0.087% 0.019 51.429 108.820 0.008 0.138

Crisis 0.051% 0.031 100.212 246.782 0.014 0.318

After Crisis 0.068% 0.020 92.043 187.810 0.006 0.182

As shown in Figure 1b, in 2003, at the time of the dot com bubble, the stock market was at an illiquidity level of around 0.02. It went down in the following years to around 0.01. In late 2007, the stock illiquidity level increased dramatically and reached its peak in early 2009. In late 2011, the illiquidity level peaked again and gradually went back to its original level. The average illiquidity level is close to 1%, which is in line with existing literature (Acharya and Pedersen, 2005; Amihud, 2002). Comparing to the stock market, the bond market displayed a delayed feature (Figure 1a). The illiquidity level of the bond market started to increase from end 2008 and last until 2012. Using the same corporate bond data from TRACE, Dick-Nielsen et al. (2012) calculated the Amihud ILLIQ median of 0.0044 based on the data from 2005 to 2009, which is close to our findings in the before crisis period of 0.002. Both the bond and stock markets are less liquid in the crisis period.

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b.

Figure 1. The illiquidity level of the bond and stock markets over the year 2003-2014.

1a) The bond illiquidity level measured on a daily basis. 1b) The stock illiquidity level measured on a daily basis. The blue bars represent the illiquidity level. The red lines separate the three periods defined. The before crisis period is from year 2003 to 2006. The crisis period is from 2007 to2010. The after crisis period is from 2011 to 2014.

4. Empirical Method

The cointegration of the bond and stock illiquidity was tested using Johansen’s cointegration test. Cointegrated variables were further tested using Vector Error Correlation model (VEC). We used a Granger Causality test to determine whether changes in one variable cause changes in the other variable and not backwards. Impulse

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response function (IRF) was also employed to compute the changes in the dependent variable given an unexpected exogenous shock.

4.1 Johansen’s Cointegration Test

Cointegration means that there is a certain degree of long-run equilibrium relation which ties the individual variables together. Johansen’s test exams the number of independent linear combinations for a time series regression that yields a stationary process. More than one independent variables represents that the data are cointegrated (Johansen, 1991). Non-cointegrated sample will be proceed to Vector Autoregression (VAR) model and cointegrated sample will be proceed to Vector Error Correlation (VEC) model.

4.2 Vector Error Correction Model

Since the data are cointegrated, the correlation of the illiquidity of the stock and bond markets is tested using Vector Error Correction (VEC) Model. The VEC model is able to capture both the short-run and long-run equilibrium relationship between the data. The model specification is the following:

𝛥𝑦_1,𝑡= ₁𝛥𝑦_2,𝑡+₁(𝑦_1,𝑡−1−𝑦_2,𝑡−1−₁) +_1,𝑡， (2a) 𝛥𝑦_2,𝑡 =₂𝛥𝑦_1,𝑡+₂(𝑦_1,𝑡−1−𝑦_2,𝑡−1−₂) +_2,𝑡， (2b)

where 𝑦1,𝑡 represents the illiquidity of the bond market at time t and 𝑦2,𝑡 represents the

illiquidity of the stock market at time t, which were measured using Amihud ILLIQ method as described above. 𝑦1,𝑡−1−𝑦2,𝑡−1−1 and 𝑦1,𝑡−1−𝑦2,𝑡−1−2 are the

deviation from the long-run equilibrium. ₁ and ₂ capture the speed of the adjustment back to the equilibrium therefore should lie between (0,-1).  is the long-run multiplier of the stock illiquidity. ₁₁ and ₂₂ are the constant. _1,𝑡 and _2,𝑡 are the residuals.

4.3 VAR Lag Order Selection

The number of lag is selected based on either Akaike Information Criterion (AIC) or Bayesian information criterion (BIC), which is also called Schwartz Criterion. Since it is possible to rise the likelihood of the model by increasing the number of parameters, both

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AIC and BIC introduce a penalty term for the number of parameters used (Akaike, 1973; Schwarz, 1978). The test output given the minimum value of output is selected.

4.4 Granger Causality

To exam the causal relation of the liquidity of the two markets as proposed, Granger causality test is performed to determine whether the illiquidity of one market can be explained by the illiquidity of the other market in the past period, thereby forming a causal relation (Granger, 1969). With only two variables, the coefficient is tested using t-test.

4.5 Impulse Response Function (IRF)

To have a better understanding about the illiquidity of the two markets and their correlation, we estimated the impulse response function (IRF). A one time input signal is called an impulse. IRF computes the dynamic reaction of the output as a function of time given an unexpected exogenous shock to the system. As showed in the two variable VEC model, a shock to the _1,𝑡 holding all other variables constant result in changes in both 𝛥𝑦1,𝑡 and 𝛥𝑦2,𝑡. IRF presents the behavior of 𝛥𝑦1,𝑡 and 𝛥𝑦2,𝑡 over time in response to

such a shock (Sims, 1980).

5. Empirical Results

As shown in Table 2, we performed Dickey-Fuller test and verified the stationarity of the illiquidity data. The Johanson’s test indicates that the data are cointegrated, meaning that there is a long-run equilibrium relation between the bond and stock illiquidity level. However, the speed of the adjustment to the long-run equilibrium changes over the periods. Before the crisis, the  for the bond illiquidity is -0.037 and the  is 0.753. Based on the VEC model component for the bond market given in (2a),  represents the speed of the adjustment. Therefore, a negative deviation from the equilibrium is corrected positively in the bond market and a position deviation is corrected in the negative direction. For the stock market, the  is -0.728, indicating a faster correction back to the long-run equilibrium than the bond market. During the crisis period, the bond  moves to -0.547 and  increases to 3.657. Deviations from the equilibrium seem to be corrected at

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a much faster speed in the crisis period. However, at the same time, the stock market  changes to -0.007. Even though the  increases to 3.657, it still provides a much slower adjustment speed comparing to its previous period and the bond market. At a 95% confidence level, the after crisis  is not significant different from zero. Therefore, we conclude that in the time of the financial crisis, the adjustment speed back to the long-run equilibrium of the bond and stock illiquidity level increases in the bond market and decreases in the stock market.

Apart from the long-run equilibrium relationship, the short-run is also displayed in the lower part of Table 2. According to the AIC and BIC lag selection criteria, 5 lags were selected for the daily Amihud ILLIQ measure. The coefficients on their own lags are mostly significant up to 4 or 5 lags. Before the crisis, the change in the stock illiquidity have significant negative correlation with the 2nd, 3rd and 4th lag (ΔB_t−2: -0.498, ΔB_t−3: -0.746 and ΔBt−4: 0.518) of the changes in the bond market, meaning an increase in the

bond liquidity change is correlated with a delayed decrease in the stock liquidity change. During the crisis, the bond market is correlated with the 1st, 2nd and 3rd lag (ΔS_t−1: 2.571, ΔS_t−2:1.908 and ΔS_t−3: 1.712) of the stock market. A drop in the stock liquidity decreases the bond liquidity level. In the after crisis period, the change in the bond liquidity is still correlated with the 1st and 2nd (ΔSt−1: -4.310 and ΔSt−2:-4.510) change in

the stock market however, in an opposite direction, meaning an increase in the stock liquidity is correlated with a decrease in the bond liquidity level.

To sum up, before the crisis, the correlation between the bond and stock liquidity is negative. The market liquidity level is led by bonds. When bond liquidity increases, the stock liquidity will decrease in the next 2-4 days, which may imply a certain degree of capital movement between the two markets. Besides, there is bidirectional Granger causality between the illiquidity levels of the two markets. Therefore, to investors who have concerns in the stock liquidity movements, it is possible to obtain early alerts by closely watching the bond market liquidity changes.

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During the crisis period, the correlation between the two markets became positive and the liquidity level is no longer led by bonds but by stocks. A decrease in the stock liquidity level is correlated with a decrease in the bond liquidity in the following 1-3 days.

Table 2. Results of the VEC and Granger causality of the bond and stock illiquidity computed on a daily basis.

Unit root test and Johansen’s cointegration test were performed on all data throughout the three time periods. The VEC model and Granger causality test were performed based on 5 lags. λ and  are from the VEC model: 𝛥𝑦𝑡=0𝛥𝑥𝑡+ 𝑦𝑡−1−𝑥𝑡−1− +𝑡𝑦. Prob. is short for probabilities. Coeff is short for coefficient. B and S represent Bond and Stock, respectively. S_ill is the stock illiquidity level and B_ill is the bond illiquidity level. t statistics are included in parentheses. * indicates significant at 10% level; ** indicates significant at 5% level; *** indicates significant at 1% level.

Test

t-test Prob.

Unit Root Bond -4.911*** 0.000

Stock -5.657*** 0.000

Cointegration At most 1* - 0.000

Trace test indicates 2 cointegrating equations at the 0.05 level

Before Crisis Crisis After Crisis

VEC C -0.009 -0.001 -0.106

Trend 2.83E-6*** 2.24E-4*** 1.60E-4***

(3.386) (-6.541) (4.687)

B Coeff 1.000 1.000 1.000

S Coeff () 0.753*** 3.657** -2.972

(8.95) (2.548) (-1.388)

Bond Stock Bond Stock Bond Stock

 -0.037** -0.728*** -0.547*** -0.007* -0.768*** 0.003 (-2.284) (-8.997) (-9.253) (-1.744) (-11.077) (1.395) 𝜟𝑩𝒕−𝟏 -0.933*** -0.047 -0.281*** 0.006 -0.103 -0.001 (-25.833) (-0.262) (-4.855) (1.506) (-1.600) (-0.302) 𝜟𝑩𝒕−𝟐 -0.837*** -0.498** -0.270*** 0.000 -0.150** -0.000 (-19.308) (-2.319) (-5.040) (0.421) (-2.572) (-0.005) 𝜟𝑩𝒕−𝟑 -0.709*** -0.746*** -0.252*** -8.410 -0.108** -0.001 (-15.629) (-3.321) (-5.253) (-0.028) (-2.100) (-0.615) 𝜟𝑩𝒕−𝟒 -0.511*** -0.518** -0.206*** -0.003 -0.082* 0.000 (-12.044) (-2.464) (-5.028) (-1.162) (-1.936) ( 0.076) 𝜟𝑩𝒕−𝟓 -0.097*** 0.187 -0.042 0.000 -0.074** -0.001 (-2.953) (1.157) (-1.302) (0.178) (-2.319) (-1.241) 𝜟𝑺𝒕−𝟏 0.024* -0.370*** 2.571*** -0.768*** -4.310*** -0.788*** (1.920) (-6.105) (4.824) (-22.742) (-3.672) (-24.704) 𝜟𝑺𝒕−𝟐 0.009 -0.364*** 1.908*** -0.653*** -4.510*** -0.618*** (0.784) (-6.340) (3.034) (-16.379) (-3.134) (-15.798) 𝜟𝑺𝒕−𝟑 0.002 -0.316*** 1.712*** -0.495*** -2.445 -0.485*** (0.200) (-6.173) (2.603) (-11.860) (-1.619) (-11.819) 𝜟𝑺𝒕−𝟒 -0.016* -0.194*** 1.122* -0.341*** -0.412 -0.338*** (-1.838) (-4.512) (1.824) (-8.739) (-0.287) (-8.635) 𝜟𝑺𝒕−𝟓 0.009 0.004 0.816 -0.021 -0.924 -0.099*** (1.340) (0.126) (1.630) (-0.662) (-0.797) (-3.127) 𝐑𝟐 _0.563 _0.532 _0.426 _0.420 _0.449 _0.405 Adj. 𝐑𝟐 0.558 0.527 0.419 0.414 0.443 0.398 Null Hypothesis F-test Prob. F-test Prob. F-test Prob. Granger

Causality

S_ill does not

granger cause B_ill 6.167*** 1E-5 0.676 0.6417 2.274** 0.045 B_ill does not

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After the crisis, the market is still led by stocks yet, the correlation became negative. An increase in stock liquidity is followed by a decrease in the bond liquidity in the next 1-2 days. Although using different time periods, Chordia et al., (2005), Goyenko and Ukhov (2009) all studied the correlation between the stock and the Treasury bond market. Both papers documented a positive correlation ranging from 0.114 to 0.611, which is different than our findings in the corporate bond market. It seems that the corporate bond market and Treasury bond market are differently correlated with the stock market under various economic backgrounds.

Table 3 displays the same test results as Table 2 yet, measured on a monthly basis. In the before crisis period, the bond and stock VEC model showed a similar result with the daily measure. The bond  is -0.350, the stock  is -1.919 and the  is 0.295. The stock market exhibits a faster adjustment speed than the bond market. In the crisis period, the bond  changes to -0.595 and the  increases to 12.461, implying a faster correction than the before crisis period whereas the stock  is not significant different from zero. After the crisis, the bond  is -0.191 and the  is -29.266, indicating that deviations from the equilibrium is not corrected in the bond market and will stay in the next period. The stock

 of 0.014 represents that a negative deviation from the equilibrium is corrected however, a positive deviation will stay. That’s to say, after the crisis, deviation from the long-run bond stock illiquidity equilibrium is not corrected in the bond market and only negative correlation is corrected in the stock market.

In the short-run, 1 lag was computed in the regression. Apart from the bond market in the after crisis period, the other coefficients regressed on their own lags are not significant. The bond illiquidity changes are shown to be correlated with the lags of the stock illiquidity movements in all three periods (ΔSt−1: 0.121, 8.203 and -5.641), which

only occurs to the last two periods in the daily measurement. The correlation increased dramatically in the crisis period than before and becomes negative in the after crisis period. Before the crisis, the stock market is correlated with the lag of the bond market.

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The IRF is employed as an additional check for the interaction between the bond and stock market liquidity level. As shown in Figure 2, the bond and stock market both give strong initial responses to shocks happened to their own market in all three periods and the effect dies out quickly. The linkage between the two markets seems to be limited. Interestingly, in the before crisis period, the daily and monthly measurement provides opposite image of the bond market in response to shocks in the stock market. The initial response is positive in the daily measurement and negative in the monthly measurement. The monthly measure also pictured a delayed positive reaction of the bond market in response to shocks in the stock market.

Table 3. Results of the VEC and Granger causality of the bond and stock illiquidity computed on a monthly basis.

Unit root test and Johansen’s cointegration test were performed on all data throughout the three time periods. The VEC model and Granger causality test were performed based on 5 lags. λ and  are from the VEC model: 𝛥𝑦𝑡=0𝛥𝑥𝑡+ 𝑦𝑡−1−𝑥𝑡−1− +𝑡𝑦. Prob. is short for probabilities. Coeff is short for coefficient. B and S represent Bond and Stock, respectively. S_ill is the stock illiquidity level and B_ill is the bond illiquidity level. t statistics are included in parentheses. * indicates significant at 10% level; ** indicates significant at 5% level; *** indicates significant at 1% level.

Test

t-test Prob.

Unit Root Bond -3.641** 0.030

Stock -3.479** 0.046

Cointegration At most 1 - 0.100

Trace test indicates 1 cointegrating equations at the 0.05 level

Before Crisis Crisis After Crisis

VEC C -0.005 -0.119 0.256

Trend 8.48E-6 7.18E-3*** 3.87E-3**

(0.618) (-3.125) (-2.053)

B Coeff 1.000 1.000 1.000

S Coeff () 0.295*** 12.461** -29.266***

(3.755) (2.479) (-4.919)

Bond Stock Bond Stock Bond Stock

 -0.350** -1.919*** -0.595*** -0.006 -0.191*** 0.014*** (-2.368) (-4.133) (-3.945) (-0.881) (-5.401) (2.628) 𝜟𝑩𝒕−𝟏 -0.130 1.210** -0.138 0.001 -0.324*** -0.004 (-0.829) (2.456) (-0.992) (0.109) (-3.141) (-0.270) 𝜟𝑺𝒕−𝟏 0.121*** -0.105 8.203** -0.197 -5.641*** -0.226 (2.829) (-0.782) (2.367) (-1.245) (-5.670) (-1.485) 𝐑𝟐 _0.292 _0.371 _0.403 _0.083 _0.546 _0.312 Adj. 𝐑𝟐 0.241 0.326 0.360 0.018 0.513 0.262 Null Hypothesis F-test Prob. F-test Prob. F-test Prob. Granger

Causality

S_ill does not

granger cause B_ill 0.109 0.7433 0.943 0.337 0.643 0.427 B_ill does not

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Figure 2. Impulse response function (IRF) based on the daily and monthly Amihud ILLIQ measure. The left column is based on the daily measurement. The right column is based on the

monthly measurement. As indicated, panel A displays the IRF before the crisis (2003-2006), panel B displays the IRF during the crisis (2007-2010) and panel C displays the IRF after the crisis (2011-2014). B_ill is abbreviated for bond illiquidity level and S_ill is abbreviated for stock illiquidity level.

6. Conclusions and Discussion

In this paper, we analyzed the interaction between the liquidity level of the corporate bond and stock market. The liquidity level was determined using Amihud (2002) ILLIQ measure on both a monthly and a daily basis. Since the two variables are cointegrated, we applied the VEC model to detect the long-run and short-run dynamics. In the long-run,

.000 .004 .008 .012

1 2 3 4 5 6 7 8 9 10 Response of S_ill to S_ill

.000 .004 .008 .012

1 2 3 4 5 6 7 8 9 10 Response of S_ill to B_ill

-.05 .00 .05 .10 .15 .20 1 2 3 4 5 6 7 8 9 10 Response of B_ill to S_ill

-.05 .00 .05 .10 .15 .20 1 2 3 4 5 6 7 8 9 10 Response of B_ill to B_ill

-.04 .00 .04 .08 .12 1 2 3 4 5 6 7 8 9 10 Response of B_ill to B_ill

-.04 .00 .04 .08 .12 1 2 3 4 5 6 7 8 9 10 Response of B_ill to S_ill

.000 .001 .002 .003 .004 .005 .006 .007 1 2 3 4 5 6 7 8 9 10 Response of S_ill to B_ill

.000 .001 .002 .003 .004 .005 .006 .007 1 2 3 4 5 6 7 8 9 10 Response of S_ill to S_ill

Daily Monthly A Before Cri s is B Cris is C Af ter Cris is -.0002 .0000 .0002 .0004 .0006 .0008 .0010 1 2 3 4 5 6 7 8 9 10

Response of B_ill to B_ill

-.0002 .0000 .0002 .0004 .0006 .0008 .0010 1 2 3 4 5 6 7 8 9 10

Response of B_ill to S_ill

-.001 .000 .001 .002 .003 .004 .005 1 2 3 4 5 6 7 8 9 10

Response of S_ill to B_ill

-.001 .000 .001 .002 .003 .004 .005 1 2 3 4 5 6 7 8 9 10

Response of S_ill to S_ill

-.0004 -.0002 .0000 .0002 .0004 .0006 .0008 1 2 3 4 5 6 7 8 9 10 Response of B_ill to B_ill

-.0004 -.0002 .0000 .0002 .0004 .0006 .0008 1 2 3 4 5 6 7 8 9 10 Response of B_ill to S_ill

-.001 .000 .001 .002

1 2 3 4 5 6 7 8 9 10 Response of S_ill to B_ill

-.001 .000 .001 .002

1 2 3 4 5 6 7 8 9 10 Response of S_ill to S_ill

-.05 .00 .05 .10 .15 .20 .25 1 2 3 4 5 6 7 8 9 10 Response of B_ill to B_ill

-.05 .00 .05 .10 .15 .20 .25 1 2 3 4 5 6 7 8 9 10 Response of B_ill to S_ill

-.002 .000 .002 .004 .006 .008 1 2 3 4 5 6 7 8 9 10 Response of S_ill to B_ill

-.002 .000 .002 .004 .006 .008 1 2 3 4 5 6 7 8 9 10 Response of S_ill to S_ill

-.002 -.001 .000 .001 .002 .003 .004 1 2 3 4 5 6 7 8 9 10 Response of S_ill to S_ill

-.002 -.001 .000 .001 .002 .003 .004 1 2 3 4 5 6 7 8 9 10 Response of S_ill to B_ill

-.01 .00 .01 .02 .03 .04 1 2 3 4 5 6 7 8 9 10 Response of B_ill to S_ill

-.01 .00 .01 .02 .03 .04 1 2 3 4 5 6 7 8 9 10 Response of B_ill to B_ill

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both the daily and monthly measure suggest that before the financial crisis, the stock market provides a faster adjustment speed back to the equilibrium than the bond market. During the crisis, the bond correction speed increases and stock correction speed decreases. The market changed from bond leading to stock leading. After the crisis, the monthly measurement suggests that deviations from the long-run equilibrium are not corrected apart from increases in the stock liquidity level.

In the short-run, both two measurements suggest that during the crisis, changes in the stock liquidity play the leading role. Bond liquidity follows the changes in the stock market and in the same direction. Before the crisis, daily measurement suggested that the correlation between the bond and stock liquidity is negative. The market liquidity level is led by bonds. When bond liquidity increases, the stock liquidity will decrease in the next 2-4 days. After the crisis, the correlation between the two markets became negative again. It seems that the corporate bond market behaves differently in times of the crisis. It has negative correlation with the stock liquidity during normal times and positive correlation during crisis times. It looks more like a safer investment when the economy is doing well and behaves similar to the stock market in terms of liquidity changes as shocks hit. A liquidity contagion from the stock market to the bond market seems to exist during the market down turn. Therefore, holding corporate bonds when the economy is stable can be seen as a good diversification in terms of liquidity concern while not in the crisis time. This is similar to what Dick-Nielsen et al., (2012) found in their paper. They studied the corporate bond data from TRACE and suggested that flight to quality occurs only to AAA-rated corporate bonds. To further investigate the similarities, we would need to include the bond ratings data. This falls outside the scope of the thesis, but would be interesting for further studies.

The results also presented the differences between the daily and monthly Amihud ILLIQ measure, both in the long-run and short-run relation. We thought of two possible reasons which may lead to this discrepancy. One is that the equally weighted average may not be representative for the monthly illiquidity level computation. Trading information particularly trading volumes may vary largely over the days which are not considered into the model. Second is the distribution of the daily illiquidity level. The

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skewed distribution (three period skewness: 10.71) may also influence the measure. Besides, the liquidity of a market is highly dynamic. A daily measure is able to capture the correlation and causal relation better than a monthly measure and possess larger explanation power as indicated by the coefficients of determination (the adjusted R2). In nearly all equations (5 out of 6), the coefficients of determination are higher in the daily measurement than the monthly measurement.

A major limitation of this study is that errors in the TRACE database cannot be fully eliminated as documented by Dick-Nielsen (2009). Certain reporting errors are difficult to identify, which may influence the outcome. Besides, the Johanson’s cointegration test was performed based on data throughout the three periods instead of individually. The cointegration relation may change overtime thereby influencing the following tests.

To conclude, by using the data from 2003 to 2014, we analyzed the interaction between the bond and stock liquidity level based on the Amihud ILLIQ measure. There presents both a long-run and a short-run equilibrium relation between the two markets. During the financial crisis, the stock market plays a leading role and is positively correlated the bond market, which is different than the other time periods. The corporate bond market liquidity behavior changed dramatically with the onset of the financial crisis, from a conservative investment asset which is negative correlated with the stock market to a more stock-like investment, following the movement of the stock market. In other words, the liquidity of the corporate bond market is not promising when the stock market experiences difficulties. On the other hand, when the economy is doing well, capital movements tend to favor either the stock market or the bond market, suggesting a capital flow between the two markets. Further efforts are required from researchers who could include the Treasury bond market the grading scheme of the corporate bond market under various economic conditions to improve and establish the findings.

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Liquidity correlation between the bond and stock market

Master of International Finance

Master Thesis