Cross Country Liquidity in Stock Markets:Case of Indian and US Stock Markets

Term Paper: Financial Econometrics EC 794

Apoorva Javadekar, Boston University, Departmentof Economic

1 Introduction

The fact that developed world (especially USA) is investing increasingly inrisky asset markets of developing world implies that we will observe higherco movement between asset markets in developed and developing markets.Even more tight will be the link between liquidity in stock markets acrossthe countries. When macro conditions in developed country implies lowerliquidity in asset markets, it would imply lower liquidity in developing mar-kets too. Liquidity in asset markets refers to an ease with which a relativelylarge transaction can take place without impacting price of that asset bymuch because of that trade. Hence drop in liquidity can occur in a situationwhere there is aggregate buying or selling pressure.

The main objective of this term paper is to identify if the liquidity in In-dian equity markets and US equity markets is linked to each other. Themain methodology used is VAR (vector Auto regression). The motivationfor suspecting such a link is two fold

� Indian companies are increasingly becoming global in their operationsand which imply that global conditions will affect Indian stock marketsmore and more.

� US investors (mutual funds and otherwise) are increasingly investing inIndian markets. Nice documentation of this fact is found in Mendoza,Quadrini and Rios-Rull (2010)

I describe the data and the liquidity measure I used In the next section andthen present some simple statistical properties of the data and then in thelast section report the results of Bivariate VAR.

2 Data

I use the equity markets data from India and USA. In particular, I use S&P500 Index to proxy US stock market and BSE 30 Index to proxy Indianstock market. The data period is 2003-2010. I work with daily equity datagiven the fact that I want to compute liquidity measure on daily basis. The

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data period was motivated by the fact that the Indian stock markets startedattracting capital inflows after 2003. The choice of the indices is motivatedby the fact that globalisation is likely to reflect in the equity properties oflarge corporations. Also large indices capture aggregate macro conditionsin the country. I collected the data from Yahoo finance website. The datacontained opening, closing value of indices and the volume in the market ondaily basis.

3 Liquidity Measure

Liquidity captures the depth of the market. If a small order induces a largechange in the price, then we suspect that market liquidity is low. Amihud(2002) introduced a measure of illiquidity in the market.

Ai,t =

Nt∑j=1

|ri,j |(Vi,j × Pi,j)

(1)

where t is the time period in question, Nt are number of trading days duringtime period t, ri,j is the return on asset i on jth day and Vi,j and Pi,j denotethe volume and price of asset i on jth day, where j indexes the days in thethe time period t. This is the Amihud’s measure of illiquidity. Higherthe absolute value of return for a given dollar volume in the market, higherthe illiquidity in the market. I consider t to be a month and hence monthlyilliquidity measure is average of daily illiquidity measure over the month.Note that this is the measure of illiquidity.

The main advantage of this liquidity measure is that it can be convenientlyused on daily data and averaged out over a longer period. The monthlyliquidity is really an average liquidity over a period of month. This assumesthat monthly liquidity is a function of mean of daily liquidity but not thevariance of series of daily liquidity. Note that second moment of liquiditymeasure refers to liquidity risk. But we are concerned with level of liquidity.Hence such linear averaging is tenable.

4 Preliminary Analysis of Illiquidity

� Indian markets are less liquid than US markets. But liquidity is in-creasing in Indian markets relatively more than US markets. (Figure1)

� Higher illiquidity in USA is accompanied by Higher illiquidity in Indiaand vice versa. (Figure 2)

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� The time series for monthly Illiquidity is non-stationary in both themarkets. This is tested by using Augmented D-F test statistic. Hence,I filtered out the time series using HP filter. The filtered time seriesis stationary according to D-F test statistic.

� There is strong common cyclicality in the illiquidity in both these mar-kets. After filtering out the trend (HP filter as we want to concentrateon high frequency cycle), the time series for illiquidity shows extremelyhigh correlation (around 0.99). (Figure 3)

� Even before filtering the correlation is around 0.70, which is consider-ably high.

� Both the markets show strong persistence properties in illiquidity atmonthly frequency. The correlograms dies out after 12 or 13 periodsfor both the markets. This persistence is observed with and withoutfiltering the data. Hence persistence is not a result of trend in thedata. (Figure 4 and 5). The 95% Confidence region for persistenceimplies that 3 lags are significant for both the time series. Hence thecurrent liquidity conditions persist for 3 months, which is significant.

5 VAR Analysis

After analyzing that liquidity in each market has strong persistence proper-ties, we turn to the VAR analysis with 1 lag. Precisely, I estimate followingmodel [

ILust

ILint

]=

[α1

α2

]+

[ρ11 ρ12ρ21 ρ22

]×[ILus

t−1

ILit−1n

]+

[ε1tε2t

](2)

where ILust and ILin

t refers to illiquidity in USA and India respectively forperiod t. This is a typical Bivariate VAR system. It detects if there is anycross border impact of liquidity with some lag. As the time frame under theconsideration is one month, we are asking if liquidity pressure this monthaffects the liquidity situation in the home and the foreign capital marketsnext month. Why we expect the the liquidity situation in USA to affect theliquidity situation in Indian markets with a lag? One institutional explana-tion could be that portfolio rebalancing decisions would be taken with somelag in practice. Some explanation is needed to justify why the liquidity inIndian markets should affect the bigger market which is USA. The reason istwo fold; As I mentioned above, the increasing global nature of Indian firmsmakes the liquidity situation Co move. But equally important is the factthat there are significant number of funds in developed markets focusing onemerging economies. They invest not only in Indian markets but also in

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Figure 1: Positively Correlated Illiquidity

0

20

40

60

80

100

120

140

Aug-

03

Dec

-03

Apr-

04

Aug-

04

Dec

-04

Apr-

05

Aug-

05

Dec

-05

Apr-

06

Aug-

06

Dec

-06

Apr-

07

Aug-

07

Dec

-07

Apr-

08

Aug-

08

Dec

-08

Apr-

09

Axi

s Ti

tle

Illiquidity India & USA, 2003-2009

Monthly_illiqudity_usa

Monthly_illiqudity_india

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Figure 2: Positively Correlated Illiquidity

020

4060

80M

onth

ly_l

iqud

ity_u

sa

0 50 100 150Monthly_liqudity_india

Market Illiqudity S&P 500 VS BSE India

®

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Figure 3: Scatter of Filtered Illiquidity India Vs USA

1020

3040

5060

usa_

illiq

udity

_hp

20 40 60 80india_illiqudity_hp

HP filtered Illiqudity BSE 30 VS S&P 500 (2003−2010)

®

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Figure 4: Persistence of Illiquidity in Indian Stock Market

−0.

500.

000.

501.

00A

utoc

orre

latio

ns o

f ind

ia_i

lliqu

dity

_hp

0 5 10 15Lag

Bartlett’s formula for MA(q) 95% confidence bands

AR illiqudity India (HP filtered)

®

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Figure 5: Persistence of Illiquidity in USA Stock Market

−0.

500.

000.

501.

00A

utoc

orre

latio

ns o

f usa

_illi

qudi

ty_h

p

0 5 10 15Lag

Bartlett’s formula for MA(q) 95% confidence bands

Auto−Correlations illiqudity USA (HP Filtered)

®

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other Asian and developing countries. The equity markets of these develop-ing countries will show a high co movement with each other. This in turnimplies that though one market is relatively small, all these markets takentogether would imply large portfolio rebalancing undertaken by US fundsfocusing on emerging markets. This could be one explanation of Indian liq-uidity situation affecting the liquidity situation in US equity markets. Butof course, the channel is not expected to be as strong as the converse.

I estimate this equation using data of 70 months with STATA on HP filtereddata. The results are reported in following matrix[

ρ11 ρ12ρ21 ρ22

]=

[1.07 −0.0790.148 0.84

](3)

All the coefficients are statistically significant at more than 99% confidencelevel. The standard errors and other major test statitsics are reported inthe table at the end of the paper.From these, we can conclude following

� There are cross border transmission of stock market liquidity betweenIndia and USA

� Liquidity situation in the US stock market affect the liquidity in Indianstock markets positively

� Higher liquidity in Indian stock markets predict lower liquidity in USAstock markets next month.

� Indian markets are affected more by lagged liquidity measure in USmarkets than lagged liquidity measure in Indian markets

I also ran the VAR with two lags and the second lags turns out to beinsignificant while first lag remains significant. This implies the robustnessof significance of first lag.

6 Conclusion

I used the Amihud’s measure of illiquidity to compute the illiquidity in In-dian and US stock markets. The liquidity is trending upwards over the timeperiod 2003 to 2010. Liquidity in Indian and US markets has strong com-monality in cyclical component which is apparent from the highly correlatedfiltered time series. VAR suggests that lagged liquidity in either market af-fects the liquidity in other market. Liquidity in Indian markets is moreaffected by US liquidity than the other way round. This empirical analysispoints towards the impact of portfolio rebalancing strategy the institutionsin US market conduct. It would be interesting to study if cross border liq-uidity is priced in the equity returns. For this Macbeth type regression can

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be employed, where for each stock liquidity beta would be computed usingtime series regressions and then the relation between returns and liquiditybeta would be studied on cross section.

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7 References

� Amihud, Yakov, 2002. ”Illiquidity and stock returns: cross-sectionand time-series effects,” Journal of Financial Markets, Elsevier, vol.5(1), pages 31-56, January.

� Mendoza, Enrique G., Jose-Victor Rios-Rull and Vincenzo Quadrini.”Financial Integration, Financial Deepness and Global Imbalances.”Journal of Political Economy 117, 3 (2009): 371-410

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8 Appendix

8.1 Test Statistic on Stationarity

Table 1: Dickey-Fuller Test for Stationarity on Non-Filtered Data

Statistic Illiquidity (USA) Illiquidity (India)

Z(t) -1.623 -1.523Significance low low

Table 2: Dickey-Fuller Test for Stationarity on HP-Filtered Data

Statistic Illiquidity (USA) Illiquidity (India)

Z(t) -32.32 -14.29Significance *** ***

where *** implies significance at at least 99% confidence interval.

8.2 VAR Results

Table 3: VAR ResultsVariable Illiquidity (USA) Illiquidity (India)

Constant 0.77 1.93Own Lag coefficient 1.071 0.148

Std Errors (Own lag) 0.004 0.004Cross Lag coefficient -0.079 0.848std Errors (Cross lag) 0.09 0.008significance own Lag *** ***Significance cross lag *** ***

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