Liquidity Has So Many Facets Finance Essay

CERTIFICATE

This is to certify that the project titled "Illiquidity and Stock Return: Evidence from Indian Stock Market" submitted in partial fulfillment of the requirements for the Degree of Master of Business Administration is a record of original research work carried out by myself. Any material borrowed or referred to is duly acknowledged.

Chandan Kumar Mandal

Roll No. F-093

MBA FT 2011-13

This is to certify that the above mentioned project titled "Illiquidity and Stock Return: Evidence from Indian Stock Market", submitted by Chandan Kumar Mandal, MBA (FT) Batch of 2013, Roll No F-093 has been carried out under my supervision.

Dr. Pankaj Sinha

Project Guide

Faculty of Management Studies

University of Delhi

Table of Content

Figures and Tables

Executive Summary

Using a new illiquidity measure proposed by Amihud (2002), I have tried to first find out the new measure of the stocks of Nifty-50 stocks. I have also tried to relate the Amihud ratio with the existing measures of liquidity. Results show that there is a negative relation between the traditional measures and Amihud ratio.

I have tried to do a comprehensive study on the relationship between illiquidity, illiquidity risk and stock returns among stocks listed on the Nifty-50 of NSE India. I have looked at the time series relationship between illiquidity and stock returns. Again, the results are not totally consistent with those found by Amihud. While unexpected illiquidity does have a negative impact on contemporaneous stock returns, the expected illiquidity does not have any impact on expected stock returns.

I have also examined the cross-sectional relationship between illiquidity and stock returns and find that illiquidity has a positive impact on stock returns in India in general. Five stocks out of 50 have been selected and regression has been run to find the relation among the variables. Even after using a control to account for up and down markets, we still fail to find a significant relationship between illiquidity and stock returns. Therefore, the results are not totally consistent with those of Amihud (2002).

Keywords: Illiquidity, Amihud Ratio, Stock Return

Section-1: Introduction

"Unfortunately the word ‘liquidity’ has so many facets that is often counter-productive to use it without further and closer definition" - Charles Good hart (Banque de France, 2008)

Liquidity is an evasive concept and cannot be understood easily. Liquidity or illiquidity is of concern because it has important practical as well as academic implications. As far as Indian security market is concern there are only a few research papers available which deals with the liquidity of financial market. This project uses the new illiquidity measure proposed by Amihud (2002) to examine the illiquidity of Indian stock market and the relationship between illiquidity and stock returns. This project also tries to price the same liquidity risk.

The financial crisis of 2008 originated in the relatively small subprime lending market of the US, but lately affected the world financial markets quickly and had devastating effect on the global economy. One of the important characteristics of this crisis was the existence of "Simultaneous liquidity problems" across financial institutions and financial markets spread across many countries. The financial crisis has had a severe and prolonged impact on equity markets and economies around the world. It first started hitting the equity markets in July 2007 after investment banks and commercial banks reported substantial write-downs related to mortgage-backed securities caused by the US subprime crisis. Initially, the market participants and governments around the world played down the severity of the crisis until the US government refused to rescue Lehman Brothers, which was forced to file for bankruptcy protection, creating the domino effect of the global liquidity crisis. The shocks of market liquidity wiped out Lehman Brothers, and also resulted in Washington Mutual, Merrill Lynch, and Wachovia being taken over by their competitors. Finally government has to intervene which resulted in Troubled Asset Relief Program funds and bail out of many institutions. The shortage of market liquidity quickly spread all over the world and interbank lending rates surged across the globe. In Europe also governments had to bail out big lenders such as HBOS, Hypo Real Estate, and B&B. The credit crunch enlarged the impact of market liquidity risk on asset values and led to investors’ fears of severe global economic recessions.

Most of the researchers who work on liquidity primarily focus on the United States, arguably the most liquid market in the world. In contrast, this research focuses on markets where liquidity effects may be particularly strong, namely Indian, an emerging market. In a survey by Chuhan (1992), poor liquidity was mentioned as one of the main reasons that prevented foreign institutional investors from investing in emerging markets. If the liquidity premium is an important feature of these data, the focus on emerging markets like India should yield particularly powerful tests and useful independent evidence.

Liberalizations of 190’s gave foreign investors the opportunity to invest in domestic equity securities and domestic investors the right to transact in foreign equity securities. This provides an additional verification of the importance of liquidity for expected returns, since, all else equal (including the price of liquidity risk), the importance of liquidity for expected returns should decline post liberalization.

The U.S. market is vast in the number of traded securities and it has a much diversified ownership structure, combining long-horizon investors (less subject to liquidity risk) with short-term investors. Hence, we may observe clientele effects in portfolio choice that mitigate the pricing of liquidity. Such diversity in securities and ownership is lacking in India market, potentially strengthening liquidity effects. Moreover, as an important side benefit, we can test whether improved liquidity contributes to the decline in the cost of capital post liberalization that is documented by various authors.

The rest of the paper is organized as follows. The next section constructs literature review of the existing literature available on the topics including on the emerging markets and provides us the motivation of this particular research in the given field of Indian market. Section-3 lists the theoretical measures of liquidity and liquidity risk premium relates it to some other traditional ones. Section-4 gives the data source and analysis of data which includes Amihud ratio and cross-sectional relationship between the Amihud ratio and stock returns. This section also looks at the time series effect of illiquidity on stock returns. Section-5 provides concluding remarks and limitation of the study.

Section-2: Literature Review

Although there is no perfect measure of liquidity, a simple and intuitive measure aiming to balance the limits of data availability and accuracy has been developed in the recent work of Amihud (2002). This measure only requires the input of daily data to construct and is applicable to all securities and time periods.

The measure proposed by Amihud (2002) is the daily ratio of absolute stock return to its dollar trading volume averaged over a given period (Amihud ratio hereafter). Intuitively, this can be interpreted as the daily stock price response associated with one dollar of trading volume.

This is consistent with Kyle’s (1985) concept of illiquidity, i.e. the response of price to order flow, and Silber’s (1975) thinness measure, i.e. the ratio of absolute price change to absolute excess demand for trading. After comparing a few alternative liquidity measures, Hasbrouck (2002) concludes that the Amihud ratio appears the best.

With this new measure, Amihud (2002) examines the relationship between illiquidity and stock returns and finds that illiquidity not only affects stock returns cross-sectionally but also over time. Many studies have documented that illiquidity can explain differences in the expected returns across stocks,for example, Amihud and Mendelson (1986), Pastor and Stambaugh (2003), among others. Using mainly market microstructure data from the US and various estimation techniques, these authors report a positive relationship between illiquidity and stock returns across companies.

It is generally acknowledged that liquidity is important for asset pricing. Illiquid assets and assets with high transaction costs trade at low prices relative to their expected cash flows, that is, average liquidity is priced [e.g., Amihud and Mendelson (1986); Brennan and Subrahmanyam (1996); Datar et al. (1998); Chordia et al. (2001b)]. Liquidity also predicts future returns and liquidity shocks are positively correlated with return shocks. Furthermore, if liquidity varies systematically securities with returns positively correlated with market liquidity should have high expected returns (Pastor and Stambaugh (2003); Goyenko (2005); Martinez et al. (2005); Sadka (2006) for recent empirical work). Acharya and Pedersen (2005) develop a model that leads to three different risk premia associated with changes in liquidity and find these risk premia to be highly significant in U.S. data.

According to Amihud and Mendelson (1980) and Amihud (2002), illiquidity reflects the impact of order flow on price. Since illiquidity is not observed directly but rather has a number of aspects that cannot be captured in a single measure, various proxies for illiquidity have been used in previous studies. Some easily obtained proxies are turnover, trading volume or value, firm size, etc; however, as pointed out by Lesmond (2002), these proxies may capture the effect of variables not related to liquidity. On the other hand, some finer and more accurate measures based on market microstructure data, such as bid-ask spread, amortized effective bid-ask spread, price response to signed order flow and probability of information-based trading (PIN), are not generally available, especially over a long period of time.

Recently, a number of studies have examined the presence of commonality in individual stocks liquidity measures. Hasbrouck and Seppi (1999) look at the 30 constituent stocks from the Dow Jones Industrial Index and conclude, on the basis of principal component and canonical correlation analyses, that the source of commonality in intra-daily liquidity measures for these stocks is rather small. Chordia et al. (2000) reach a distinct conclusion however after examining the sources of commonality in the changes of several daily liquidity measures for 1169 US stocks during the year 1992. Using a market model for liquidity, they find that common market and industry influences on individual stocks liquidity measures such as their quoted spreads or depth are significant and material. In particular, they find that a stock bid and ask spread is negatively related to the aggregate level of market trading. They interpret this result as being consistent with a diminution in inventory risk resulting from greater market trading. Their findings are however less supportive of common factors driving asymmetric information based stock trading. Thus, their results can explain common liquidity factors influence on stocks_ expected returns through increased average trading costs. Huberman and Halka (1999) also explore the commonality in liquidity, using the depth as well as the bid–ask spread as proxies for the liquidity of 240 US traded stocks. Their findings are similar to the results of Chordia et al. (2000), and they attribute commonality in stocks_ liquidity to the presence of noise traders. These studies have left open the question as to whether illiquidity is a systematic risk factor, in which case stocks that are more sensitive to unexpected market illiquidity shocks, should offer higher expected returns. An exception is to be found in Pastor and Stambaugh (2001) who introduce a market-wide liquidity measure and show that cross-sectional expected stock returns are related to fluctuations in aggregate liquidity. Along the same lines, the recent study by Amihud (2002) introduces a new measure of illiquidity defined as the ratio of a stock absolute daily return over its daily trading volume (in dollars) and applies it to NYSE stocks traded during the period 1964–1997. He tests whether expected market liquidity has a positive effect on ex ante stock excess returns and whether unexpected market illiquidity has a negative effect on contemporaneous stock returns. The empirical results support the conjectured hypotheses.

By examining whether aggregate market liquidity risk is priced in a time-series framework, we intend to complement the latter stream of recent literature on commonality in stocks liquidity risk measures. For that purpose, we examine the significance and magnitude of systematic liquidity risk pricing for an actively traded well-diversified US stock portfolio, which is the S&P 500 stock market index.

Two important difficulties are related with the concept of aggregate market liquidity risk. First, one needs to define a proxy for the state variable describing aggregate market liquidity and second to specify a joint stochastic process for the latter and the excess returns of the market portfolio. While several candidate variables have emerged in the market microstructure literature to measure liquidity (for instance, Kyle_s lambda (1985), the bid–ask spread, the effective spread or the market depth), they are essentially intended as proxies of the liquidity of individual stocks. Furthermore, these measures are primarily suited to study the cross-sectional and time-series determinants of liquidity over short-term horizons.

Very few studies are available on the liquidity risk measuring the Indian stock market. Some studies like Geert Bekaert, Campbell R. Harvey, Christian Lundblad(2007) find that zero daily firm return significantly predicts future returns, whereas alternative measures such as turnover do not. Consistent with liquidity being a priced factor, unexpected liquidity shocks are positively correlated with contemporaneous return shocks and negatively correlated with shocks to the dividend yield.

Samuel Xin Liang , John K.C. Wei(2011), in there paper find that local liquidity risk, in addition to the local market, value and size factors, demands a systematic premium across stocks in 11 developed markets. This local pricing premium is smaller in countries where the country-level corporate boards are more effective and where there are less insider trading activities. They also discover that global liquidity risk is a significant pricing factor across all developed country market portfolios after controlling for global market, value, and size factors. The contribution of this risk to the return on a country market portfolio is economically and statistically significant within and across regions.

The literature review proves us the motive to investigate the liquidity risk of Indian stock market using Amihud ratio also find time series and correlation of this illiquidity measure with other liquidity variables.

Section-3: Theoretical Framework

3.1 Amihud Ratio

Easley et al. (1999) introduced a new measure of microstructure risk, the probability of information-based trading, that reflects the adverse selection cost resulting from asymmetric information between traders, as well as the risk that the stock price can deviate from its full information value. This measure is estimated from intra-daily transaction data.

They found that across stocks, the probability of information-based trading has a large positive and significant effect on stock returns. These fine measures of illiquidity require for their calculation microstructure data on transactions and quotes that are unavailable in most markets around the world for long time periods of time. In contrast, the illiquidity measure used in this study is calculated from daily data on returns and volume that are readily available over long periods of time for most markets. Therefore, while it is coarser and less accurate, it is readily available for the study of the time series effects of liquidity.

Amihud gave a very handy tool to calculate illiquidity of stock. Stock illiquidity is defined as the average ratio of the daily absolute return to the (INR) trading volume on that day. This ratio gives the absolute price change per INR of daily trading volume, or the daily price impact of the order flow. This follows Kyle’s concept of illiquidity -the response of price to order flow Fand Silber’s (1975) measure of thinness, defined as the ratio of absolute price change to absolute excess demand for trading.

The daily stock illiquidity ILLid (the Amihud ratio based on Amihud (2002)) is computed as the ratio of absolute daily return to daily trading value.

------------equation (1)

Where,

|Rid| is the absolute return for stock i on day d.

VALid is the trading value for stock i on day d in millions of INR, and

ILLid represents the absolute percentage price change per million INR of trading value.

Monthly and yearly Illiquidity are calculated as average of the daily illiquidity.

------------equation (2)

------------equation (3)

Where,

Dim and Diy is the number of trading days in month ‘m’ and year ‘y’ respectively.

3.2 Time Series Effect of Illiquidity

A very important argument given by Amihud (2002) that stock is not only riskier but also less liquid than short-term treasury securities. Hence, stock return in excess of the T-bill rate (risk premium) includes a premium for illiquidity. It follows that if investors anticipate higher market illiquidity, they will expect higher returns. More specifically, expected stock returns should be positively related to expected illiquidity while unexpected illiquidity should be negatively related to contemporaneous unexpected stock return.

Following Amihud (2002), the market illiquidity used in the time-series test is the logarithmic form of the average illiquidity across stocks. Since the yearly time series is short, with only 10 data points from 2003-2012, I will focus on the monthly data (120 observations). The expected and unexpected market illiquidity are estimated through the Auto Regressive AR(1) model

------------equation (4)

Where,

is the monthly market illiquidity as defined in previous section and

ʋm is the residual representing the unexpected market illiquidity in .

Investors determine the expected illiquidity at the beginning of a month based on information from the previous month,

------------equation (5)

The market price is then set at the beginning of the month through the following model to generate the expected return,

------------equation (6)

In this equation, and

is the return of market portfolio M (all stocks in my sample) in month m and

is the risk free rate for month m.

can be decomposed into the unexpected illiquidity ln ILLUmM and an error term wm.

The final time-series regression of the excess market return on the market illiquidity is as follows

------------equation (7)

The two testable hypotheses are:

H1: expected market illiquidity is positively related to expected market excess return (g1>0).

H2: unexpected market illiquidity is negatively related to contemporaneous market excess return (g2<0).

Amihud (2002) further puts forward and tests the "flight to liquidity" hypothesis. Amihud, Mendelson and Wood (1990) point out that there are two effects on expected stock returns when expected market illiquidity rises.

On the one hand, the stock price declines and expected returns rise for all stocks, while on the other, capital flies from less liquid to more liquid stocks.

These two effects reinforce each other for illiquid stocks but offset each other for liquid ones. Increasing market illiquidity not only negatively affects prices for illiquid stocks but also induces investors to switch to more liquid stocks, which further depresses the price for illiquid stocks. However, increasing market illiquidity leads to an increase in demand for liquid stocks, which mitigates their price decline. Therefore, the illiquidity effect should be stronger for small stocks and weaker for large stocks because firm size is negatively correlated with illiquidity.

3.3 Cross-Sectional Relationship between Illiquidity and Stock Returns

For comparison purposes, I first follow Amihud (2002) to estimate the following Fama- MacBeth type cross-sectional regression model for each month during my sample period, where monthly stock return, is a function of illiquidity and a set of control variables, Xij,m-1

------------equation (8)

Equation is the general equation of the relation between stock return and various variables.

Other stock characteristics or control variables included in the regression are for ith stock:

Firm size, lnSIZEi,m-1 , which is the logarithm market capitalization at the end of month m-1;

Beta, βi,m-1, which is the beta in month m-1;

Total risk, STDi,m-1 , which is the standard deviation of the daily return on stock i in month m-1 (multiplied by 102);

Dividend yield, DYi,m-1 , which is the dividend yield in month m-1;

Past stock returns, Ri,m-1.

------------equation (9)

Equation (9) considers only beta and past month return for regression other that illiquidity.

----------equation (10)

Equation (10) is very broad and considers all listed independent variables for regression.

3.4 The sign of the systematic liquidity risk premium

This section introduces a ‘‘heuristic’’ framework in which the sign of the systematic liquidity risk premium is discussed. Unfortunately, although the relationship between a stock’s expected return and its liquidity measures is well documented in the market microstructure literature for developed markets, there is no theoretical model that is directly applicable to study the effect of aggregate market liquidity risk on expected stock returns. In the spirit of Chen et al. (1986), I have assumed that a pre-specified two-factor model is driving securities returns in a continuous-time economy. This research assumes that these two factors in the economy are the market factor and the systematic liquidity factor. In that context, I have interested in testing whether the following equation characterizing stock market expected excess returns is satisfied:

----------equation (11)

Where,

denotes the stock market excess return,

variance of stock market excess return,

is the instantaneous covariance between the excess market return and the liquidity of the market.

is the unitary price of market risk,

is the unitary price of liquidity risk.

Assuming that is positive (which will be discussed in the empirical section), we thus conjecture that the sign of the systematic liquidity risk premium should be negative.

Section-4: Data Source and Analysis

All data for this project has been taken form data stream of PROWESS and NSE website. The sample period of this project extends from 2002 to 2012. S&P Nifty-50 has been used for this study. In the Nifty fifty only those stocks are selected whose data are available for all 10 years.

Since most of the Indian firms use March as their fiscal year-end and financial reports may not be available until June, I have used daily stock returns and trading values from July 1 in the current year till June 30 in the following year to compute the annual illiquidity. For example, the annual stock illiquidity in 2003 is averaged from July 1, 2002 to June 30, 2003, so on and so forth.

Following Amihud, a stock admitted to my sample must meet the following criteria:

It must have valid observations of daily return and trading value for more than 200 days in year ‘y’ so that the illiquidity estimate is more reliable

The year-end stock price must be greater than INR 1 so that stock returns are not affected too much by the minimum tick size of INR 0.0025.

The stock must be traded for whole period of the years for simplicity of the analysis.

4.1 Amihud Ratio

Table 1: Amihud Ratio of all stocks selected

Company Name

2003

2004

2005

2006

2007

A C C Ltd.

0.00016

0.00003

0.00003

0.00003

0.00002

Ambuja Cements Ltd.

0.00057

0.00010

0.00006

0.00005

0.00003

Asian Paints Ltd.

0.00536

0.00144

0.00175

0.00147

0.00103

Axis Bank Ltd.

0.00536

0.00112

0.00064

0.00025

0.00010

Bank Of Baroda

0.00219

0.00010

0.00014

0.00014

0.00017

Bharat Heavy Electricals Ltd.

0.00016

0.00007

0.00005

0.00005

0.00001

Bharat Petroleum Corpn. Ltd.

0.00006

0.00006

0.00008

0.00019

0.00016

Bharti Airtel Ltd.

0.00284

0.00017

0.00005

0.00005

0.00003

Cipla Ltd.

0.00033

0.00017

0.00009

0.00006

0.00006

Dr. Reddy'S Laboratories Ltd.

0.00011

0.00007

0.00011

0.00009

0.00004

G A I L (India) Ltd.

0.00108

0.00005

0.00005

0.00007

0.00012

Grasim Industries Ltd.

0.00044

0.00008

0.00007

0.00006

0.00004

H C L Technologies Ltd.

0.00011

0.00010

0.00009

0.00009

0.00006

H D F C Bank Ltd.

0.00064

0.00019

0.00011

0.00006

0.00004

Hero Motocorp Ltd.

0.00021

0.00009

0.00008

0.00007

0.00007

Hindalco Industries Ltd.

0.00043

0.00011

0.00008

0.00004

0.00003

Hindustan Unilever Ltd.

0.00007

0.00004

0.00005

0.00003

0.00003

Housing Development Finance Corpn. Ltd.

0.00049

0.00015

0.00007

0.00004

0.00003

I C I C I Bank Ltd.

0.00026

0.00006

0.00007

0.00004

0.00002

I T C Ltd.

0.00007

0.00005

0.00003

0.00002

0.00002

Infosys Ltd.

0.00001

0.00001

0.00001

0.00001

0.00001

Jindal Steel & Power Ltd.

0.00159

0.00112

0.00050

0.00067

0.00046

Kotak Mahindra Bank Ltd.

0.00769

0.00195

0.00179

0.00054

0.00025

Larsen & Toubro Ltd.

0.00010

0.00004

0.00005

0.00004

0.00002

Lupin Ltd.

0.00175

0.00089

0.00093

0.00058

0.00055

Mahindra & Mahindra Ltd.

0.00030

0.00005

0.00004

0.00005

0.00003

Oil & Natural Gas Corpn. Ltd.

0.00026

0.00003

0.00001

0.00001

0.00001

Punjab National Bank

0.00129

0.00006

0.00004

0.00007

0.00007

Ranbaxy Laboratories Ltd.

0.00005

0.00002

0.00003

0.00003

0.00004

Reliance Industries Ltd.

0.00001

0.00001

0.00000

0.00000

0.00000

Reliance Infrastructure Ltd.

0.00156

0.00013

0.00010

0.00006

0.00007

Sesa Goa Ltd.

0.00885

0.00069

0.00006

0.00009

0.00010

Siemens Ltd.

0.00775

0.00164

0.00126

0.00013

0.00003

State Bank Of India

0.00008

0.00001

0.00001

0.00001

0.00001

Sun Pharmaceutical Inds. Ltd.

0.00347

0.00067

0.00031

0.00022

0.00010

Tata Motors Ltd.

0.00006

0.00001

0.00001

0.00002

0.00002

Tata Power Co. Ltd.

0.00047

0.00006

0.00007

0.00010

0.00012

Tata Steel Ltd.

0.00005

0.00001

0.00001

0.00001

0.00001

Wipro Ltd.

0.00003

0.00003

0.00003

0.00004

0.00003

Company Name

2008

2009

2010

2011

2012

A C C Ltd.

0.00004

0.00025

0.00004

0.00004

0.00004

Ambuja Cements Ltd.

0.00009

0.00113

0.00006

0.00008

0.00006

Asian Paints Ltd.

0.00119

0.00634

0.00034

0.00007

0.00007

Axis Bank Ltd.

0.00004

0.00003

0.00001

0.00001

0.00001

Bank Of Baroda

0.00016

0.00017

0.00005

0.00004

0.00005

Bharat Heavy Electricals Ltd.

0.00001

0.00002

0.00001

0.00001

0.00002

Bharat Petroleum Corpn. Ltd.

0.00014

0.00047

0.00005

0.00003

0.00005

Bharti Airtel Ltd.

0.00001

0.00002

0.00001

0.00001

0.00001

Cipla Ltd.

0.00007

0.00016

0.00003

0.00003

0.00004

Dr. Reddy'S Laboratories Ltd.

0.00008

0.00076

0.00004

0.00002

0.00002

G A I L (India) Ltd.

0.00006

0.00016

0.00002

0.00003

0.00004

Grasim Industries Ltd.

0.00007

0.00066

0.00004

0.00008

0.00010

H C L Technologies Ltd.

0.00013

0.00114

0.00006

0.00004

0.00004

H D F C Bank Ltd.

0.00003

0.00005

0.00001

0.00001

0.00001

Hero Motocorp Ltd.

0.00016

0.00024

0.00002

0.00002

0.00002

Hindalco Industries Ltd.

0.00005

0.00019

0.00002

0.00001

0.00002

Hindustan Unilever Ltd.

0.00004

0.00004

0.00002

0.00002

0.00002

Housing Development Finance Corpn. Ltd.

0.00002

0.00004

0.00001

0.00001

0.00001

I C I C I Bank Ltd.

0.00001

0.00003

0.00000

0.00000

0.00001

I T C Ltd.

0.00002

0.00003

0.00001

0.00001

0.00001

Infosys Ltd.

0.00001

0.00002

0.00001

0.00000

0.00000

Jindal Steel & Power Ltd.

0.00008

0.00006

0.00001

0.00002

0.00002

Kotak Mahindra Bank Ltd.

0.00004

0.00026

0.00003

0.00004

0.00005

Larsen & Toubro Ltd.

0.00001

0.00003

0.00001

0.00001

0.00001

Lupin Ltd.

0.00041

0.00473

0.00008

0.00004

0.00005

Mahindra & Mahindra Ltd.

0.00005

0.00038

0.00002

0.00001

0.00001

Oil & Natural Gas Corpn. Ltd.

0.00002

0.00002

0.00001

0.00001

0.00002

Punjab National Bank

0.00007

0.00009

0.00004

0.00004

0.00005

Ranbaxy Laboratories Ltd.

0.00004

0.00026

0.00003

0.00004

0.00005

Reliance Industries Ltd.

0.00000

0.00001

0.00000

0.00000

0.00001

Reliance Infrastructure Ltd.

0.00001

0.00006

0.00001

0.00002

0.00003

Sesa Goa Ltd.

0.00006

0.00020

0.00001

0.00002

0.00004

Siemens Ltd.

0.00007

0.00042

0.00007

0.00004

0.00013

State Bank Of India

0.00001

0.00002

0.00000

0.00000

0.00000

Sun Pharmaceutical Inds. Ltd.

0.00011

0.00016

0.00005

0.00004

0.00003

Tata Motors Ltd.

0.00003

0.00022

0.00001

0.00001

0.00001

Tata Power Co. Ltd.

0.00004

0.00015

0.00003

0.00003

0.00006

Tata Steel Ltd.

0.00002

0.00005

0.00001

0.00000

0.00001

Wipro Ltd.

0.00006

0.00010

0.00002

0.00002

0.00003

I further relate the Amihud ratio to three traditional liquidity proxies via cross-section regressions employed year by year from 2003 to 2012. The three proxies are market capitalization, trading value, and turnover. The results are evident that the annual Amihud ratio is mostly negatively related to all three traditional liquidity measures. This is consistent with common sense: the larger the firm size, the larger the trading value or the higher the trade turnover, and the less illiquid the stock is.

Table 2: Relation between Amihud Ratio and traditional liquidity measure.

Correlation

Market Capitalization

Trading Value

Turnover

Amihud Ratio

-ve

-ve

-ve

Size, or the market value of the stock, is also related to liquidity since a larger stock issue has smaller price impact for a given order flow and a smaller bid–ask spread. Stock expected returns are negatively related to size (Banz, 1981; Reinganum, 1981; Fama and French, 1992), which is consistent with it being a proxy for liquidity (Amihud and Mendelson, 1986). The negative return-size relationship may also result from the size variable being related to a function of the reciprocal of expected return (Berk, 1995).

There are other measures of liquidity that use data on volume. Brennan et al. (1998) found that the stock (dollar) volume has a significant negative effect on the cross-section of stock returns and it subsumes the negative effect of size. Another related measure is turnover, the ratio of trading volume to the number of shares outstanding. By Amihud and Mendelson (1986), turnover is negatively related to illiquidity costs, and Atkins and Dyl (1997) found a strong positive relationship across stocks between the bid–ask spread and the reciprocal of the turnover ratio that measures holding period. A number of studies find that cross-sectionally, stock returns are decreasing in stock turnover, which is consistent with a negative relationship between liquidity and expected return. These measures of liquidity as well as the illiquidity measure presented in this study can be regarded as empirical proxies that measure different aspects of illiquidity. It is doubtful that there is one single measure that captures all its aspects.

4.2 Time series effect of Illiquidity

Table 4: Descriptive Statistics of Excess Return and Illiquidity for market

Variables

Excess Return

Illiquidity

Mean

-0.3452

0.0011

Median

-0.3338

0.0008

Maximum

-0.1272

0.0292

Minimum

-0.6338

0.0004

Skewness

-0.4013

9.8788

Kurtosis

0.3908

98.9712

Standard Deviation

0.0892

0.0028

Above table lists the descriptive statistics for two variable used for analysis, Excess market return and Illiquidity measure.

My estimation of equation (5) provides the following results for the time-series test with monthly illiquidity.

is stationary in the given format.

(p value: 0.1078)

Conclusion: The coefficient c1 is not significant at 5% level of accuracy. This give a very important result that the illiquidity in month ‘m’ is not a function of liquidity in month ‘m-1’. It seems significant at the level of 10%.

Table 3: AR(1) of Illiquidity(ILL)

Dependent Variable: ILL

Method: Least Squares

Date: 03/10/13 Time: 13:37

Sample (adjusted): 2 102

Included observations: 101 after adjustments

Convergence achieved after 2 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

-7.088986

0.059432

-119.2783

0.0000

AR(1)

0.161016

0.099209

1.622997

0.1078

R-squared

0.025918

    Mean dependent var

-7.088787

Adjusted R-squared

0.016078

    S.D. dependent var

0.505192

S.E. of regression

0.501114

    Akaike info criterion

1.475636

Sum squared resid

24.86038

    Schwarz criterion

1.527420

Log likelihood

-72.51961

    Hannan-Quinn criter.

1.496600

F-statistic

2.634118

    Durbin-Watson stat

2.029436

Prob(F-statistic)

0.107770

Inverted AR Roots

      .16

The monthly unexpected illiquidity is calculated as a residual from the above autoregressive model using the adjusted coefficients.

(p value: 0.2053) (p value: 0.1993)

Conclusion:: The coefficient c1 is not significant even at 10% level of significance. This is indeed in line with the earlier result that we cannot relate the return of market with liquidity in Indian market. The coefficients are not different from zero. There is no point of checking the null hypothesis mentioned for equation (7).

Table 4: Regression of Excess market return and AR(1) of ILL and ILLU

Dependent Variable: RP

Method: Least Squares

Date: 03/10/13 Time: 13:56

Sample (adjusted): 1 101

Included observations: 101 after adjustments

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

-0.504754

0.125202

-4.031523

0.0001

ILL

-0.022466

0.017620

-1.274998

0.2053

ILLU

-0.023066

0.017850

-1.292181

0.1993

R-squared

0.032532

    Mean dependent var

-0.345522

Adjusted R-squared

0.012788

    S.D. dependent var

0.089576

S.E. of regression

0.089001

    Akaike info criterion

-1.971076

Sum squared resid

0.776283

    Schwarz criterion

-1.893399

Log likelihood

102.5393

    Hannan-Quinn criter.

-1.939630

F-statistic

1.647676

    Durbin-Watson stat

1.412264

Prob(F-statistic)

0.197784

Figure 1: Liquidity and Excess Return for Nifty 50 Index

The figure indicates for Indian market there is no clear relationship between excess return and market liquidity.

4.3 Cross Sectional relationship between Illiquidity and stock return.

Among wide array of stocks available I have selected five stocks of different sector to check and analyze the cross sectional studies of the illiquidity and stock return. Descriptive statistics of various variables are listed below.

Table 4: Descriptive Statistics of the variables for 5 stocks

Return(Ri)

Variables

Axis Bank Ltd.

BHEL

Hero Moto

Infosys Ltd.

Ranbaxy Lab Ltd.

Mean

0.0272

0.0214

0.0162

0.0151

0.0048

Median

0.0373

0.0299

0.012

0.0251

0.0199

Maximum

0.5007

0.284

0.2039

0.2024

0.5189

Minimum

-0.3713

-0.2981

-0.2026

-0.3746

-0.7417

Skewness

0.131

-0.144

-0.1722

-0.7436

-1.2319

Kurtosis

1.5874

0.4729

-0.4151

1.7287

8.0141

Standard Deviation

0.14

0.1071

0.0895

0.0932

0.1377

Illiquidity(ILL)

Variables

Axis Bank Ltd.

BHEL

Hero Moto

Infosys Ltd.

Ranbaxy Lab Ltd.

Mean

0.0626

0.0044

0.0761

0.0118

0.0202

Median

0.0336

0.0037

0.0400

0.0088

0.0145

Maximum

0.3679

0.0549

3.3391

0.3396

0.5503

Minimum

0.0060

0.0017

0.0152

0.0018

0.0042

Skewness

2.1369

9.2609

10.7693

10.6002

10.6784

Kurtosis

4.8257

95.1763

117.2400

114.7820

115.9082

Standard Deviation

0.0758

0.0049

0.3021

0.0305

0.0492

Beta(β)

Variables

Axis Bank Ltd.

BHEL

Hero Moto

Infosys Ltd.

Ranbaxy Lab Ltd.

Mean

0.9787

0.9834

0.4677

0.8813

0.7322

Median

1.0100

1.0000

0.4400

0.6900

0.7300

Maximum

1.2200

1.0600

0.7300

1.4600

0.8700

Minimum

0.7000

0.9000

0.3100

0.4500

0.6300

Skewness

-0.2618

-0.1086

1.0072

0.2860

0.6400

Kurtosis

-1.3428

-1.2765

0.5532

-1.7491

0.3291

Standard Deviation

0.1858

0.0532

0.1133

0.4102

0.0636

Ln(Market Capitalization,SIZE)

Variables

Axis Bank Ltd.

BHEL

Hero Moto

Infosys Ltd.

Ranbaxy Lab Ltd.

Mean

12.0825

13.2487

12.1669

13.7733

12.0133

Median

12.3004

13.4299

11.9860

13.8302

12.0848

Maximum

13.3507

14.0868

13.0115

14.4969

12.4374

Minimum

10.1267

11.5745

11.3457

12.7041

11.0530

Skewness

-0.4693

-0.9171

0.2153

-0.6047

-1.4503

Kurtosis

-1.0541

-0.4182

-1.3780

-0.4072

2.3940

Standard Deviation

0.9549

0.7262

0.5141

0.4652

0.2823

Volatility (STD)

Variables

Axis Bank Ltd.

BHEL

Hero Moto

Infosys Ltd.

Ranbaxy Lab Ltd.

Mean

0.0326

0.0057

0.2091

0.0238

0.0393

Median

0.0130

0.0028

0.0335

0.0072

0.0125

Maximum

0.4996

0.2293

14.7923

1.4627

2.4014

Minimum

0.0039

0.0014

0.0133

0.0027

0.0027

Skewness

6.0340

9.5771

9.6212

9.6233

9.6269

Kurtosis

45.9604

92.1283

92.7047

92.7330

92.7805

Standard Deviation

0.0581

0.0235

1.5298

0.1509

0.2477

Dividend Yield (DY)

Variables

Axis Bank Ltd.

BHEL

Hero Moto

Infosys Ltd.

Ranbaxy Lab Ltd.

Mean

0.9643

0.9790

3.1929

1.3308

1.3623

Median

0.9700

0.7750

2.5800

1.1750

1.6350

Maximum

1.7300

2.9700

7.5100

3.3400

5.0400

Minimum

0.0000

0.4200

0.0000

0.2600

0.0000

Skewness

-0.0765

1.9513

0.5619

0.8022

0.4793

Kurtosis

0.9202

3.2357

-0.7281

-0.0780

-0.5136

Standard Deviation

0.2965

0.5781

1.8076

0.7264

1.2429

Below the results of the cross sectional relation of the return of stocks with illiquidity measures and other measures of liquidity as mentioned by Amihud(20002).

The final equation after stabilization of the variables comes out as in the given format.

The above equation only considers beta and past month return for regression other that illiquidity.

The comprehensive equation for return in various measure of illiquidity comes out in the given format after the stabilization of the various variables.

Where,

Firm size, LnSIZEi,m-1 , which is the logarithm market capitalization at the end of month m-1;

Beta, βi,m-1, which is the beta in month m-1;

Total risk, STDi,m-1 , which is the standard deviation of the daily return on stock i in month m-1 (multiplied by 102);

Dividend yield, DYi,m-1 , which is the dividend yield in month m-1;

Past stock returns, Ri,m-1

Table 5: Cross sectional relation of Return and Illiquidity and other measures

Constant

Illiquidity

Beta

AR(1)

M-Cap

Volatility

Yield

Adj R2

Axis Bank

Coefficient

0.0203

-0.0955

0.5574

-0.0930

0.1170

p-value

0.0780

0.0000

0.2233

0.3265

Coefficient

0.0113

-0.1073

0.5965

-0.2336

0.2812

-0.2279

0.0569

0.1395

p-value

0.3193

0.0000

0.1821

0.2075

0.0748

0.3039

0.1604

BHEL

Coefficient

0.0213

-0.0232

-0.1320

0.0375

-0.0100

p-value

0.0421

0.2206

0.8327

0.6940

Coefficient

0.0131

-0.0282

0.2450

-0.3545

0.3799

-0.1109

-0.0063

-0.0125

p-value

0.1030

0.1966

0.6842

0.0116

0.0065

0.7854

0.8529

Hero Motor Corp

Coefficient

0.0173

-0.0108

-0.4116

-0.1511

0.0250

p-value

0.0155

0.3694

0.0993

0.1158

Coefficient

0.0251

-0.0160

-0.3966

0.3209

-0.4391

-0.0064

-0.0006

0.0342

p-value

0.0401

0.1495

0.1009

0.0166

0.0008

0.1230

0.9245

Infosys

Coefficient

0.0151

-0.0307

0.0885

-0.0346

0.0073

p-value

0.0719

0.0538

0.6251

0.7127

Coefficient

0.0146

-0.0396

0.0963

-0.0499

0.0326

-0.0639

0.0060

-0.0044

p-value

0.1836

0.0314

0.6007

0.9201

0.9455

0.2614

0.8087

Ranbaxy

Coefficient

0.0045

-0.0080

-0.1634

0.0091

-0.0240

p-value

0.7335

0.6957

0.8038

0.9249

Coefficient

0.0038

-0.0218

-0.1575

-0.0519

0.1019

-0.0829

-0.0016

-0.0218

p-value

0.7643

0.3349

0.8114

0.9122

0.8224

0.0922

0.9621

The result of the cross sectional series is not in line with the developed market. It shows that that is very difficult to relate the illiquidity of the market

Figure 2: Graph of Return vs Illiquidity of Axis Bank

Figure 3: Graph of Return vs Beta of Axis Bank

Figure 4 : Graph of Return vs Market Cap of Axis Bank

Figure 5: Graph of Return vs Volatility of Axis Bank

Figure 6: Graph of Return vs Dividend Yield of Axis Bank

Section-5: Conclusion and Limitations

Using a new illiquidity measure proposed by Amihud (2002), I have conduct a tried to firesr find out the new measure of the stocks of Nifty-50 stocks. I have also tried to relate the Amihud ration with the existin measures of liquidity viz Market Capatilaziation, turnover and stock traded. Resuls show that thera is a negative relation between the traditional measures and Amihud ratio.

I also try to do a comprehensive study on the relationship between illiquidity, illiquidity risk and stock returns among stocks listed on the Nifty-50 of NSE India.

I look at the time series relationship between illiquidity and stock returns. Again, the results are not totally consistent with those found by Amihud. While unexpected illiquidity does have a negative impact on contemporaneous stock returns, the expected illiquidity does not have any impact on expected stock returns. In addition, evidence for the "fly to liquidity" hypothesis associated with expected illiquidity is not supportive. Separating the whole sample into two sub-periods produces similar results.

I have also examined the cross-sectional relationship between illiquidity and stock returns and find that illiquidity has a positive impact on stock returns in India in general. Five stocks out of 50 have been selected and regressin has been run to find the relation among the variables. Even after using a control to account for up and down markets, we still fail to find a significant relationship between illiquidity and stock returns. Therefore, the results are not totally consistent with those of Amihud (2002).

Till now only developed economies which are considered very liquid has been the source of these kind of research. This study tries to reflect the concepts in the Indian context. But the results are not consistent with the results of the liquid markets like America. Even in the markets like Japan which is the second most traded market in the world the same does not hold well.

So that applicability of the measures provided by Amihud is questionable in the emerging economies in general and India in particular.

Limitation of the study: the project tries to explore Amihua ration in Indian context. But the available data stream is limited to only ten years which limits the use of the study. Also data available are not many time correct and been collected in fragmented way.

To evaluate the good impact of the study may be more liquid form of market would be required. May be after one decade these studies can be done in better way because now the data is not available for longer time period. Sensex data can be used but the problem with it is that it does not reflect the true trading volume in India. It now only account for 20% volume traded in India, so it would again be a matter of question if we take BSE-30 as my benchmark index.

Section-6: Bibliography

Samuel Xin Liang, John K.C. Wei(2011), Liquidity risk and stock returns around the world, Journal of Banking & Finance

Amihud, Y. (2002), Illiquidity and Stock Returns: Cross-Section and Time-Series Effects.

Journal of Financial Markets 5, 31-56.

Geert Bekaert, Campbell R. Harvey, Christian Lundblad (2007), Liquidity and Expected Returns: Lessons from Emerging Markets, Advance Access publication

Rajna Gibson, Nicolas Mougeot (2004),The pricing of systematic liquidity risk: Empirical evidence from the US stock market, Journal of Banking & Finance 157–178

Jing Fang, Qian Sun & Changyun Wang (2006), Illiquidity, Illiquidity Risk and Stock Returns: Evidence from Japan, European Financial Management

Pastor, Lubos and with Robert F. Stambaugh, 2003, Liquidity risk and expected stock returns, Journal of Political Economy 111, 642—685

Amihud, Y. & Mendelson, H. (1980). Dealership market: market making with inventory. Journal

of Financial Economics 8, 311–353.

Amihud, Y. & Mendelson, H. (1986). Asset pricing and the bid–ask spread. Journal of Financial

Economics 17, 223–249.

Amihud, Y., Mendelson, H. & Wood, R. (1990). Liquidity and the 1987 stock market crash.

Journal of Portfolio Management 16, 65–69.

Bekaert, G., Harvey, C. & Lundblad, C. (2003). Liquidity and Expected Returns: Lessons from

Emerging Markets. New York: Columbia University.

Acharya, V. & Pederson, L. (2005). Asset Pricing with Liquidity Risk. Journal of Financial

Economics 77, 375-410.

Ahn, J., Cai, J., Hamao, Y. & Ho, R(2002). The components of the bid-ask spread in a limitorder

market: evidence from the Tokyo Stock Exchange. Journal of Empirical Finance 9, 399-

430.

Bekaert, G., Harvey, C. & Lundblad, C. (2003). Liquidity and Expected Returns: Lessons from

Emerging Markets. New York: Columbia University.

Black, F., Jensen, M. & Scholes, M. (1990). The capital asset pricing model: some empirical

tests, in Michael Jensen (ed.), Studies in the Theory of Capital Markets. Praeger, New York.

Bremer, M. & Hiraki, T. (1999). Volume and individual security returns on the Tokyo Stock

Exchange. Pacific-Basin Finance Journal 7, 351–370.

Brennan, M., Chordia, T. & Subrahmanyam, A. (1998). Alternative factor specifications,

security characteristics, and the cross-section of expected stock returns. Journal of Financial

Economics 49, 345–373.

Brennan, M. & Subrahmanyam, A. (1996). Market microstructure and asset pricing: on the

compensation for illiquidity in stock returns. Journal of Financial Economics 41, 441–464.

Chalmers, J. & Kadlec, G. (1998). An empirical examination of the amortized spread. Journal of

Financial Economics 48, 159–188.

Chan, L., Hamao, Y. & Lakonishok, J. (1991). Fundamental and Stock Returns in Japan. Journal

of Finance 46, 1739-1764.

Chan, L. & Lakonishok, J. (1993). Are the Reports of Beta’s Death Premature? Journal of

Portfolio Management 19(4), 51-62.

Section-8: Appendix

Table 6: Number of shares included in study

Year

July 200x-June 200x+1

Trading Day

Initial Stock

Final Stocks

(Trading Day>200 & Stock Price > INR 1)

2003

249

39

39

2004

255

39

39

2005

255

39

39

2006

249

39

39

2007

248

39

39

2008

250

39

39

2009

241

39

39

2010

248

39

39

2011

253

39

39

2012

250

39

39

Table 7: Correlation between Amihud ratio and other liquidity measures

Correlation

Company

Amihud Ratio & MCap

Amihud Ratio & Turnover

Asian Paints Ltd.

0.10726

-0.00683

Axis Bank Ltd.

0.00848

-0.01901

Bank Of Baroda

-0.05891

-0.17105

Bharat Heavy Electricals Ltd.

-0.61712

-0.05008

Bharat Petroleum Corpn. Ltd.

-0.12850

-0.02722

Bharti Airtel Ltd.

0.14017

-0.01537

Cipla Ltd.

0.00367

-0.10278

Dr. Reddy'S Laboratories Ltd.

-0.41807

-0.04394

G A I L (India) Ltd.

-0.09020

-0.01916

Grasim Industries Ltd.

-0.03784

-0.04945

H C L Technologies Ltd.

-0.10606

-0.02122

H D F C Bank Ltd.

0.04934

-0.01570

Hero Motocorp Ltd.

-0.05973

-0.08293

Hindalco Industries Ltd.

-0.35557

-0.02515

Hindustan Unilever Ltd.

0.02510

-0.09110

Housing Development Finance Corpn. Ltd.

-0.42540

-0.03274

I C I C I Bank Ltd.

-0.08314

-0.10061

I T C Ltd.

-0.31023

-0.09942

Infosys Ltd.

-0.40742

-0.04208

Jindal Steel & Power Ltd.

0.10833

-0.00001

Kotak Mahindra Bank Ltd.

0.08009

-0.09095

Larsen & Toubro Ltd.

-0.31918

-0.09362

Lupin Ltd.

-0.29722

#DIV/0!

Mahindra & Mahindra Ltd.

0.05292

-0.02525

Oil & Natural Gas Corpn. Ltd.

-0.02663

-0.01470

Punjab National Bank

-0.00084

-0.13130

Ranbaxy Laboratories Ltd.

-0.37877

-0.03789

Reliance Industries Ltd.

0.14134

-0.02896

Reliance Infrastructure Ltd.

-0.09642

-0.00424

Sesa Goa Ltd.

0.20893

-0.11910

Siemens Ltd.

-0.36778

-0.01526

State Bank Of India

-0.01838

-0.06028

Sun Pharmaceutical Inds. Ltd.

-0.28712

-0.01756

Tata Motors Ltd.

0.02995

-0.08317

Tata Power Co. Ltd.

-0.31587

-0.01144

Tata Steel Ltd.

-0.08978

-0.04015

Wipro Ltd.

0.07472

-0.04678

Table 8: Unit root test for Illiquidity

Null Hypothesis: ILL has a unit root

Exogenous: Constant

Lag Length: 0 (Automatic - based on SIC, maxlag=12)

t-Statistic

  Prob.*

Augmented Dickey-Fuller test statistic

-8.413450

 0.0000

Test critical values:

1% level

-3.497029

5% level

-2.890623

10% level

-2.582353

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(ILL)

Method: Least Squares

Date: 03/13/13 Time: 10:31

Sample (adjusted): 2 101

Included observations: 100 after adjustments

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

ILL(-1)

-0.839443

0.099774

-8.413450

0.0000

C

-5.950172

0.708779

-8.394954

0.0000

R-squared

0.419384

    Mean dependent var

-0.001964

Adjusted R-squared

0.413459

    S.D. dependent var

0.657593

S.E. of regression

0.503624

    Akaike info criterion

1.485823

Sum squared resid

24.85642

    Schwarz criterion

1.537926

Log likelihood

-72.29114

    Hannan-Quinn criter.

1.506910

F-statistic

70.78613

    Durbin-Watson stat

2.027899

Prob(F-statistic)

0.000000

Table 9: Regression Result-1 of Axis Bank

Dependent Variable: AXIS

Method: Least Squares

Date: 03/13/13 Time: 10:49

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 10 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.020250

0.011386

1.778509

0.0780

D(AXIS_ILL)

-0.095467

0.022617

-4.220955

0.0000

D(AXIS_B)

0.557399

0.455186

1.224551

0.2233

AR(1)

-0.093016

0.094388

-0.985464

0.3265

R-squared

0.139658

    Mean dependent var

0.028531

Adjusted R-squared

0.117017

    S.D. dependent var

0.140426

S.E. of regression

0.131955

    Akaike info criterion

-1.179408

Sum squared resid

1.984967

    Schwarz criterion

-1.085487

Log likelihood

73.58510

    Hannan-Quinn criter.

-1.141274

F-statistic

6.168464

    Durbin-Watson stat

2.003346

Prob(F-statistic)

0.000636

Inverted AR Roots

     -.09

Table 10: Regression Result-2 of Axis Bank

Dependent Variable: AXIS

Method: Least Squares

Date: 03/13/13 Time: 10:48

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 150 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.011301

0.011298

1.000336

0.3193

D(AXIS_ILL)

-0.107317

0.023397

-4.586774

0.0000

D(AXIS_B)

0.596539

0.444271

1.342738

0.1821

D(AXIS_M)

0.281193

0.156333

1.798677

0.0748

D(AXIS_STD)

-0.227916

0.220669

-1.032841

0.3039

D(AXIS_Y)

0.056879

0.040253

1.413035

0.1604

AR(1)

-0.233588

0.184243

-1.267825

0.2075

R-squared

0.183601

    Mean dependent var

0.028531

Adjusted R-squared

0.139471

    S.D. dependent var

0.140426

S.E. of regression

0.130266

    Akaike info criterion

-1.180988

Sum squared resid

1.883583

    Schwarz criterion

-1.016625

Log likelihood

76.67827

    Hannan-Quinn criter.

-1.114252

F-statistic

4.160476

    Durbin-Watson stat

2.062380

Prob(F-statistic)

0.000826

Inverted AR Roots

     -.23

Table 11: Regression Result-1 of BHEL

Dependent Variable: BHEL

Method: Least Squares

Date: 03/13/13 Time: 11:09

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 7 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.021343

0.010384

2.055366

0.0421

D(BHEL_ILL)

-0.023241

0.018868

-1.231743

0.2206

D(BHEL_B)

-0.131993

0.623513

-0.211692

0.8327

AR(1)

0.037523

0.095124

0.394467

0.6940

R-squared

0.015925

    Mean dependent var

0.021809

Adjusted R-squared

-0.009971

    S.D. dependent var

0.107938

S.E. of regression

0.108475

    Akaike info criterion

-1.571279

Sum squared resid

1.341424

    Schwarz criterion

-1.477357

Log likelihood

96.70545

    Hannan-Quinn criter.

-1.533144

F-statistic

0.614954

    Durbin-Watson stat

1.994642

Prob(F-statistic)

0.606684

Inverted AR Roots

      .04

Table 12: Regression Result-2 of BHEL

Dependent Variable: BHEL

Method: Least Squares

Date: 03/13/13 Time: 11:09

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 12 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.013133

0.007988

1.644070

0.1030

D(BHEL_ILL)

-0.028194

0.021703

-1.299074

0.1966

D(BHEL_B)

0.244974

0.600668

0.407836

0.6842

D(BHEL_M)

0.379892

0.136952

2.773912

0.0065

D(BHEL_STD)

-0.110867

0.406195

-0.272940

0.7854

D(BHEL_Y)

-0.006270

0.033730

-0.185874

0.8529

AR(1)

-0.354507

0.138162

-2.565889

0.0116

R-squared

0.039425

    Mean dependent var

0.021809

Adjusted R-squared

-0.012498

    S.D. dependent var

0.107938

S.E. of regression

0.108611

    Akaike info criterion

-1.544601

Sum squared resid

1.309392

    Schwarz criterion

-1.380238

Log likelihood

98.13146

    Hannan-Quinn criter.

-1.477865

F-statistic

0.759293

    Durbin-Watson stat

1.975507

Prob(F-statistic)

0.603418

Inverted AR Roots

     -.35

Table 13: Regression Result-1 of Hero Motor Corp

Dependent Variable: HERO

Method: Least Squares

Date: 03/13/13 Time: 11:10

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 6 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.017286

0.007033

2.457729

0.0155

D(HERO_ILL)

-0.010844

0.012033

-0.901218

0.3694

D(HERO_B)

-0.411551

0.247678

-1.661640

0.0993

AR(1)

-0.151100

0.095340

-1.584858

0.1158

R-squared

0.050036

    Mean dependent var

0.017612

Adjusted R-squared

0.025037

    S.D. dependent var

0.088971

S.E. of regression

0.087850

    Akaike info criterion

-1.993067

Sum squared resid

0.879804

    Schwarz criterion

-1.899145

Log likelihood

121.5910

    Hannan-Quinn criter.

-1.954932

F-statistic

2.001512

    Durbin-Watson stat

1.944489

Prob(F-statistic)

0.117740

Inverted AR Roots

     -.15

Table 14: Regression Result-2 of Hero Motor Corp

Dependent Variable: HERO

Method: Least Squares

Date: 03/13/13 Time: 11:10

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 7 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.025070

0.012070

2.077022

0.0401

D(HERO_ILL)

-0.015990

0.011017

-1.451418

0.1495

D(HERO_B)

-0.396597

0.239754

-1.654183

0.1009

D(HERO_M)

-0.439091

0.127509

-3.443617

0.0008

D(HERO_STD)

-0.006359

0.004091

-1.554151

0.1230

D(HERO_Y)

-0.000554

0.005827

-0.095035

0.9245

AR(1)

0.320860

0.131885

2.432884

0.0166

R-squared

0.083735

    Mean dependent var

0.017612

Adjusted R-squared

0.034207

    S.D. dependent var

0.088971

S.E. of regression

0.087436

    Akaike info criterion

-1.978338

Sum squared resid

0.848594

    Schwarz criterion

-1.813975

Log likelihood

123.7219

    Hannan-Quinn criter.

-1.911602

F-statistic

1.690666

    Durbin-Watson stat

1.985729

Prob(F-statistic)

0.129819

Inverted AR Roots

      .32

Table 15: Regression Result-1 of Infosys

Dependent Variable: INFOSYS

Method: Least Squares

Date: 03/13/13 Time: 11:11

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 6 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.015144

0.008337

1.816446

0.0719

D(INFOSYS_ILL)

-0.030724

0.015767

-1.948644

0.0538

D(INFOSYS_B)

0.088452

0.180511

0.490009

0.6251

AR(1)

-0.034586

0.093685

-0.369173

0.7127

R-squared

0.032747

    Mean dependent var

0.014553

Adjusted R-squared

0.007293

    S.D. dependent var

0.092445

S.E. of regression

0.092108

    Akaike info criterion

-1.898409

Sum squared resid

0.967153

    Schwarz criterion

-1.804488

Log likelihood

116.0061

    Hannan-Quinn criter.

-1.860274

F-statistic

1.286529

    Durbin-Watson stat

1.975123

Prob(F-statistic)

0.282467

Inverted AR Roots

     -.03

Table 16: Regression Result-2 of Infosys

Dependent Variable: INFOSYS

Method: Least Squares

Date: 03/13/13 Time: 11:11

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 11 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.014574

0.010891

1.338206

0.1836

D(INFOSYS_ILL)

-0.039646

0.018194

-2.179010

0.0314

D(INFOSYS_B)

0.096341

0.183556

0.524859

0.6007

D(INFOSYS_M)

0.032567

0.475100

0.068547

0.9455

D(INFOSYS_STD)

-0.063936

0.056637

-1.128870

0.2614

D(INFOSYS_Y)

0.006025

0.024822

0.242725

0.8087

AR(1)

-0.049866

0.495913

-0.100555

0.9201

R-squared

0.047082

    Mean dependent var

0.014553

Adjusted R-squared

-0.004428

    S.D. dependent var

0.092445

S.E. of regression

0.092650

    Akaike info criterion

-1.862492

Sum squared resid

0.952821

    Schwarz criterion

-1.698130

Log likelihood

116.8870

    Hannan-Quinn criter.

-1.795756

F-statistic

0.914043

    Durbin-Watson stat

1.976347

Prob(F-statistic)

0.487694

Inverted AR Roots

     -.05

Table 17: Regression Result-1 of Ranbaxy Pharm

Dependent Variable: RANBAXY

Method: Least Squares

Date: 03/13/13 Time: 11:12

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 6 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.004461

0.013072

0.341289

0.7335

D(RANBAXY_ILL)

-0.007984

0.020358

-0.392167

0.6957

D(RANBAXY_B)

-0.163416

0.656116

-0.249066

0.8038

AR(1)

0.009060

0.095935

0.094443

0.9249

R-squared

0.002259

    Mean dependent var

0.004725

Adjusted R-squared

-0.023998

    S.D. dependent var

0.138719

S.E. of regression

0.140374

    Akaike info criterion

-1.055708

Sum squared resid

2.246343

    Schwarz criterion

-0.961786

Log likelihood

66.28675

    Hannan-Quinn criter.

-1.017573

F-statistic

0.086023

    Durbin-Watson stat

1.996940

Prob(F-statistic)

0.967563

Inverted AR Roots

      .01

Table 18: Regression Result-2 of Ranbaxy Pharm

Dependent Variable: RANBAXY

Method: Least Squares

Date: 03/13/13 Time: 11:12

Sample (adjusted): 3 120

Included observations: 118 after adjustments

Convergence achieved after 15 iterations

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

C

0.003774

0.012555

0.300559

0.7643

D(RANBAXY_ILL)

-0.021793

0.022502

-0.968456

0.3349

D(RANBAXY_B)

-0.157453

0.658157

-0.239233

0.8114

D(RANBAXY_M)

0.101949

0.453161

0.224972

0.8224

D(RANBAXY_STD)

-0.082903

0.048804

-1.698701

0.0922

D(RANBAXY_Y)

-0.001616

0.033897

-0.047683

0.9621

AR(1)

-0.051932

0.469859

-0.110528

0.9122

R-squared

0.030645

    Mean dependent var

0.004725

Adjusted R-squared

-0.021752

    S.D. dependent var

0.138719

S.E. of regression

0.140220

    Akaike info criterion

-1.033724

Sum squared resid

2.182432

    Schwarz criterion

-0.869361

Log likelihood

67.98969

    Hannan-Quinn criter.

-0.966987

F-statistic

0.584861

    Durbin-Watson stat

2.016763

Prob(F-statistic)

0.741766

Inverted AR Roots

     -.05

Table-19: Correlation in Independent variables

Axis Bank

Correlation

ILL

Beta

Mcap

Std

Size

ILL

1.0000

-0.7095

-0.7789

0.8628

0.7647

Beta

 

1.0000

0.9353

-0.5640

-0.6195

Std

 

 

1.0000

-0.6665

-0.8123

Dy

 

 

 

1.0000

0.6931

Size

 

 

 

 

1.0000

BHEL

Correlation

ILL

Beta

Mcap

Std

Size

ILL

1.0000

0.0676

0.1476

0.9620

-0.0648

Beta

 

1.0000

0.1201

0.1061

0.2117

Std

 

 

1.0000

0.0758

0.1293

Dy

 

 

 

1.0000

-0.0604

Size

 

 

 

 

1.0000