INTRODUCTION:
Volatility is a measure of variation in the price of an asset and is associated with unpredictability and unawareness about the price. It is frequently used as a substitute of risk. Generally, the volatility factor is linked with risk aspect, it is believed that higher the volatility, high the risk and vice-versa. In other terms, we can also say that volatility leads to improper functioning of markets. Volatility may be defined as the amount of uncertainty involved in a security's value. An increased and rapid movement in the stock prices may throw out risk adverse investors from the market and needs to be taken care of.
The vigorous and changing behaviour of the stock market volatility has been getting huge importance now a days. Many authors have studied and mentioned the dynamic nature of volatiltiy. Pindyck (1984) considers volatility as the biggest reason for the decline in equity prices. Some other studies give blame to the increasing inflation rate as the main cause of the market decline, e.g. Modigliani and Cohn (1979), Fama (1981), Feldstein (1980) and Summers (1981). On the other hand, their argument is in congruity with Black’s (1986) finding that stock returns and changes in volatility are negatively correlated. As we have already said that volatility, to some extent causes inefficiency in market. One of the parameter through which one can understand market anomalies is noise trading. Shiller (1984) stated that there are two type of traders in the financial markets: the first category consists of smart money traders, i.e., they are rational traders and the second category is of the noise traders who primarily depend on rumors and news for taking their investment decisions. Shleifer and Summers (1990) defined the noise traders as those traders who believe that they possess a lot of essential information about market and they can earn very good profits using this information. But, in reality they have a deficit of true information and majority of their decisions are based on their intuitions, feelings and misperceptions. The return volatility in financial markets also depends on the nature, behavior and perceptions of the trader. The behavior of traders in the financial market can also be divided into two parts: short-term traders and long-term traders. So this study aims at analyzing the relationship between volatility and noise trading in specific relation to Indian stock Market.
REVIEW OF LITERATURE:
Koski, et al. (2004) examined the interlinked connection between volatility and noise trading. The study covered the aspect whether the day traders can be considered as noise traders. Stock message board postings have been used for the purpose of the study. The data from Raging Bull and Yahoo have been taken as a proxy for day trading. it has been found that the day trading enhances volatility. Regulators have also agreed that day trading disrupts stock prices. Although we support the argument that day trading causes increase in volatility, has been supported by the study.
Bloomfield, et al. (2007) examined the behavior of noise traders and their impact on the market. It has been studied by authors that, how trader behavior is affected by a transaction tax. The study included three types of traders for the purpose: liquidity traders, informed traders and noise traders. First, the study revealed that noise traders put some positive effects on market liquidity. Secondly noise traders adversely affect the informational efficiency of the market. The studies show that, when the extent of adverse selection is large, a negative relation has been found between noise traders and informational efficiency. It also shows that they do not affect spreads and price impact measures, and a weak effect on the informational efficiency of prices has been detected.
Verma &Verma (2007) also investigated the possibility of asymmetric impact of the individual and institutional investor sentiments on stock market by examining the coefficients αi,j coupled with δj. Significant negative α1,2 and α13 coupled with a significant positive δ2 and δ3 imply that volatility spillover mechanism is asymmetric in both the cases. Specifically, there is greater effect of bullish than bearish investor sentiments on stock market volatility. This finding is inconsistency with the DHS model and other behavioural explanations
DSSW (1990) studied the impact of four types of effects of investor sentiments on stock returns and volatility. The first effect took into consideration the trading done by bullish or bearish investors which pull the price away from the fundamental value of securities. The second effect emphasized on the result of the adjustment in the market risk due to the changes in noise traders’ demand of stocks.
Brown and Cliff (2004) found that both individuals and institutions may have different systematic misevaluation. It has been revealed that although both individuals and institutions exhibit significant sentiments, only institutions have enough capability to affect prices. It has been evaluated that, it is important to jointly model the sentiments of both types of investors to avoid misspecification. Multivariate version of Nelson’s EGARCH extended by Koutmos and Booth (1995) and Koutmos (1998) can be used to interrogate the asymmetric effects of positive and negative sentiments on stock volatilities.
Bollerslev (1986) gave the extended version of ARCH, that is popularly known as GARCH, or the generalized ARCH. GARCH model consists of a very simple structure for studying the various aspects of conditional. Another important supplement of ARCH is the ‘ARCH in mean’ model, which relates the conditional variance with the mean. Engle, Lilien and Robins (1987) used this model and highlighted strong evidence of this link between risk and return in the term structure of interest rates. Bollerslev (1987) found that the conditional standard deviations help to explain variations in the expected return of the S&P500 index. Bollerslev, Engle and Wooldridge (1988) also reported notable time-changing risk premiums in a multivariate GARCH-M model.
Various models of noise trading such as Campbell, DeLong et al. (1990), and Kyle (1993), Grossman, Campbell and Wang (1993), or Llorente et al. (2002) studied that the contribution of noise trading activities to idiosyncratic volatility. It has been shown that, if individual investors act as “noise traders”, retail trading will be related positively to volatility. Evidence also show results in support of this hypothesis. Further, individual investors’ trades consist of a systematic component factor (see, for instance, Kumar and Lee (2006), Dorn, Huberman, and Sengmueller (2008), and Barber, Odean, and Zhu (2009)). Individual investors’ trades can vary stock prices (see, for instance, Titman (2008), Hvidkjaer (2008) Kumar and Lee (2006), Huberman, Dorn, and Sengmueller (2008), Kaniel, Saar.
Kyle (1985) analyzed that liquidity is a multi-faceted concept that encloses a number of transactional properties of markets. Two angles of liquidity: volume and noisiness have been considered.
Admati and Pfleiderer (1988) represented the price discovery process with the help of discretionary traders. The order imbalance (illiquidity) is, positively related to price volatility in the situation when information acquisition is endogenous. An inverse relationship has been found between liquidity trading and volatility in alternative models (with exogenous) such as Glosten and Milgrom (1985). Thus, rational noise traders get losses in trading since informed traders profit from the decisions of noise traders. In rational expectation models of price discovery, although, asset price is accommodated according to full information level as informed trading takes place. In such case, noise traders contributes to liquidity, but does not affect the asset pricing (see Glosten and Milgrom1985; Kyle 1985). Noise trades’ timings, size and style affect the price dynamics. Thus, microstructure theory anticipates an inverse liquidity–price volatility relation.
Along these lines, the relationship between volatility and the bid-ask spread for prices could be used to construct variance estimates for returns [see e.g. Bollerslev and Domowitz (1993). Waldmann (1990) show that if risk averse arbitrageurs know that prices may deviate further away from fundamentals before they join closer, they may take smaller positions. Earlier, previous researches only provide a theoretical model, explaining the relevance of investor sentiments in asset pricing. Before global financial crisis, markets were following the efficiency market theory, which is based on three fundamental conditions: uncorrelated errors, investor’s rationality and, unlimited arbitrage. Although this theory was well accepted and has been applied for a long time. Some of the assumptions of efficient market hypothesis need discussion and investors rationality is one such assumption. There are a number of factors which affects traders decision making such as studying the economic condition, the cycle of the industry, the company’s position, and financial statements. In addition to the above, there are some other factors which affect traders decision making i.e., their past experience, information collected from friends, relatives and co-workers
OBJECTIVE:
The present study is focused to examine the varying volatility of Indian stock market and its relation with noise trading with specifically in banking stocks of Nifty 50.
THE DATA:
The present study has considered Nifty 50 index of National Stock Exchange for analyzing the volatility presence in Indian stock market. Only banking stocks are picked for the purpose of the study. The daily closing prices of seven banking stocks have been considered for the period from January 2007 to December 2017. First, the beta value of each stock is calculated with respect to three indices i.e. Nifty 50, Nifty 100 and Nifty 100 Liquid 15. A total of 2501 daily observations have been taken for the study period. The difference in beta values of the three indices has been considered as a proxy for noise.
Statistical Analysis and Model Identification:
Unit
Root Tests: Augmented Dickey–Fuller (ADF) test is most frequently used test of unit root. It is based on simple logic. In econometrics and statistics, an augmented Dickey–Fuller test (ADF) check the null hypothesis whether
a unit root exists in a time series sample or not. The alternative
hypothesis may be dissimilar depending on
which stage of the test is used, but is generally trend-stationarity
or stationarity. It is an enlarged version of the Dickey–Fuller test
for a big and more difficult set of time series models. Therefore, it behaves like
AR (1) process with
.
Dickey Fuller test is designed to examine if
.
Let;
In
ADF test we test the hypothesis if
. The test procedure is similar to usual t-test but standard
critical values of the t-test are not valid in this case. The modified critical
values tabulated in MacKinnon (1991) are used for ADF test. To get white
noise the lagged terms of 
are also included in the regression. The complete model
will look like this:
Depending on which terms we include in model specification, the following hypotheses are tested:
i. Unit root vs. stationary process with zero mean
ii. Unit root with drift vs. stationary process with constant mean
iii. Unit Root with drift and trend vs. stationary process with trend.
ARCH-LM:
The ARCH effect is concerned with a relationship within the heteroskedasticity, also termed as serial correlation of the heteroskedasticity. It often becomes apparent when there is bunching in the variance or volatility of a particular variable, producing a pattern which is determined by some factor. Given that the volatility of financial assets can be used as a symbol of their risk, it can be argued that the ARCH effect is capable in measuring the risk of an asset. Given the following model:
This suggests the error term is normally distributed with zero mean and conditional variance depending on the squared error term lagged one time period. The conditional variance is the variance given the values of the error term lagged once, twice etc.
GARCH Model:
The most popular among the models of conditional
volatility is the Generalized ARCH or the GARCH (r,m) model proposed by Bollerslev
(1986). Theoretically the GARCH model is considered as equal to ARCH model or it
may also be defined as Generalized ARCH model. In GARCH (r,m ) model the conditional
volatility 
is derived out by using the incidences of
past conditional volatility 
. The past squared innovations in mean equation
are
also considered. The GARCH (1,
1) model is quite useful and predicting the volatility of stock prices. The equation
for the stock returns can be written as follows:
The equation of unconditional (average) variance from this model is as follows :
is taken as an indicator of the persistence of volatility. It is observed
from various studies that the value of generally remains close to one which is a sign of presence of continuous volatility
in assets returns. The effect of any shock, if present, in volatility generally
dies out at a rate of 
. If
it is believed that the
effect of shock will never subside. The presence of volatility will be considered
only if
.Therefore, this assumption is put while estimating
the GARCH model. As it should be remembered that the variance cannot be negative
in value, another parameter restriction which should be there while estimating a
GARCH model is the non-negativity of
, and coefficients.
In the study the difference between the beta as obtained from CAPM and BAPM model is considered as the measure of the noise trading in the stock market for the companies selected in the study. In order to analyze the impact of noise trading on the stock volatility the GARCH (1,1) model with the noise trading as an exogenous variable is used. The GARCH (1,1) model with exogenous variable is used to study the impact of noise trading with the stock on its volatility.
Table 1: The result of ADF unit root test:
|
|
ADF Value |
P |
|
Axis |
-40.485 |
0.000 |
|
HDFC Bank |
-49.532 |
0.000 |
|
ICICI |
-42.053 |
0.000 |
|
Indus bank |
-45.148 |
0.000 |
|
Kotak Mahindra |
-45.402 |
0.000 |
|
SBI |
-40.573 |
0.000 |
|
Yes Bank |
-42.923 |
0.000 |
Stationarity of data is a prerequisite for application of ARCH and GARCH model. Keeping this in view ADF unit root test is applied and the p value <0.05, one can reject the null hypothesis means data is stationary. As a result, Liquid companies are founded stable, the regression model can be established.
Table 2: The result of ARCH effect:
ARCH effect finds out the relationship within the heteroskedasticity also termed as serial correlation of the heteroskedasticity. As literature suggests that volatility of financial assets represents the risk component & this risk is measured through ARCH effect.
|
Stocks |
F |
R square (t *R^2) |
P |
|
|
Axis |
14.527 |
14.436 |
0.000 |
|
|
HDFC Bank |
57.871 |
56.707 |
0.000 |
|
|
ICICI |
18.649 |
18.494 |
0.000 |
|
|
Indus bank |
59.461 |
57.788 |
0.000 |
|
|
Kotak Mahindra |
27.619 |
27.267 |
0.000 |
|
|
SBI |
3.219 |
3.217 |
0.072 |
|
|
Yes Bank |
43.380 |
42.589 |
0.000 |
Due to Heteroscedasticity presence ARCH test can be used. The result of ARCH-LM test is given in the table. It shows that one can reject the null hypothesis as the p value < 0.05 for all the companies. Both the F version & LM statistic significant which shows the presence of ARCH effect in the residuals.