Stock Return Volatility Patterns In India


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WORKING PAPER NO. 124
STOCK RETURN VOLATILITY PATTERNS IN INDIA
AMITA BATRA March, 2004
INDIAN COUNCIL FOR RESEARCH ON INTERNATIONAL ECONOMIC RELATIONS Core-6A, 4th Floor, India Habitat Centre, Lodi Road, New Delhi-110 003

Contents

Foreword .............................................................................................................................i

Abstract ..............................................................................................................................ii

I

Introduction ...........................................................................................................1

II Theoretical Motivation..........................................................................................4

III Survey of Literature ..............................................................................................6

IV Data.........................................................................................................................8
IV.1 Basic Data ..............................................................................................................8 IV.2 Sample Period ........................................................................................................9 IV.3 Sources of Data ......................................................................................................9 IV.4 Descriptive Statistics..............................................................................................9
V Estimating Volatility: Exponential GARCH (E-GARCH) ..............................10

VI The Analysis: Our Approach .............................................................................12
VI.1 Naïve Model.........................................................................................................12 VI.2 Augmented GARCH Model ................................................................................16 VI.3 Characteristics of Stock Market Cycles ...............................................................22
VII Conclusions ..........................................................................................................28

APPENDIX ......................................................................................................................30

References ........................................................................................................................32

Foreword
Financial crises in the last decade have revealed that financial asset price volatility has the potential to undermine financial stability. Available empirical evidence indicates that financial stability is endangered more by sudden shifts in volatility rather than by a sustained increase in the level of volatility. Understanding volatility is therefore central to risk management in an economy.
This paper examines the time variation in volatility in the Indian stock market during 1979-2003. Using monthly data and asymmetric GARCH methodology augmented by structural change analysis the paper identifies sudden shifts in stock price volatility and the nature of events that cause these shifts in volatility. The paper also undertakes an analysis of the stock market cycles in India to see if the bull and bear phases of the market have exhibited greater volatility in recent times.
The empirical analysis in the paper reveals that the period around the BOP crisis and the subsequent initiation of economic reforms in India is the most volatile period in the stock market. Sudden shifts in stock return volatility in India are more likely to be a consequence of major policy changes and any further incremental policy changes may have only a benign influence on stock return volatility. Stock return volatility in India seems to be influenced more by domestic political and economic events rather than by global events. The analysis in the paper also reveals that stock market cycles in India have not intensified after financial liberalization. A generalized reduction in stock market instability is observed in the post reform period in India.
I do hope that this paper will serve as a useful source and provide valuable reference material for researchers, policymakers and market participants.

March 2004

Arvind Virmani Director & Chief Executive
ICRIER

i

STOCK RETURN VOLATILITY PATTERNS IN INDIA
Amita Batra*
Abstract
In this paper we analyze the time variation in volatility in the Indian stock market during 1979-2003. We examine if there has been an increase in volatility persistence in the Indian stock market on account of the process of financial liberalization in India. Further, we examine the shifts in stock price volatility and the nature of events that apparently cause the shifts in volatility. We also make an attempt to characterize the evolution of the stock market cycles over time in India and examine if in recent times the stock market cycles have exhibited greater amplitude and volatility. In an overall sense, therefore, the aim of this paper is to give economic significance to changes in the pattern of stock market volatility in India during 1979-2003.
Monthly stock returns have been used for analysis. Asymmetric GARCH model has been used to estimate the element of time variation in volatility. The model is further augmented with dummy variables, an outcome of the structural change analysis, to examine volatility persistence. For the characterization of the stock market cycles, the Pagan and Sussoumov (2003) methodology is adopted.
Our analysis reveals that the period around the BOP crisis and the initiation of economic reforms in India is the most volatile period in the stock market. Structural shifts in volatility are more likely to be a consequence of major policy changes and any further incremental policy changes may have only a benign influence on stock return volatility. Stock return volatility in India seems to be influenced more by the domestic political and economic events rather than global events. In particular there appears to be no coincidence between volatility of portfolio capital flows in and out of the stock market and the volatility shifts in stock returns in India. Our analysis also shows that stock market cycles in India have not intensified after financial liberalization. We observe a generalized reduction in market instability in the post reform period in India. In general, in the post liberalization period in India, the bull phases are longer, the amplitude of bull phases is higher and the volatility in bull phases is also higher than in the bear phases. In comparison with its pre liberalization character, however, the bull phases are more stable in the post liberalization period.
Key Words: Persistence of volatility shocks; structural change; stock market cycles
JEL Number: G15; F30; C22
* Sincere thanks are offered to Prof. Arvind Virmani for giving invaluable suggestions that helped me finalize the paper. Thanks are due to an anonymous referee for making useful comments on the first draft. Thanks are also offered to Dr. Reena Aggarwal and Dr. Carla Inclan for giving the relevant econometric packages and to Mr. Vipul Bhatt for technical assistance. Research assistance provided by Ms. Zeba Khan is deeply appreciated.
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I

Introduction

In the aftermath of the many crises that the last decade has been witness to, a return to the old- world order of regulated/restricted flows has been proposed by many economists and policymakers. The clamor for restrictions on capital inflows has largely been on account of the notion that unregulated cross – border movement of portfolio capital causes “excessive” booms and busts and thus volatility/instability in the financial markets. Financial market volatility can have a wide repercussion on the economy as a whole. There is clear evidence of the important link between financial market uncertainty1 and public confidence. Policy makers therefore rely on market estimates of volatility as a barometer of the vulnerability of financial markets. The existence of excessive volatility or “noise” also undermines the usefulness of stock prices as a “signal” about the true intrinsic value of a firm, a concept that is core to the paradigm of informational efficiency of markets. Further, volatility estimation and forecasting have become a compulsory risk –management exercise for economies and many financial institutions around the world ever since the first Basle Accord was established in 1996. Understanding volatility is therefore central to risk management in an economy.

In the asset pricing literature volatility refers to asset price variability. Volatility may be measured as the standard deviation of daily price changes, or as a by-product of estimation of an econometric volatility model. The standard approach to modeling volatility is through the so-called GARCH class of ARCH models. The availability of long series of asset price data has resulted in a large number of econometric studies on volatility. A general finding across asset markets is that volatility shocks are highly persistent.

1 When volatility is interpreted as uncertainty it becomes a key input into many investment decisions and portfolio creations. Investors and portfolio managers have certain levels of risk, which they can bear. A good forecast of the volatility of asset prices over the investment holding period is a good starting point for assessing risk.
1

In this paper we analyze the time variation in volatility2 in the Indian stock market during 1979-2003. We examine if there has been an increase in volatility persistence in the Indian stock market on account of the process of financial3 liberalization in India. Further, we examine the shifts in stock price volatility and the nature of events that apparently cause the shifts in volatility. This will enable us to identify if a coincidence between the shifts in stock return volatility and financial liberalization exists. We also make an attempt to characterize the evolution of the stock market cycles over time in India and examine if in recent times the stock market cycles have exhibited greater amplitude and volatility. The analysis of bear and bull markets allows us to investigate in greater detail and in an episodic manner, the evolution of stock market instability. In an overall sense, therefore, the aim of this paper is to give economic significance to changes in the pattern of stock market volatility in India during 1979-2003.
Monthly stock returns have been used for analysis as the presence of more noise at higher frequencies makes it difficult to isolate cyclical variations, obscuring thus the analysis of the driving moments of switching behavior in stock price volatility. Asymmetric GARCH model has been used to estimate the element of time variation in volatility. The model is further augmented with dummy variables, an outcome of the structural change analysis, to examine volatility persistence. For the characterization of the stock market cycles, the Pagan and Sussoumov (2003) methodology is adopted.
Our analysis of sudden shifts in stock index volatility reveals that the period around the 1991 BOP crisis and the subsequent initiation of economic reforms in India is the most volatile period in the stock market. Structural shifts in volatility are more likely to be a consequence of major policy changes and any further incremental policy changes may have only a benign influence on stock return volatility. Further, stock return
2 Stock return/market volatility may not be increasing in recent years or before /after an event but there may be variation in volatility over time
3 While we seek to analyze volatility changes as a consequence of stock market liberalization and portfolio inflows, we refer to financial liberalization in the paper, as the period of reference encompasses a large number of economic reform measures simultaneously undertaken to open the domestic financial sector.
2

volatility in India is influenced more by the domestic political and economic events rather than global events. In particular there appears to be no coincidence between volatility of portfolio capital flows in and out of the stock market and the volatility shifts in stock returns in India.
Our analysis also shows that stock market cycles in India have not intensified after financial liberalization. We observe a generalized reduction in instability in the post reform period in India. Interestingly our findings are in line with the nature of evolution of financial cycles in other emerging markets. An informal analysis shows that external linkages of the Indian stock market seem non-existent prior to 1998. After October 1998, coincidence with financial cycles in the US is visible. Specifically for the peak observed in the year 2000 a coincidence of peaks across the US and the emerging markets is observed. In general, in the post liberalization period in India, the bull phases are longer, the amplitude of bull phases is higher and the volatility in bull phases is also higher than for the bear phases. In comparison with its pre liberalization character, however, the bull phases are more stable in the post liberalization period.
The rest of the paper is organized as follows: In section 2 we present the theoretical motivation for our analysis. Section 3 gives a brief review of literature on the subject. Section 4 lists the data and data sources used for the analysis in this paper. Some summary descriptive statistics for the stock returns over our reference period are also presented in this section. Section 5 explains the exponential GARCH methodology. The empirical analysis is presented in section 6. The empirical analysis is undertaken in three parts viz: time variation in volatility using the asymmetric GARCH (E-GARCH) methodology, augmented E-GARCH using dummy variables for structural change in stock return volatility and volatility analysis using the stock market cycles approach. Main conclusions of our analysis are summarized in section 7.
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II Theoretical Motivation
Both volatility persistence and stock market cycle characterization are currently empirical phenomena without a theoretical explanation; some theoretical underpinnings of the link between stock market volatility and liberalization have however evolved. We discuss below the channels through which stock market liberalization may affect volatility. The discussion is based on the model proposed by Tauchen and Pitts (1983) and subsequently used by Kwan and Reyes (1997). The model relates stock price and volume traded in the speculative market with clear implications for liberalization and stock return volatility.

Assume that there are J active traders in the market. Within the day, the market passes through a sequence of distinct Walrasian equilibria. The movement from the (I1)st to the ith equilibrium in a given day is caused by the arrival of new information to the market. The desired net position, Qij of trader j at the time of the ith equilibrium is assumed to be a linear function of the following form:

Qij = a [P*ij – Pi]

(j = 1,2…..J)

(1)

Where
a > 0 = constant P*ij = jth trader’s reservation price Pi = current market price

A positive value for Qij represents a desired long position in a contract while negative

value represents a desired short position. Equilibrium requires that the following holds

true:

Ê J

Qij = 0

(2)

j1

This implies that the average of the reservation price clears the market:

Ê J

Pi =1/J

P*ij

(3)

j1

4

The price change can then be written as:

Ê J

DP = 1/J D P*ij

(4)

j1

Where P*ij = P*ij-P*I-1, j is the increment to the jth trader’s reservation price.

Assuming a variance – components model with an information component that is common to all traders, ji, and one that is specific to the jth trader, yij

Equation (4) can then be re - written as:

Ê J

DPi = fI +1/J j ij

(5)

j1

The first two moments of the price change are then derived as the following:

E[DPi] = 0

(6)

Var[D p i] = s2¡ + s2/J

(7)

Equation (7) suggests that other things being equal, an increase in the number of traders J tends to reduce the stock price variance. On the other hand, an increase in the variance of information sets available to traders – a common component and/or a unique component - tends to raise the stock price variance.

Stock market liberalization will attract a new group of investors, the FIIs. An increase in the number of traders in the market may then reduce the stock price variance. Stock market opening may also simultaneously trigger an increase in the variance of information sets available to the FII thereby implying a possibility of an increase in the stock return volatility. Theoretical literature therefore does not provide us with an unambiguous conclusion on the impact of stock market liberalization on stock return volatility.

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III Survey of Literature
Most recent studies on financial market volatility are placed in the context of transmission of volatility across economies and the contagion effects of a financial crisis. These include studies by Forbes and Rigobon (2002), Bekaert, Harvey and Lumsdaine (2002a,b), Edwards (2000) and others. Rogobon (2003) has focussed on alternative measures of volatility in the equity and bond markets in the period surrounding the financial crises. Bekaert and Harvey (2000) analyzed equity returns in a group of emerging markets before and after financial reforms. The empirical studies investigating the volatility of returns have yielded mixed conclusions. Aggarwal, Inclan and Leal (1999) analyze volatility in emerging stock markets during 1985-95. Using an ICSS algorithm to identify the points of sudden changes in the variance of returns they examine the nature of events that cause large shifts in stock return volatility in these economies. Aggarwal et al find that mostly local events cause jumps in the stock market volatility of the emerging markets. Kim and Singal (1997) and De Santis and Imorohoroglu (1994) study the behavior of stock prices following the opening of a stock market to foreigners or large foreign inflows. They find that there is no systematic effect of liberalization on stock market volatility. These findings corroborate Bekaert’s findings that volatility in emerging markets is unrelated to his measure of market integration. Richards (1996) used three different methodologies and two sets of data to estimate volatility of emerging markets. A common claim of all these studies is that, the proposition that liberalization increases volatility is not supported by empirical evidence. However, Levine and Zervos (1995) suggest that volatility may increase after liberalization.
Hamao and Mei (2001) examined the impact of foreign and domestic trading on market volatility for Japan and find no systematic evidence that foreign trading tends to increase market volatility more than trading by domestic groups. The study however relates to the time period during which the foreign portfolio investment in Japan was rather small. Folkerts – Landau and Ito (1995) computed volatility of emerging markets in periods that differ in their intensity of portfolio flows. Their evidence is rather mixed
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Stock Return Volatility Patterns In India