Heteroskedastic behavior of the Indian stock market: evidence and explanation

Journal of the Academy of Business and Economics, Jan, 2003 by Madhusudan Karmakar

ABSTRACT

This paper investigates the heteroskedastic behavior of the Indian stock market using 'vanilla' GARCH (1, 1) model for a period of about 24 years from January 1980 to June 2003. The study reports an evidence of time-varying volatility which exhibits clustering, high persistence and predictability. Conditional volatility shows a clear evidence of volatility shifting over the period where the level of volatility for the decade Nineties is considerably higher than that of the decade Eighties and violent changes in share prices cluster around the boom of 1992, surpassing all previous records. Though the gradual shift of volatility started in response to strong economic fundamentals, the real cause for abrupt movement appears to be the imperfection of the market.

1. INTRODUCTION

The behavior of speculative price series has attracted the attention of researchers for nearly 100 years. Mandelbrot and Fama provided the first generally accepted evidence that suggests that the distribution of such asset prices are characterized by a number of stylized 'facts' such as kurtosis and heteroskadasticity (Mandelbrot, 1963 and Fama, 1965). Most importantly, asset returns are approximately uncorrelated but not independent through time as large (small) price changes tend to follow large (small) price changes. This temporal concentration of volatility is commonly referred to as 'volatility clustering' and it was not fully exploited for modeling purposes until the introduction of the Auto Regressive Conditional Heteroskedasticity (ARCH) model by Engle (1982). The ARCH model was unique in that it specified the variance of the error term in a regression equation as conditional on squared past errors. Hence, volatility in the ARCH model will exhibit periods of relative tranquility and volatility effectively capturing this volatility clustering characteristic so common to economic and financial time series data.

Bollerslev extended this idea into Generalized Autoregressive Conditional Heteroskedastic (GARCH) models which give more parsimonious results than ARCH models (Bollerslev, 1986). ARCH and GARCH models have become widespread tools for dealing with time series heteroskedastic models. The goal of such models is to provide a volatility measure--like a standard deviation--that can be used in financial decision concerning risk analysis, portfolio selection and derivative pricing.

Considering the importance of the models, the ARCH literature has developed so rapidly that there currently exists a veritable family of ARCH models incorporating the original ARCH model of Engle, GARCH model of Bollerslev as well as a host of other suitably acronymed models (see Bollerslev et al., 1994, or Bera and Higgins, 1993 for a survey). Curiously all of these models have been developed based on economic and financial time series data mostly taken from developed countries, where each of these subsequent contributions to the ARCH family have concentrated on refining both the mean and variance equations to better capture the stylized characteristics of the data. ARCH and GARCH literature on emerging markets is, however, scanty though comparatively higher reported returns of many of these markets have recently attracted increased interest of global portfolio investors in the developed countries. Indian stock market too promoted an accelerated growth and development both in qualitative and quantitative measures, particularly after the structural changes and financial liberalization policies initiated in 1991 and has opened a new vista to foreign institutional investors to diversify their global portfolios. Surprisingly enough in my knowledge there is no study identifying stochastic behavior particularly concerning volatility, using ARCH and GARCH methods on Indian data. Hence an attempt is made in the present study to fill up the gap in this direction. The objective of the study is simply to examine heteroskedastic behavior of the Indian stock market using plain GARCH model which allows for changing conditional volatility. We focus our attention on the following questions:

1. Does stock return volatility change over time? If so, are volatility changes predictable? To address these issues we will try to fit an appropriate GARCH model which may help to forecast the conditional variance of the daily price change.

2. What are the reasons behind volatility shifting? We will try to provide here only subjective explanation on the basis of available information.

We find strong evidence of time-varying volatility. Our results resemble those of many studies on developed markets: periods of high / low volatility tend to cluster, volatility shows high persistence and is predictable. High volatility though partially is explained by fundamental economic factors, a considerable part of the excessive movement may be attributed to 'fads' or 'bubble'.

We do hope the findings of the study would help investors for derivative pricing, VaR calculation and portfolio diversification. The findings may also be interest to policy makers interested in stock market movements, since internationalization of market could represent significant capital inflows or outflows, and this influences saving and consumption decision.