A Study on Volatility in Indian stock market

Literature

Engle (1982) conducted in study that measured the time-varying volatility. His model, ARCH, is based on the idea that a natural way to update a variance forecast is to average it with the most recent squired "surprise"(i.e. the squired deviation of the rate of return from its mean).While conventional time series and econometric models operate under an assumption of constant variance, the ARCH process allows the conditional variance to change over time as a function of past errors leaving the unconditional variance constant. In the empirical application of the ARCH model a relatively long lag in the conditional variance equation is often called for, and to avoid problems with negative variance parameters a fixed lag structure is typically imposed.

        Bollerslev (1986) conducted in study to overcome the ARCH limitations introduced his model, GARCH that generalized the ARCH model to allow for both a longer memory and a more flexible lag structure. As noted above, in the empirical application of the ARCH model, a relatively long lag in the conditional variance equation is often called for, and to avoid problems with negative variance parameters a fixed lag structure is typically imposed. In the ARCH process the conditional variance is specified as a linear function of past sample variance only, whereas the GARCH process allows lagged conditional variances to enter in the model as well.

       

        Engle, Lilien, and Robins (1987) conducted in study introduced the ARCH-M model by extending the ARCH model to allow the conditional variance to be determinant of the mean. Whereas in its standard form, ARCH model expresses the conditional variance as a linear function of past squired innovations in this new model they hypothesize that, changing conditional variance directly affect the expected return on a portfolio. Their results from applying this model to three different data sets of bond yields are quite promising. Consequently, they conclude that risk premia are not time invariant; rather they vary systematically with agent's perceptions of underlying uncertainty.

       

Nelson (1991) conducted in study extended the ARCH framework in order to better describe the behavior of return volatilities. Nelson's study is important because of the fact that it extended the ARCH methodology in a new direction, breaking the rigidness of the G/ARCH specification. The most important contribution was to propose a model (EARCH) to test the hypothesis that the variance of return was influenced differently by positive and negative excess returns. His study found that not only was the statement true, but also that excess returns were negatively related to stock market variance

        Engle and Ng (1993) conducted in study measure the impact of bad and good news on volatility and report an asymmetry in stock market volatility towards good news as compared to bad news. More specifically, market volatility is assumed to be associated with the arrival of news. A sudden drop in price is associated with bad news on the other hand, a sudden increase in price is said to be due to good news. Engle and Ng find that bad news create more volatility than good news of equal importance. This asymmetric characteristic of market volatility has come to be known as the "leverage effect". The studies of Black (1976), Christie (1982), FSS (1987), Schwert (1990) and Pagan and Schwert (1989) also explain this volatility asymmetry with the" leverage effect". However, their models do not capture this asymmetry.Engle and Ng (1993) provide new diagnostic tests and models, which incorporate the asymmetry between the type of news and volatility, they advise researchers to use such enhanced models when studying volatility.

  

Batra (2004) conducted in study in an article entitled" stock return volatility patterns in India” examined the time varying pattern of stock return volatility and asymmetric Garch methodology. He also examined sudden shifts in volatility and the possibility of coincidence of these sudden shifts with significant economic and political events both of domestic and global origin. Also, he examined stock market cycles for variation in amplitude, duration and volatility of the bull and bear phases over the reference period. His analysis revealed that liberalization of the stock market or the FII entry in particular does not have any direct implications for the stock returns volatility. No structural changes in the stock price volatility around any liberalization event or more importantly around the dates of breaks for volatility in FII sales and purchases in India were observed. The apparent link generally drawn between stock price volatility and the sudden withdrawal or heavy purchase by the FIIs i.e. the volatile FII investment in the stock market did not seem to hold true for India. In all the phases, as delineated by their structural break analysis, the period between 1991:05 and 1993:12 was the most volatile period with the standard deviation of stock returns exceeding that in the other periods. The study also showed that in general over the references period the bull phases are longer, the amplitude of the bull is higher and the volatility in the phases is also higher. He also concluded that the gains during expansions are larger than the losses during the bear phases of stock market cycles. The bull phase, in comparison with its pre liberalization character was more stable in the post liberalization phase. The results of their analysis also, showed that the stock market cycles have dampened in the recent past. Finally, the study showed that volatility has declined in the post liberalization phase for both the bull and bear phase of the stock market cycles.

Kumar (2006) conducted in study in an article entitled “comparative performance of volatility forecasting models in Indian markets"evaluated the comparative ability of different statistical and economic volatility forecasting models in the context of Indian stock and Forex markets. Based on the out of sample forecasts and the number of evaluated measures that rank a particular method as superior he concluded that it is possible to infer that EWMA will lead to improvements in volatility forecasts in the stock markets and the GARCH (5,1) will achieve the same in the Forex market. As he concluded, his findings were contrary to the findings of Brailsford and Paff (1996) who found no single method as superior, but the results in stock market were similar to the findings of Akigray (1989), McNillian (2001), Anderson and Bollerslev(1998) and Anderson et al (1999) in the Forex market.

Banerjee and Sarkar (2006) conducted in study in an article entitled” long memory property of stock returns; evidence from India” examined the presence of long memory in asset returns in the Indian stock market. They found that although daily returns are largely uncorrelated, there is strong evidence of long memory in its conditional variance. They concluded that FIGARCH is the best-fit volatility model and it outperforms other Garch type models. They also observed that the leverage effect is insignificant in Sensex returns and hence symmetric volatility models turn out to be superior as they expected.

Rogobon (2003) conducted in study has focused on alternative measures of volatility in the equity and bond markets in the period surrounding the financial crises.

       

        Bekaert and Harvey (2000) conducted in study analyzed equity returns in a group of emerging markets before and after      financial reforms. The empirical studies investigating the volatility of returns have yielded mixe conclusions.

           

Nilsson (2002) conducted in study has explored that stock market liberalization can lead to excess volatility possibly on account of noise trading for Nordic stock markets using the Markov regime-switching model. He finds evidence of higher expected return, higher volatility and stronger links with international stock markets characteristic of the deregulated period in all Nordic stock markets.

Richards (1996) conducted in study 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.

Aggarwal, Inclan and Leal (1999) conducted in study 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.

        - Cost effectiveness and maximization of returns are the objectives of every investment decisions. These objectives can be achieved by a proper choice of the instruments bearing in mind their features. Volatility is the most basic statistical risk measure. It can be used to measure the market risk of a single instrument or an entire portfolio of instruments. While volatility can be expressed in different ways, statistically, volatility of a random variable is its standard deviation.