Impact of Options Introduction on Different Charactersitics of Underlying Stocks in NSE, India.

Student Name: Manisha Joshi

Financial derivatives are one of the fastest growing and popular innovations in the field of financial engineering. Though derivatives have been around for quite some time in the Western markets, they are still a recent phenomenon in India. This study attempts to examine the effect of introduction of one type of derivative instruments, namely, options on the index as well as on individual securities, on different characteristics of underlying stocks listed in the National Stock Exchange (NSE), India. Three characteristics of the underlying stocks are examined for a change post introduction of options. These are Price, Risk or Volatility, and Liquidity. In the literature, Risk has been divided into three catogories namely, total risk, sytematic risk and unsystematic risks. Here the notion of unsystematic risk has been further classified into two types - conditional unsystematic risk and unconditional unsystematic risk. Change in all these risk categories have been studied.

Index options were introduced on 4th June 2001 followed by options on individual securities on 2nd July 2001. Due to the temporal proximity of these two events, possibility of an interaction of the effects of these two events cannot be eliminated and this is handled by employing an intelligent sampling design. Three groups of stocks are considered - the first group consists of the initial group of 29 stocks on which Options first started tranding on 2nd July 2001, options were subsequently introduced in other stocks and till September 2003 options were introduced on another 25 stocks and these stocks comprise the second group, and finally a control group of stocks is obtained by randomly selecting 29 stocks from the list of stocks on which options were not traded. For the first and second group of stocks, the characteristics of interest are observed daily for one year before and one year after the date of their introduction of options; while for the third group, the characteristics of interest are observed daily for one year before and one year after the date of Index option introduction.

The effect on Price is studied by considering only the first and second group of stocks, and employing standard methodology used in the literature. All existing definitions in the literature have been used to compute the different excess retruns and cumulative excess returns of the stocks on each day in an event window of ± 20 days around the event date. Then for each of these days it is tested whether the mean values of these different metrics across the portfolio (made from stocks with the same event date) of stocks are significantly different from 0, using Sign test, Wilcoxon Signed Rank test and t-test. It is found that option introduction does not have any significant impact on the price of the stocks.

The sampling design (of three groups of stocks mentioned above) has been utilized in disentagling the two effects of Index Option introduction and individual stock option introduction on the Risk and Liquidity measure as follows. First for each group of stocks, change in a given characteristic post an event is measured using either a quantitative or a qualitative variable, the summary of which is given below (as it varies from characteristic to characteristic). This measure carries the effect of, both the events for the first group of stocks, only the individual option introduction for the second group of stocks, and only the Index option introduction for the third group of stocks. Accordingly using dummy variable, for the quantitative measure an ANOVA model, and for the qualitative measure a logistic regreesion model, is used to extract the main effects of the index option and individual stock option introduction and their interaction.

Before summarizing the measures that have been used for measuring change in different characteristics, it is important to recognise that this first involves dividing observations for each stock into a before and after period. In the literature this has been done by subjectively assuming ± 5, ± 10, ± 15, ± 20, ± 25 or ± 30 days around the event date as the so called event window and then considering observations before and after this event window. In this thesis, for the risk measures, an objective method has been suggested for resolving this issue of event window determination which as a by-product also confirms whether indeed a change has set in following an event. The method is called Bayesian Change Point Analysis (BCPA). For implementing BCPA one first computes the continuously compounded rate of return for each stock for the entire observational period. Next this return series is modeled using an ARMA or ARMA-GARCH model with a discrete unknown change-point parameter thrown in, which allows the order and/or the parameter values of the fitted model differ for the days before and after this change-point. The marginal posterior p.m.f. of this change-point parameter is then studied. If most of the posterior mass is found to be concentrated around the date of the event then that confirms that a change has indeed set in. In such a situation a Bayesian interval estimate based on this posterior around the posterior mode such as a highest posterior density credible set, yields an objective event window around the event date. On the other hand if there has not been any change, that will also be reflected in the posterior p.m.f. of the change-point parameter exhibiting no obvious peak on and around the event date. Each stock in the three groups are subjected to BCPA and for most of the stocks the event window is found to be ± 20 days. Thus even for a few stocks which did not exhibit any significant change, for the sake of uniformity, the event window is taken to be ± 20 days. Thus for all the stocks the "before" period is defined as the first day of the observation to 20 days before the event date, and the "after" period is defined as 20 days after the event date till the last day of the observation.

For checking the effect on the total risk, for each stock, before and after period return variances are checked using both F-test and Ansari-Bradley test, and the results of these tests are coded as a 0-1 valued variable which are then modeled using logistic regression, in order to isolate the two main effects and the interaction. Furthermore the before and after ratio of the return variances of the stocks in the three groups are also analysed using the ANOVA model. From these analyses it is concluded that index option introduction seems to have increased the total risk while individual option introduction seems to have decreased it, with the effect of the former event being more pronounced than the later, and the interaction effect is such that the combined effect of the two is leading to an increase in total risk.

Difference between before and after OLS, Scholes-Williams and Fowler-Rorke betas for each stock in the three groups are analysed using the ANOVA model for checking the change in systematic risk and these analyses suggest that there has not been any signficant change in sytematic risk due to either of the events. Excess returns, which are residuals of OLS regression of a stock return on the market or NSE Nifty return, are modeled using an ARMA as well as ARMA-GARCH of an appropriate order and ARMA-GARCH(1,1) (for the convenience of interpretation of parameter values), and then the before and after variance of these excess returns computed according to these models are compared for testing the change in unsystematic risk. While for the ARMA model, ratios of both before and after conditional and unconditional variances are analysed using the ANOVA model, for the ARMA-GARCH of appropriate order, due to non-uniformity in the structure of the conditional variances, only the ratio of the unconditional variances are analysed using the ANOVA model. For facilitating comparison of unconditional variances based on a GARCH model, ARMA-GARCH(1,1) are fitted to returns of all the stocks in the three groups, and then the differences in the before and after news and persistent coefficients of the GARCH(1,1) models are analysed using the ANOVA model. Based on the ARMA model it is found that individual option introduction has led to a decrease in both conditional and unconditional unsystematic risk, while index option introduction does not seem to have any siginificant effect on the unsystematic risk. On the other hand, both ARMA-GARCH of appropriate order and ARMA-GARCH(1,1) models suggest no significant effect of either events on the unconditional unsystematic risk, except that news coefficients are sharper post index option introduction indicating information is being absorbed at a faster rate post index option introduction.

Finally for checking the impact on liquidity, two measures have been compared between the before and after periods - daily relative trading volume, defined as the ratio of the total trading volume on a given day in Rs. terms to the market capitalization, and the daily bid-ask spread, computed using Roll's formual from high frequency intra-day data. Since neither of these series are stationary, for each stock, the before and after period measures are compared using Wilcoxon Rank Sum test, the results are coded using -1, 0, 1 for decrease, no change, and increase, these results are anlysed using a multinomial logistic regression to disentangle the effects of the two events and finally based on this model the probabilities of decrease, no change and increase are computed for each group of stocks. From these analysis it is concluded that though individual option introduction has led to an increase in relative trading volume i.e. liquidity, index option introduction has lead to a decrease in it with the effect of the later being more pronounced. However contradictory results are obtained based on the spread measure - index option introduction seems to have led to a decrease in spread (and thus better liquidity) while individual option introduction appears to have caused an increase in spread.