Results and Conclusion

The probability distribution $p(x)$ constructed for each of the sensex scrips and two scrips in the rolling settlement (which we have done after the fact to see the effect of the settlement system if any) shows a remarkable feature.

The feature is that at a return level of about -0.08 and +0.08, which corresponds to a return of +8% and -8% respectively, there is a huge mass in $p(x)$. This feature is present in almost all the sensex scrips. This is so predominant that there must be a reason for it.

A little thought shows that the markets also have a circuit breaker for trading precisely at this level of price changes. This means that the circuit breaker is being hit at significantly many times more than it should (because the tails in the distribution should not have a huge mass if there is no unusual influence and the returns behave according to normal distribution or any other pareto distribution and such). We summarize our findings below. We also summarize a simple calculation of the VaR for the different sensex scrips at 99%, 95% and 90% confidence levels for inspection.

We also give the graphs of $p(x)$ as a function of x for a few scrips at the end, so that the reader can see the striking feature of the distribution.

• We found that not only there is no Gaussian behaviour, but there is a huge mass sitting at both the positive and negative tails of the distribution which was rather surprising at the first look.

• However on closer look, it turns out that these masses occur at about $\pm 8\%$ return level and given the fact that the markets have circuit breakers for the scrips at the $8\%$ level this mass is explained as the effect of the circuit breaker on the distribution.

• The mass at the tail of the distribution is present even for scrips that are in the rolling settlement.

• The circuit breakers in the market seems to increase the VaR for the investor.

The data used by us and the paper are availabe at the location http://www.imsc.res.in/~krishna/finance/index.html.

It is our conclusion that the "circuit breakers" are acting negatively in the present market conditions, at least as far as the investor risk is concerned and their influence on the market itself should be studied further.

We recommend that SEBI undertake a study of the riks in the markets from the investor point of view, and reevaluate the effect of "circuit breakers" as a means of regulating the market at least as far as the price movements of individual share prices are concerned.

We also feel that a theoretical study, perhaps from a Game theoretic point of view on the effect of circuit breakers on the markets should yield interesting results. One of the reasons is that unlike a market with no circuit breakers, the agents in the market with circuit breakers all have a common value to use as a goal and hence could act in co-ordination, though they may not even exchange any information.

In short the Indian stock markets exhibit some interesting, though disturbing for the common investor, behaviour which should be studied further.

Acknowledgment: We thank Mr Gangadharan, IFMR for helping us collect the data used in this work.