Estimating the Accuracy of Value at Risk in Measuring Risk in Equity Investment in India

Over the past few years, Value-at-Risk (VaR) has become a standard measure of market risk embraced by banks, trading firms, mutual funds and others, including even the non-financial firms. But any risk measure is useful and reliable only insofar as it can be verified for its accuracy. This paper evaluates the accuracy of VaR in estimating the risk in equity investment in India. For this purpose, the study uses the daily data for 30 securities comprising BSE-Sensex and two major stock indicesBSE-Sensex and NSE Nifty for the period January 2006 to February 2007 and portfolio-normal method (parametric approach to VaR calculation) for calculation of VaR. The hypothesis regarding the accuracy of VaR estimates was tested using the chi-square test. The results reveal that VaR estimate does not accurately measure the risk in equity investment in India as VaR overestimates the loss in 24 out of 30 securities. It is only in the case of four securities that the observed number of violations is exactly equal to the expected number. These results may be attributed to non-normal distribution of equity returns in Indian securities market as against the normally distributed returns assumed under portfolio-normal method. All the securities showed excess kurtosis estimate, exhibiting the leptokurtic returns' distribution and also, out of 30 securities, 20 are showing negatively skewed returns and 10 are showing positively skewed returns. Moreover, the assumption of past representing the future is also not validated in the present case in the context of stock volatility observed during the period. The study also observes that portfolio-normal method of VaR computation is a better risk measure for estimating the portfolio risk as compared to risk on individual securities.