Estimating the Accuracy of Value-at-Risk (VAR) in Measuring Risk in Equity Investment in India

Abstract

Over the past few years, the 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 attempts to evaluate the accuracy of VaR in estimating the risk in equity investment in India. For this purpose we have used daily data for 30 securities comprising BSE-Sensex and two major stock indices- BSE 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 accuracy of VaR estimates has been tested using Chi-square test. The results show that VaR estimate does not accurately measure the risk in equity investment in India as VaR overestimates the loss in 24 securities out of 30 securities. It is only in case of 4 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 are showing 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. We have also observed that portfolio- normal method of VaR computation is a better risk measure for estimating portfolio risk as compared to risk on individual securities.

Keywords: VaR, Normal distribution,Equity Investment

JEL Classification: G14