Predictive ability of Value-at-Risk methods: evidence from the Karachi Stock Exchange-100 Index

Value-at-risk (VaR) is a useful risk measure broadly used by financial institutions all over the world. VaR is popular among researchers, practitioners and regulators of financial institutions. VaR has been extensively used for to measure systematic risk exposure in developed markets like of the US, Europe and Asia. In this paper we analyze the accuracy of VaR measure for Pakistan’s emerging stock market using daily data from the Karachi Stock Exchange-100 index January 1992 to June 2008. We computed VaR by employing data on annual basis as well as for the whole 17 year period. Overall we found that VaR measures are more accurate when KSE index return volatility is estimated by GARCH (1,1) model especially at 95% confidence level. In this case the actual loss of KSE-100 index exceeds VaR in only two years 1998 and 2006. At 99% confidence level no method generally gives accurate VaR estimates. In this case ‘equally weighted moving average’, ‘exponentially weighted moving average’ and ‘GARCH’ based methods yield accurate VaR estimates in nearly half of the number of years. On average for the whole period 95% VaR is estimated to be about 2.5% of the value of KSE-100 index. That is on average in one out of 20 days KSE-100 index loses at least 2.5% of its value. We also investigate the asset pricing implication of downside risk measured by VaR and expected returns for docile portfolios sorted according to VaR of each stock. We found that portfolios with higher VaR have higher average returns. Therefore VaR as a measure of downside risk is associated with higher returns.