Financial institutions face the important task of estimating the controlling of their exposure to market risk, which arises through different risk factors in their Portfolio. Measurement of market risk has focused on a metric called Value at Risk (VaR). VaR quantifies the maximal amount that may be lost in a portfolio for a given period of time, at certain confidence level. For large portfolios the risk factor can be taken as an index. In this chapter we come up with a method of estimating Historical VaR for a portfolio that reflects the S&P CAX Nifty index at any point of time. We assume that the value of index X(t) is independent of time and the distribution of X(t) is not necessarily Gaussian.