Value at Risk – Historical Simulation

Historical simulation is a non-parametric approach of estimating VaR, i.e. the returns are not subjected to any functional distribution. VaR is estimated directly from the data without deriving parameters or making assumptions about the entire distribution of the data. This methodology is based on the premise that the pattern of historical returns is indicative of future returns. All that needs to be determined is an appropriate look back period for the relevant price data. In our analysis, for the look back period of 01-Jan-08 to 15-Apr-09, the following are the number of daily return observations for the given data:


Observations (#)

Listed equities on KSE indices
(50 average volume leaders)*


KSE 30 equity index*


KSE 100 equity index*


Foreign Exchange rates


Currency Pairs


PKRV rates


KIBOR rates


Commodity prices


* The period of the floor (i.e.28-Aug-08 to 14-Dec-08) has been removed

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The first step is to order these daily returns from largest to smallest. Viewing the sorted data from the tail end of this ordered distribution, the 99% daily historical VaR is obtained by identifying the corresponding percentile entry.

For example, in the case of KIBOR rates with an estimation window of 362 observations over a look-back period of 471 days, the first percentile corresponding with a 99% VaR lies somewhere between the 4th and 5th lowest returns. The daily historical VaR is equal to the absolute value of this interpolated return. The 10-day holding period VaR is calculated by applying the square root of time formula as mentioned above.