Value at Risk (VaR) is fast becoming an industry benchmark for managing financial risk. VaR is a useful concept, which is widely used for financial risk management and for evaluating the riskiness of financial investments. VaR is a single number, which measures the risk of a portfolio of financial assets. Intuitively, what VaR says is; that we are X percent certain that we will not lose more than 'V' rupees in the next N trading days.
The 'V' over here is the VaR of the portfolio. VaR is calculated for a certain time horizon (normally either for a 1 or 10 trading days time period) and for a certain confidence level (usually assumed to be 1%; as specified in the Basel regulations). The capital requirements for financial institutions are also based on the VaR. In short, VaR tells you how bad things can get; ie there is a 1% probability that financial losses can be greater then 'V' rupees.
Despite its short comings and most importantly the fact that it does not give you any information on what the size of a financial loss will be in the 1% worst case scenario, the VaR is still the most widely used measure of financial risk. VaR analysis, as per Basel regulations, should be supplemented by back-testing and stress- testing.
Basel Regulations give financial institutions the choice over the methodology for estimating VaR. VaR can be sensitive to the methodology employed for calculation. In this article we calculate VaR over a 10 trading day time period for 11 individual stocks listed on KSE. We can think of our financial portfolio as comprising of only individual stock. We compute the 10 day VaR using 3 alternative methods; simple variance method, GARCH variance method and from Monte Carlo Simulation.
Even though 1-day trading horizon is more meaningful (due to the assumptions inherent in VaR), but we select a 10 day time period to make the comparison of VaR, based on 3 methods, more meaningful. As per Basel Regulations a 1 day, VaR can be extended to 10 day VaR by multiplying the 1 day VaR by.
This holds true for the 1st two methods, which we employ but for the third one rather than using this approximation, we dynamically compute the VaR over the 10 day time period using Monte Carlo Simulation. We report the VaR in percentage terms ie the number reported can be interpreted as a 1% probability of losing more than the reported VaR (percentage) of the portfolio value in the next 10 trading days.
To convert this to nominal (monetary) terms, one can multiply it by the portfolio value. Methodology 1 uses the simplest measure of variance, by giving constant weight to all the observations and thus assuming that the variance is constant over the sample period. On the other hand, methodology 2 takes into account that the variance is conditional on the time period ie is changing over time, therefore gives more weight to the recent most observations.
While the 3rd methodology uses the GARCH variance forecasts, but then dynamically updates it recursively using random numbers drawn at every step from a standard normal distribution. The VaR for 11 stocks, selected so as to represent most of the sectors, are reported below (computed by the 3 methods).
It is clearly evident from the table that the 3 methods yield significantly different results and in most cases the simple method calculates a higher value of the VaR. Stocks with high values of VaR would be considered more riskier, as there is a probability of suffering a greater loss in case things do get bad (the worst case scenario as predicted by VaR).
Even through in some cases the values appear very close, but in monetary terms when multiplied by portfolio value (in million/ billion of rupees), these small differences can translate into large differences. In cases where simple method overstates the VaR, capital allocation based on this method can lead to the inefficient allocation of resources or uselessly tied up capital.
The VaR is normally supplemented by stress-testing and back-testing, to test the robustness of the estimated VaR. Given the results, even though VaR is a useful guide for risk management and risk evaluation, but it is sensitive to the methodology employed. The VaR numbers, therefore, are useful, but should be carefully interpreted. If interpreted correctly VaR can serve as a useful guide for financial investors given the current financial crisis.

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COMPANY                                     SYMBOL         10-DAY VAR(%)
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                                                    SIMPLE-     GARCH  MONTE CARLO
                                                     STATIC  VARIANCE   SIMULATION
                                                     METHOD    METHOD       METHOD
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MCB Bank                                    MCB      23.703    19.781      23.4786
Oil and Gas development Company Limited     OGDC     17.405     8.335       8.7377
Jahangir Siddiqui and Cos Limited           JSCL     53.491    53.587       53.166
Pakistan State Oil                          PSO      18.349    10.015       11.283
Engro Chemical Pakistan Limited             ENGRO    19.596    10.910       11.777
Pakistan Telecommunication Company Limited  PTC      19.726    19.894       17.515
The Hub Power Company Limited               HUB      17.409    11.565       16.024
Nishat Mills Limited                        NML      24.108    19.366       20.202
D.G. Khan Cement  Company Limited           DGKC     28.693    24.218       29.406
EFU General Insurance Limited               EFUG     34.947    33.919       35.853
Netsol technologies Limited                 NETSOL   26.448    24.040       23.050
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