A Comparison of Values-at-Risk (VAR) Methods

This article broadly compares the three VAR methods: delta-normal, historical simulation and Monte-Carlo VAR.

1)     The delta-normal VAR, also called the variance-covariance method simplifies the computation of VAR by assuming that risk factors are normally distributed.  The problem with this method is that the effect of the non-linear instruments like options is not taken into account. This problem does not exist with the other methods like historical simulation method and the monte-carlo method because the assumption of normality does not exist for them.

2)     Distribution of risk factors: The delta-normal method assumes that the risk factors are normally distributed which means that the shape is already been fixed.  The historical simulation method replicates the actual distribution of risk factors and in this respect the Monte-Carlo simulation is general in nature.

3)     Possibility of extreme events happening: As the distribution of risk factors is normal in the Delta-normal method the probability of extreme events happening is very minimal.  In the case of historical simulation the possibility of extreme events happening is only more relevant if it happened in recent history and the Monte-Carlo method due to its complete random nature accounts for these events completely.

4)     Implementation ease: The delta-normal method is easy to implement because it assumes a normal distribution. In Monte-Carlo simulation a huge number of iterations will have to be carried out to even get a reasonable result and hence it is very difficult to implement and the Historical Simulation VaR is somewhere in-between the other two methods.

5)     Communicability: The delta-normal method has got average level of communicability as compared to the Historical Simulation VaR which is very easily communicable. The Monte-Carlo method is very highly communicable in this respect.

6)     Precision: The variance-covariance method has a very high precision followed by the Historical Simulation method which is not very accurate for short period of time (windows) and the Monte-Carlo method predicts risk with high accuracy for a large number of iterations because as the number of iterations increase more and more possibilities of paths of rate movements have been accounted for.

7)     Major drawback of each of the models: As mentioned above the variance-covariance method has a drawback in that non-linear instruments cannot be accounted for by this method.  Also the assumption of perfectly normal distribution might not necessarily hold true as there is skew-ness and kurtosis associated with all the distributions.  This is very commonly referred to as fat tails. Historical Simulation VaR cannot account for events like spikes in risk factors (unusual events) and the variation in risk due to time. With Monte-Carlo simulation the major pitfall is that of running a risk with the financial model.