Variance/Covariance Approach 
Variance/Covariance Approach
Prerequisites
In order to calculate VAR using the variance/covariance approach, you need the volatilities and correlations of the risk factors. These can be determined from historical price changes or imported to the system from third-party vendors. In addition to calculation by the system using the statistics calculator, the RiskMetrics™ data record from JP Morgan can be imported using a file interface or a datafeed.
During the calculation, the variances and correlations for a certain holding period are estimated with the help of the statistics calculator.
If you want to calculate value at risk for a holding period that differs from the holding period of estimated variances, you can carry out a conversion to the holding period of the value at risk. For relative or absolute changes this is done in a linear way. For logarithmic changes, the conversion is carried out in accordance with the root-t-method.
You can, for example, transform a one-day standard deviation into a ten-day standard deviation by multiplying it by the root of 10.
Integration
The value at risk amounts are displayed using the risk and portfolio hierarchies.
In the delta approach, the aggregation across the risk hierarchy is based on the assumption that you can add together the NPV differences according to the +/- sign. For each portfolio on a risk factor level, the system calculates the reactivity of the NPV to the risk factors, independent of the historical market prices.
In the delta-gamma approach, non-linear terms of the second order (gamma positions) are additionally taken into account at the risk factor level. This gamma position can be used as a key figure in drilldown reporting.
Scope of Functions
The system determines the value at risk for a risk factor by calculating the value change of the position that occurs with an isolated price change of this risk factor.
The value change of the position is calculated by determining the delta position in the risk factor and multiplying it by the standard deviation of the risk factor. The delta position is calculated by the price calculators.
The sign (+/-) of the value at risk for risk factors is the same as the sign of the delta.
The aggregation of VAR along the risk hierarchy is controlled by the aggregation type of the risk hierarchy. The following aggregation types are available:
Aggregation type |
Meaning |
Totaled (according to +/- sign) |
For each consolidation level of the risk hierarchy, providing the same aggregation type is set on the nodes under the consolidation node, the value at risk is determined from individual risk factors using the total. If this is not the case, then the value at risk is determined from the lowest level of the risk hierarchy Þ positive and negative values. |
Totaled (absolute amounts) |
For each consolidation level in the risk hierarchy, the value at risk is determined from the individual risk factors using the total of their absolute amounts Þ positive value. |
Differentiated |
The values at risk of the underlying risk factors are totaled separately according to whether they are positive or negative amounts. The larger of the two values represents the value at risk Þ positive value. |
Correlated |
For each consolidation level in the risk hierarchy, the value at risk is determined from the individual risk factors by means of their correlation Þ positive value. |
Aggregated (directly preceding nodes) |
For each consolidation level of the risk hierarchy, the value at risk is calculated from the nodes of the preceding risk hierarchy nodes by totaling, without taking into account which aggregation types exist in the preceding node Þ positive and negative values. |