In this chapter, we shall study how value at risk (VaR) is aggregated bottom up—that is, measured at the most elemental deal level and then progressively aggregated up into portfolios and then into business lines. Generally, if VaR is computed using scenarios or simulations, the aggregation is done by adding PL vectors by scenarios. In the parametric method, VaR is aggregated by variance-covariance matrix multiplication. In both cases, the correlation structure is inherent and manifested as a lower overall VaR (risk diversification).
VaR reporting usually includes explaining where the risk is coming from. This VaR decomposition involves slicing the VaR number into its component parts. Depending on the needs of the risk controller, the breakdown can be by portfolio, by risk factor dimension, by business line, by bank subsidiary, or even by deal at its most granular level.
VaR reports are typically generated prior to the beginning of each trading day for position as of the end of the previous trading session. Normally, reports are custom made for various users—traders, risk controllers, top management, and regulators—and will show a relevant degree of detail and risk decomposition.
For illustration purposes, we shall use the hsVaR model as specified in Table 4.6. Six test deals (see Table 6.1) are booked into three portfolios. In practice, a large bank may deal in hundreds of thousands of deals booked in a vast array of portfolios. ...