Assessing VaR and Event Risk Aggregation Without Double Counting

Summary

The document asks whether subtracting value at risk from an event-risk estimate is a valid way to avoid double counting before combining the two in a correlation-based risk formula. It describes a proposed adjustment that reduces the event-risk amount by VaR, then aggregates the adjusted amount with VaR. A numerical illustration shows that this convention produces a lower total risk estimate than the original aggregation.

The event-risk measure is described as taking the larger upward or downward shock implied by market and macro indicators, which do not use historical returns in the same way as VaR. The document provides no statistical validation or supporting literature, and it does not establish that the risk components overlap by exactly the amount of VaR. Subtraction may therefore change the aggregate without demonstrating that the resulting measure better represents joint losses. The central issue is how to model dependence and overlap between the historical-loss and scenario-shock measures; the question remains unresolved in the supplied text.

Key ideas

• The proposed method subtracts VaR from event risk before aggregating the two risk estimates.
• The example shows that this adjustment lowers the reported combined risk.
• The event-risk indicators use market and macro shocks rather than historical-return VaR inputs.
• The document does not provide evidence that the subtraction quantifies actual overlap or avoids double counting.
• A defensible adjustment would require a model or evidence for how the two risk components overlap and depend on each other.

Tags

# Does it make sense to subtract VaR from spot shocks?


# Does it make sense to subtract VaR from spot shocks?












I have a model to compute the Event Risk (in dollars) from a shock to the spot price of an asset. I also have the 10-day VaR PnL for the same assets returns. These two numbers are then aggregated to find the total risk in dollars:

$$\sqrt{\text{VaR}^2 + \text{Event Risk}^2 + 2\rho_{\text{VaR, Event Risk}} \times \text{VaR} \times \text{Event Risk}}$$

(assuming some correlation $\rho_{\text{VaR, Event Risk}}$ between the VaR and Event Risk model)

The idea of subtracting the VaR from the Event Risk before they are aggregated as above, is that the event risk should be computed just for shocks not captured by the VaR to avoid double counting when computing the total risk. This makes the total risk in the formula above smaller.

Example:

```
Current Scheme

VaR    Event Risk    Total Risk (rho=0.2)
10     22            25.92

Proposed VaR subtraction

VaR    Event Risk    Event Risk - VaR    Total Risk (rho=0.2)
10     22            12                  17.09
```

Does it make sense to do this or is there any literature on the matter? Is there some statistical way we could show that the subtraction is valid?

EDIT: The event risk model essentially takes a max (shock up) / min (shock down) between market and macro implied indicators. The indicators do not consider historical returns as a VaR calculation would.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.