# 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.

• what you are not mentioning is how the event risk number comes about. i think the answer will depend on that – ZRH Feb 8 at 11:38
• then i struggle a little with the notion of aggregating two things with entirely different underlying concepts – ZRH Feb 10 at 20:16