Summing up two VaRs

I know that normally you can't just add two VaRs straight ahead and you need to use the formula with the sum of squares and the square root. However, in the marking scheme for the task in the image two values at risk are added without any squares and root. Can anybody explain why it is valid in this situation?

P.S. All the calculations in the task are performed for exchange rates of 1.23 and 1.4, not 0.4 and 1.28

• @noob2 : If they are perfectly uncorrelated, the total risk would be smaller than the sum of risks. – Kermittfrog Mar 24 '20 at 10:20
• You are right of course. :\$ – noob2 Mar 24 '20 at 10:22

1 Answer

Without any additional information, and disregarding potential problems of VaR subadditivity, adding VaR figures is usually deemed conservative. For a meaningful risk measure, we usually require

$$Risk(X+Y) \leq Risk(X) + Risk(Y)$$

In your example: Simply adding the VaR figures per currency is sufficiently conservative, if no correlation is assumed. Another (implicit) assumption could be that the risk drivers (i.e. the exchange rates) are (again: implicitly) assumed to be perfectly correlated.

• Thanks for your help! – ecfinstudent Mar 24 '20 at 16:12