# VAR interpretation

I definitely struggle to understand the following interpretation of VAR (value at risk) provided by Jorion

$$VAR(c)=E[X]−Q(X,c)$$

where $$X$$ is a random variable, $$E[X]$$ its expected value, $$Q(X,c)$$ the quantile of its distribution such that the associated probability is c.

Isn't VAR the quantile itself? Why should it be viewed as a deviation from the mean?

• Two reasons: 1) "Risk" is interpreted as deviation from what you would expect. 2) If VAR were equal to the quantile you would not need a new word for it.
– g g
Nov 18 '20 at 15:20

VaR is the quantile of the loss distribution but $$X$$ in your post no doubt denotes the the future value of the portfolio. If $$E[X]=10$$ (expected future value of portfolio) and the quantile $$Q(X,c)=4$$ for some $$c$$, then your VaR, that is the lost that represents the outcome at the quantile, is $$VaR(c) = E[X] - Q(X,c) = 10 - 4 = 6$$