1
$\begingroup$

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?

$\endgroup$
1
  • $\begingroup$ 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. $\endgroup$
    – g g
    Nov 18 '20 at 15:20
1
$\begingroup$

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 $$VaR(c) = E[X] - Q(X,c) = 10 - 4 = 6$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.