VaR(X ) = -t where P(X < t) = p and VaR(X ) = t where P(X < -t) = p are these the same? What is the verbal interpretation for each, esp for the second?
Yes - the only difference is what you consider to be a negative - ie if you describe the value at risk as a "loss", then it must be a positive amount. Or you can write it as if it were a cashflow - in which case, it would be negative (normally).
