In my experience, a VaR or CVaR portfolio optimization problem is usually best specified as minimizing the VaR or CVaR and then using a constraint for the expected return. As noted by Alexey, it is m... Read More

By definition, your loss cannot be positive, so you'd set the VaR to zero. But it really depends, on how you calculate your VaR. If you calculate your returns, sort them and look at the 5% quantile (... Read More

The answer to your question is no. Value at Risk is not additive in the sense that $\text{VaR}(X+Y) \neq \text{VaR}(X) + \text{VaR}(Y)$. But I guess your question is more to aimed at finding a formul... Read More

If $z\alpha$ is the so-called standard normal $z$-score of the significance level $\alpha$ such that $$ \frac 1 {\sqrt{2\pi}}\int{-\infty}^{z\alpha} e^{-\xi^2/2}d\xi=\alpha $$ and we assume normality... Read More

EVT has pluses and minuses, but (under certain conditions) provides the best estimate of extreme quantile returns in a portfolio given the data available. Probably the simplest and easiest way to do... Read More

Here is the excel formula with steps: =NORMSDIST((NORMSINV(0.02)+NORMSINV(0.999)×SQRT(0.1))/SQRT(1−0.1)) =NORMSDIST((−2.054+3.09×SQRT(0.1))/SQRT(1−0.1)) =NORMSDIST(-1.135) =12.8% They keep changing t... Read More

Standard (read: regulators will accept it) could be a one day, 99% VaR calculated with two years of historical data. A minimum of one year of history is needed although this is not the norm. Typicall... Read More

To answer you question "is it because X is a mixture of a continous and discrete Random Variable" : the answer is no. The mean reasons are (1) the sample size (which is limited / countable) (2) the f... Read More

I'm guessing you're simulating rate curves etc. inside your system, and you want to reprice your instruments over the simulated curves using QuantLib. In this case, most of the logic is in your syste... Read More

Yes, for futures I would use the Notional Value of the contracts for example Number of Contracts times 250 times S&P level for the big S&P futures, and similarly for other futures (50 for mini S&P, 1... Read More