4

When returns follow an elliptical distribution (e.g. the Gaussian distribution), then minimising VaR and ES is equivalent to minimising variance. See https://people.math.ethz.ch/~embrecht/ftp/pitfalls.pdf. Then, the frontiers will be the same.


3

If you assume that everything is normally distributed, then you just divide by normsinv(95%) and multiply by normsinv(99%).


2

The Markowitz problem is an optimization problem of a series of Gaussian distributions (symmetric) with a variance-covariance matrix This is a common misunderstanding. Markowitz (mean-variance = MV) model do not require the Normal distribution of returns, even if such condition is optimal in some sense. The only necessary distributional condition is the ...


2

This is a result of the two fund separation theorem or mutual fund separation theorem. Any (optimal) portfolio choice will take place on the efficient frontier. In a Markowitzian world, the asset universe is fully characterised by first and second (co-)moments. Hence, for any performance metric, you would always be able to obtain "more return at a given ...


2

Something like the following is likely to be acceptable to whoever looks at your VaR methodology. Convert your historical (clean) price to yields of your bond (remember to use the right historical settlement date). I think for this exercise you can get away with ignoring the convexity and also ignoring the accrued, cost of financing, and other P&L due ...


2

There are a couple of point here. This: If we consider VaR = z-score * portfolio variance (assuming >mean is zero) is not quite right. In a Gaussian model (**) VaR = z-score * sqrt(portfolio variance) = z-score * (standard deviation of the portfolio) So your math actually works out. And in a Gaussian model scaling VaR or scaling variances is the same ...


1

I doubt this is publicly available, if you do not find it on the respective websites. It's their intellectual property after all. Moreover, I think these are all enterprise solutions. As such, I am sure any vendor you reach out to and show genuine interest will be more than happy to assist you. For example, if you use Bloomberg, just ask the help desk and ...


1

it's me again... So i find out what a negative shape parameter in Generalized Pareto Distribuition means and why it's not possible to calculate EVT with it. negative shape parameter means that the distribuition has a limit, not quite what you are looking for when fitting an extreme value theory model.


1

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


1

Yes, you can check the paper Entropic Portfolio Optimization: a Disciplined Convex Programming Framework in SSRN.


1

I know this is an old question, but I encountered this problem too, years ago, and the answer is that you can actually compute confidence intervals for VaR backtesting of overlapping returns. From what I understand, banks usually derive them with heavy Monte Carlo simulations (so they generate the overlapping returns a large amount of times and look at the ...


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