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Thank you @Detective, will give it a go

Awesome thank you @Detective, Is it possible to derive the actual distribution function from the above quantile function and not the other way round? I am not too sure if the above formula is exactly correct so i will have to double check this.

Thank you @Detective, I just tried to prove it for myself, however this seems to be a bit tricky. Appreciate your help

Thank you @Detective. This is a Market Risk problems I am trying to tackle and the actual problem was to show that Variance is not a coherent Risk measure however I have tried to check every assumption of coherency for Variance so I can better understand it myseld.

Thank you @Detective, I thought the same about Z=Y-X, but unfortunately this was the best I could come up with mathematically. Analytically one could say that in case the Variance is a measure of risk and X is 'bigger' (riskier) than Y, than Var(X)>Var(Y), But I am not too sure if this is...

Thank you @Detective . The function appears to be correct as it is presentes as a quantile function. Would ah inverse of an inverse just be an actual CDF ? In this case F=ln((alpha)/(1-alpha)) Am I correct here ?

@David Harper CFA FRM , thank you very much. This is confirming my uncertainty. There is plenty of papers assuming that SD and Variance are monotonous and some give some analytical proof but none of them actually give a good math proof. Is it fair to say that it could be monotonous or not for...

@Detective, Thank you very much. I have tried to assume that rvs X>Y and therefore Z=X-Y>0 It follows that Var(Z)=\[ {sigma^2}_x-2sigma_{x,y}+{sigma^2}_y>0 ]. It looks OK to me, but I am not 100% sure Could you share your thoughts please?

What is the best way to prove that Variance is monotonious as a risk measure?

Sorry for misunderstanding, I am not exacly preparing for the exam just yet, but doing my frm masters. this question came up in past exams so I am trying to make sure I understand it all correctly

Great, thank you @Detective, I just currently study FRM and it is part of my preparation so not sure Tail VaR is exactly the same as ES in context of Market Risk ?

Thank you @Detective, just a couple of questions: Why do I pick an area of 0,45 for VaR? I understand I cannot standardize this and take the value from the tables? Is Tail VAR exactly the same as Expected Shortfall? Why is the integral in ES formula multiplied by 20? Thank you so much for...

Hello, I am struggling to find an approach to the following: Probability density function of the daily portfolio loss L: How to calculate VaR and Tail VaR with a confidence level of 0.95? Can someone help please? Thank you

Awesome thank you David

Hi David, Thank you for your answer. The only thing I cannot understand is how I can justify excluding drift from the proof ? Thank you

Mvar