Conditional Value-at-Risk (Expected shortfall) - measuring expected extreme loss (Excel) (SUB) 

Hi Guillermo, and thanks for the kind words! Stay tuned for more videos on risk management or check the playlist: ru-vid.com/group/PLE4a3phdCOasYaGX5-FoUgkzr2W7G3ROv

Hi Ellie, thank you very much for your feedback! :)

Hi Tshego, and glad you enjoyed the video! As for your question, it is due to the fact that historical distributions of returns used in the historical simulation method are almost always more heavy-tailed than the normal distribution used in VCV approach, hence the discrepancy.

@@NEDLeducation Brilliant, thank you.

Hi Hayfa, and really appreciate the feedback! Thanks for the suggestion! We are considering doing some videos on the use of statistical software packages, particularly when we start moving into econometrics and similar topics, but I really cannot say right now how soon it will be.

Hi, and thanks for the excellent question! I am actually planning to release videos on various Sharpe ratio modifications using value-at-risk in particular, however it is most common to use modified VaR in the denominator in these instances. However, nothing prohibits you from using the CVaR instead, this is logically sound.

Hi Jordan, and many thanks for your feedback! You are correct that stock returns do not usually follow normal distributions, however when parametric VaR and CVaR are introduced the normality assumption is just the starting point. We have a whole Mathematical Finance playlist where we cover different approaches to stock return modelling using heavy-tailed distributions. In terms of VaR, one of the potential solutions to tackle non-normality (with its own shortcomings though) is Modified VaR (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-z61iEgUR9V4.html). And actually later today another video will be released covering how to approach parametric VaR with non-normal distributions, so stay tuned :) With regards to T-distribution, it by all means can be used to model stock returns (see for example ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-9n--CdMIaXc.html if you are interested), however if you try and estimate parametric VaR using T-distribution confidence intervals with a high number of degrees of freedom, it will generate results very close to what you would get in the normality scenario. Hope it helps and thanks again!

NEDL thanks you for your reply, it’s very interesting ! I gonna watch your videos about Modified VaR and The model stock returns, and I’m waiting for your video today ;). If I want to calculate the Monte Carlo VaR (with combined method historical and t-distribution) can I simulate the stock prices with a t-distribution and do it for 1000 scenarios, after that I used the historical method by Arrange my data in ascending order. For finish I do the average of the 1000 VaR. That’s a good solution ? Thank you !

Hi Mauro and many thanks for your feedback! Yes, VaR and CVaR are daily estimates, as required by Basel market risk regulations. To estimate VaR or CVaR for other frequencies, you can just scale returns and volatilities for the time period you are concerned with. For example, for monthly VaR you can scale your return and volatility to a 21-day period (as there are typically 21 trading days in a month). Please check out our video on volatility scaling if you are interested :) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-_z-08wZUfBc.html

Hi George, and thanks for the question! This is due to the fact Z-stat is negative here.

Hi Deepak, and thanks for the question! Yes, it can, just plug in your portfolio returns instead of stock/index returns.

Hi Pheng, applying CVaR for a portfolio of assets is very easy, just substitute the return series here for returns of a portfolio you wish to simulate. Hope it helps!