We understandably get a lot of questions about how to calculate discrete VaR since different LRM readings define it differently. Our stance on how to approach discrete VaR has been evolving as we’ve seen more examples of how the LRM exam committee has been grading questions involving VaR.
Right now, the most practical advice I can give is to throw out any academic interpretations of VaR you may see on or off syllabus and go with the “5th worst” approach. This means that if you have 100 results sorted best to worst, the 95% VaR = 96th result. This is technically the 96th percentile and not the 95th percentile, but it is consistent with recent LRM graders’ opinions on how you should calculate discrete VaR.
Going with the first result “inside” the tail area is also conservative. It means you have enough capital to avoid ruin > 95% of the time rather than >= 95% of the time, so to speak.
You can obviously generalize this beyond 100 scenarios, but this is the most practical way I can think of to describe it right now, and I think it will work on the exam with 99.9% confidence (OK, that’s a bad joke).
Related to this, CTE would be the average of the 5% worst results (average of scenarios 96–100 in the example above). Other names for CTE include TailVaR, expected shortfall, CVaR, etc.