Expected Shortfall

[caramel]

HI David
I was a little confused and after reading thr was another thread , I was wondering if this is another Garp error

From the handbook FRM exam 2003 question 5
Given the following 30 ordered percentage returns of an asset, calculate the VAR and expected shortfall at a 90% confidence interval
-16, -14,-10, -7, -7,-5, -4, -4, -4, -3, -1, -1, 0,0, 0, .........................
Ans was given as VAR 10 and ES 15
the 10% lower cutoff point is the third lowest observation which is VAR =10 , the ES is then the avg the of the observations in the tails which is 15

this is different from the below thread.

http://forum.bionicturtle.com/threa...all-and-coherent-risk-measures-market.4153/#e below thread post-16580

 

[caramel]

So David should I stick to the solution in the thread and not go with GARP on this one

 

[David Harper CFA FRM]

Hi caramel

Yes absolutely, it's an embarrassing error in the handbook. (Although I've submitted this to GARP before in another context, given the nature of so fundamental an error, I just submitted this thread here to GARP). You might infer that the thread, to which you link, is correct since we've discussed the issue there. In the above question:

• 90% VaR = 10, the 3rd worst loss, is acceptable. I would prefer GARP followed the assignments and use the 4th worst, but under a discrete (HS) distribution, lacking a standard, there are several correct answers: 3rd worst, 4th worst, or interpolation between 3rd and 4th. Put another way, lacking a definitinal standard of VaR in the discrete distribution, VaR due the fact that it is a quantile does suffer ambiguity in the discrete case
• But 90% ES is not ambiguous. The Q&A is incorrect. The 90% ES is the (conditional) average of the 10% loss tail, which is the average of the worst 3 (out of 30), not the worst 2. ES does not depend on the discrete calibration of VaR. The answer given is the 93.33% ES; i.e., average of the worst 2/30. The only correct answer for 90% ES is average(16,14,10) = 13.33. Thanks,

 

[cqbzxk]

Hi caramel

Yes absolutely, it's an embarrassing error in the handbook. (Although I've submitted this to GARP before in another context, given the nature of so fundamental an error, I just submitted this thread here to GARP). You might infer that the thread, to which you link, is correct since we've discussed the issue there. In the above question:

• 90% VaR = 10, the 3rd worst loss, is acceptable. I would prefer GARP followed the assignments and use the 4th worst, but under a discrete (HS) distribution, lacking a standard, there are several correct answers: 3rd worst, 4th worst, or interpolation between 3rd and 4th. Put another way, lacking a definitinal standard of VaR in the discrete distribution, VaR due the fact that it is a quantile does suffer ambiguity in the discrete case
• But 90% ES is not ambiguous. The Q&A is incorrect. The 90% ES is the (conditional) average of the 10% loss tail, which is the average of the worst 3 (out of 30), not the worst 2. ES does not depend on the discrete calibration of VaR. The answer given is the 93.33% ES; i.e., average of the worst 2/30. The only correct answer for 90% ES is average(16,14,10) = 13.33. Thanks,

Hi David, I get confused about ES, I met lot of practices before, for example, there is typical question:
Confidence level -----Tail VaR
95%--------------------- 3
96% --------------------3.25
97% --------------------3.6
98% ---------------------4
99% -------------------4.75
What is ES at 95% level?
3.25+3.6+4+4.75/4 or 3+3.25+3.6+4+4.75/5 which one is correct? thanks !

 

[cqbzxk]

the notes also said, the tail mass is divided into n equal slices and the corresponding n-1 VaR are computed..

 

[David Harper CFA FRM]

Hi cqbzxk, we just discussed this question here at http://forum.bionicturtle.com/threads/level-2-post-what-your-remember-here.5923/page-14#post-24224
... i don't have the source question, so i feel like it's unproductive to keep trying to figure it out

where is this question exactly?

 

[cqbzxk]

Hi cqbzxk, we just discussed this question here at http://forum.bionicturtle.com/threads/level-2-post-what-your-remember-here.5923/page-14#post-24224
... i don't have the source question, so i feel like it's unproductive to keep trying to figure it out

where is this question exactly?

Hi David, the question I post above was not from exam, it is from Notes "Estimating Market Risk Measures" Topic 1 my version is 2011, it seems that the notes only use (3.25+3.6+4+4.75)/4 = 2.003 to explain ES at 95%, this made me a little bit confuse,

 

[cqbzxk]

my confusion is that where is the 1/1-confidence ? suppose 1/5% * (x*f(x) + .....)

 

[David Harper CFA FRM]

that method is not computing an accurate ES. I guess, I don't have the source, it is using an approximation method: you can approximate the 95% VaR by taking the average of the any (N) VaRs in the tail, as but at 3 or 4 it's totally rough estimate. Averaging the (N) tail VaRs is an approximation shortcut (very inaccurate for low N) that does not bother with the effort to retrieve the accurate 1/signficance * sum of: (loss)*f(x). Thanks,