Jorion Chapter 6 Question 10

[[email protected]]

Hi David,
For the Jorion question, can you provide the equation 6.3? Do we need to know this for the exam?
Thanks


Question 10:

A bank reports 6 exceptions to its 99 percent VAR over the last year (252 days), including 4 that follow another day of exception. Compute the likelihood-ratio tests, and discuss whether unconditional and conditional coverage is rejected.

Answer:
We build an exception table as in Table 6.5.

The fractions of exceptions is 6/252 = 2.4%, compared to the target of 1%. Using Equation (6.3), we find = 3.498, which is less than the chi-square cutoff point of 3.84, so we do not reject the hypothesis that there is no bias. From Equation (6.4), = 25.837, which is too high. So, it seems that there is bunching

 

[David Harper CFA FRM]

Hi @[email protected] No, you clearly do not need to know Jorion 6.3, it is beyond GARP's general-audience capabilities with zero chance of being directly tested (something I rarely assert). I copied it below and, in case it is helpful, here is an XLS https://www.dropbox.com/s/xgwvpbdenhkdqtu/0121-jorion-ch6-eoc-10.xlsx?dl=0
... the answer is retrieving the critical chi-square value (cutoff) of 3.84 with =CHISQ.INV(0.95, 1) per "which is asymptotically (i.e., when T is large) distributed chi-square with one degree of freedom under the null hypothesis that p is the true probability." i.e., the VaR is 99.0% but the statistical backtest confidence is apparently 95.0%. Thanks!

(this is a copy of the "Ch6-backtest-intervals" sheet in the workbook at the https://learn.bionicturtle.com/topic/learning-spreadsheet-jorion-chapter-6/ where I simply colored cell E29 that produces the given answer of 3.498; the cutoffs in the exhibit are not yet dynamically linked, I just haven't gotten to it yet, but this is en route to rendering Jorion's Table 6-2)

 

[ziminli1228]

I was going over the practice questions and got stuck with the equation 6.3/6.4, could you please help me with that? How was LR derived?

 

[Nicole Seaman]

I was going over the practice questions and got stuck with the equation 6.3/6.4, could you please help me with that? How was LR derived?

View attachment 1754

Hello @ziminli1228

Please note that I moved your question here where this has already been discussed. Please make sure to use the search function in the forum before creating a new post. With over a decade of forum discussions, it is likely that your question has been answered already. This prevents duplicate posts throughout the forum regarding the same question, and makes it much easier for our members to get answers quickly

Thank you,

Nicole

 

[David Harper CFA FRM]

Hi @ziminli1228 These test statistics are really tedious. For the first time, I've captured them into an Excel (XLS) so that we can eventually improve on Jorion's own answer: https://www.dropbox.com/s/281907dztx7s8i7/0815-hull-eoc-6-10.xlsx?dl=0 The screenshot is below, I first ensured that the answer matches Jorion's JPM example in the text, which it does. It's so tedious, I'm surprised I got it right on the first try. I don't have current time to evolve the XLS into more helpful text, but I've tasked myself to eventually do that. I hope this is currently somewhat helpful at least. Thanks!