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Jorion Chapter 6 Question 10


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

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.

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

David Harper CFA FRM
Staff member
Hi @luxsns@gmail.com 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://www.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)


Nicole Seaman

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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?

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Hello @ziminli1228

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David Harper CFA FRM

David Harper CFA FRM
Staff member
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!