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P2.T7.307. Operational risk distributions

Fran

Questions:

307.1. Analyst Sally develops the following model for her bank's daily operational risk losses, which includes the assumption that the daily frequency is a Bernoulli with probability of only 6.0% (several minor losses are expected but model ignores losses below $3,000) and, further, an assumption that loss frequency and severity are independent: Which is nearest to the estimate of daily unexpected loss (UL) with 99.0% confidence? a.$2,017
b. $4,633 c.$9,754

David Harper CFA FRM

David Harper CFA FRM
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The link (Here In Forum) goes to the source question with the answer, but it's protected to paid members. We try to be helpful, so here is the answer I have:

Expected loss = 6% * (2%*80,000 + 5%*20,000 + 7%*10,000 + 12%*5,000 + 74%*3,000) = $367.20. The worst 1.560% tail of this distribution includes the worst four tabulations:$80,000 loss with probability = 6%*2% = 0.120%;
$20,000 loss with probability = 6%*5% = 0.300%;$10,000 loss with probability = 6%*7% = 0.420%;
$5,000 loss with probability = 6%*12% = 0.720%;$3,000 loss probability = 6% * 74% = 0.440%.

As the $5,000 loss falls at the 1 - (0.120% + 0.300% + 0.420%) = 99.160% quantile, and The$3,000 loss falls at the 1 - (0.120% + 0.300% + 0.420% + 0.720%) = 98.440%, it follows that:
the 99.0% quantile occurs at the loss of $5,000; i.e., where the tail "to the right" is only 0.840%. Therefore, UL at 99.0% = OpVaR of$5,000 - EL of $367.20 =$4,632.80

Then a customer asked if we can find it by counting up "from the left" instead of "from the right", which you can:
Hi AlokS, Sure, you can work it from the other direction (from zero), which is:
94% prob of loss = 0
6%*74% = 4.44% = 0.04440 prob of loss = $3,000 6%*12% = 0.72% = 0.00720 prob of loss =$5,000
which gets us to the 99% VaR as 94%+4.44%+ 0.72% = 99.160%, so 99% VaR is \$5,000
... The rest must sum to 100%

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New Member
Thank you very much for your help! I plan to register for the November 2013 FRM Part 1 exam and now I`m trying not only to repeat and revise but to read as much relevant literature as I can. Exam is very vast and the main problem is - the boundaries of the FRM program are very vague and obscure. Thank you very much David!

Thanks

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