I might be wrong here but I'm not sure about one of the steps in this proof (ch30 p25-26) - after applying the chain rule, you end up with ((1/2)*Var(L) ^-1/2) * ( ∑ (2pi*Var(Li)) + ∑ 2pj*Cov(Li, Lj) ) where the red sigma ∑ is i= 1 to n and the blue ∑ from j= 1 to n excluding i. I don't think that red sigma should be included or am I missing something? When I tried to do this out I don't end up with the red summation, just a single 2pi*(Var(Li) (as all but the ith term should go to zero when differentiating with respect to pi). I also don't see how the final line would follow if the summation was included. Also two lines down from this there is a reference to "rho of L" for the Value of risk measure, is this meant to be F(L), and if not what is rho referring to?
Hi Alibaba Apologies for the delay in replying here. Having just worked through this, I am in agreement with you on both counts. That first summation should not be there and the errant rho(L) should be F(L). I'll put these into the corrections doc, thank you so much for spotting these. As a check, I've just tried it for the simplified case where: L = p1 * L1 + p2 * L2 and the risk measure = standard deviation is: F(L) = var(L)^0.5 = {p1^2 * var(L1) + p2^2 * var(L2) + 2p1 * p2 * cov(L1, L2)}^0.5 When I differentiate this with respect to p1, using the chain rule, I get: dF(L)/dp1 = 0.5F(L)^-0.5 * {2p1 * var(L1) + 2p2 * cov(L1, L2)} = 0.5F(L)^-0.5 * {2cov(L1, p1 * L1 + p2 * L2)} = cov(L1, L) / var(L)^0.5 Take care, hope all going ok with the revision? Anna
Thanks for that Anna, that's what I was getting when I did the proof out too. Revision is going ok I suppose, it's hard to know what to focus on - I'm half anticipating a very applied/maths question on something that hasn't come up before if they're looking to avoid examining bookwork, so just doing past papers and questions ad nauseam and hoping for the best.
Smashing, glad we get the same answer. I've now added to the Corrections doc and have just managed to sneak in the change for the 2021 version of the notes. Re the impending exam, I was expecting the same when I sat SP9 on 1st May 2020 but actually the paper was more bookworky than I've ever seen: Walker Review, bias, steps in running a model, risk measures from Mod 30, definitions of economic capital and risk taxonomy, definition and description of sensitivity / scenario / stress testing, ways to managing credit risk. So I would say it's still important to be familiar with the bookwork. I found time very tight back in May and being able to get the bookwork down quickly / know where it was in the course helped me a lot. Especially anything in bold font, ie Core Reading. Your approach of doing as many exam papers as you can, typed up in Word, is definitely the way to go. It feels like an epic task though doesn't it? The further back you can go the better as some things have started to resurface, eg BASEL II min capital requirement calculation. Also note Oct 2010 Q3 - question on a pandemic! Also, in case it's a useful suggestion ... I found it helpful to make lots of lists, eg of risks (eg operational risk broken down into many sub categories) and how to mitigate them using answers from previous exam questions to inform that list. Another list was a big picture one of things to remember to talk about in broader ERM questions along the lines of, "a company is considering introducing ERM ...' All food for thought Anna
Thanks Anna, I'll keep all that in mind. To be honest, the main thing I seem to struggle with in this exam is that I find the wording in a question misleading, give an answer they weren't looking for, and then get no credit for it. For the paper in the last sitting, I would have gone in thinking that RAROC etc is a "risk measure" given that this is how it's defined in the core reading, and that a "risk metric" refers to "qualitative and quantitative indicators of the level of risk in a specific part of the organisation". The core reading doesn't refer to RAROC, SHV, SHA etc. as anything but a risk measure, LAM also predominately uses this word in referring to these as well - and then when the examiners asked for "risk related metrics", were only looking for these risk measures, and gave no credit for more qualitative and quantitative indicators that by my understanding would fall under their own definition of risk metrics (e.g. loan to deposit ratio). I had similar issues with some of the other questions. I do feel like you need to write off about 20% of the paper from misleading questions with this exam - I feel like I'd struggle to overcome that no matter how much study I had done.
Not easy and I do empathise. I guess, where you sniff out some ambiguity, you may want to cover off multiple bases (but time consuming), or look for other clues, eg the peripheral info that was given in that part of the question on hurdle rates and prospective future growth rate, to try and place the question part in the course / core reading. Keep going, I have fingers crossed that a paper comes up that suits you better.
