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# Week in RiskWeek in risk (April 7th)

#### David Harper CFA FRM

##### David Harper CFA FRM
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1. Sample statistics versus population parameters: sample variances (when to divide by n -1?) and standard errors are queried every year by new Part 1 candidates. We talk about it here https://trtl.bz/2FXFcnM. The FRM is grounded in econometrics and statistics where a fundamental first step is distinguishing between the one "true" population that is unseen and the many various samples that might be taken from it, each generating effectively random variables like the sample mean. Most realistic situations are samples; e.g., when we observe ten or 500 trading days, those are samples! It's more academic, un-realistic and exam-like to be given a population assumption. For example, to be told that daily returns are normally distributed with volatility of 0.5% is to be given a fully-specified population's distribution. Standard errors do not exist when we've got the benefit of a population; a standard error is a standard deviation, but of sample mean that itself is a random variable.

2. Tricky terminology (Implied volatility versus vega; par yield): Speaking of classic terminology issues, two were asked about this week. First, I like yuwaising's question https://trtl.bz/2FUumis: if the implied volatility smile is flat, what is the implication on option vega? Second, Eric asked about the par yield (which is reviewed in both Hull and Tuckman) https://trtl.bz/2FVYB8P Tuckman actually uses par yields as key rates in the multi-factor key rate shift technique. It's painful to master par yields, especially in key rate shift technique, but it's a fine way to wrap together the key interest rate relationships.

3. Extreme value theory (EVT) derivations : Stuart and I geeked out a bit here https://trtl.bz/2FWv66B when we solved for certain of Dowd's extreme value theory (EVT) formulas. Johnny asked, are the EVT VaR or EVT ES formulas testable? I replied: "The EVT VaR/ES formulas are not very testable (low or no testability). How do I know? Funny you should ask! Years ago the LO read 'Compute VaR and expected shortfall using the POT approach, given various parameter values,' but these were among a set of compute/calculate verbs that we lobbied to soften given their inherently low testability. So today the EVT reading is devoid of calculate/compute action verbs; e.g., Describe the peaks-over-threshold (POT) approach." Yes, that's right, BT played a role over the years advocating to soften certain LO action verbs--from calculate to something qualitative--by providing feedback to GARP that the LOs were unrealistic time-sinks to candidates.

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