**Welcome to our Week in Risk blog! Stop by our forum to join in on the FRM discussions, and visit our YouTube channel to view in-depth videos that David Harper posts weekly! This week, we’ve included our newest FRM practice questions discussing key rates and termination events, new YouTube videos covering fixed income and a TI BA II+ tutorial, helpful FRM forum discussions, and other risk articles that we hope you will find interesting. Have a great week!**

**1. Valuation & Risk Models: **P1.T4.913. Key rates versus partial-01s versus forward-buckets (Tuckman Ch.5) https://trtl.bz/2UkQSeo *Our *

**2. Credit Risk Measurement & Management: **P2.T6.904. Trade compression and termination events (Gregory Ch.5) https://trtl.bz/2UjSZiL *From our CEO, David Harper: “As a visual and math nerd (is that a designation?), I’m a bit fascinated by Gregory’s network node graphs. Question 904.2 contains my own tweak of his simple trilateral scenario. I freely admit that I got a bit sidetracked by trade compression solutions. Thankfully, his heuristic is dead simple (I won’t give it away here), so simple that I did not trust it for about an hour! Also, I really had to do a double-take when it comes to his calculation of total notional for each scenario (that’s an intentional pun, btw).”*

**1. Valuation & Risk Models: **Fixed Income: Twists are steepening or flattening of the yield curve (FRM T4-23) https://trtl.bz/2G5Yd94 *CEO, David Harper, begins the study of fixed income risk with the most popular metrics: duration, convexity, and dollar value of ’01 (DV01). These risk measures are helpful because they simplify interest rate risk which in inherently complicated by the fact that an interest rate curve has many maturities. These are yield-based measures. That is, we are really using yield-based duration and yield-based DV01. So what is the essential simplifying assumption we rely on when using these yield-based measures? It is the assumption that a shift in the rate curve will be parallel. That is the weakness (and the strength of simplification). While there can be many non-parallel shift, Fabozzi says two are most common: twists and butterflies. A twists is when the curve steepens or flattens. This video illustrates exactly what we mean when we say the curve steepens or flattens.*

**2. R Programming: **R Programming Introduction: Subsetting (R intro-06) https://trtl.bz/2OVjaWS *Subsetting is one action we take in almost any data analysis. It is when we ask to retrieve some chunk of the overall vector, list or dataframe*.* R has three subset operators: single bracket (“[“), double brackets (“[[“), and dollar sign (“$”). In this video, David replicates Hadley Wickham’s super simple examples of how we subset. David is also fond of the old-school subset() command because it really spells it out.*

**3. Calculator Tutorial: **TI BA II+: How to compute bond price or yield when the settlement date falls on coupon date (TIBA2-03) https://trtl.bz/2KszjVp *There are two ways to price a bond with the calculator: using the built-in bond worksheet, or using the time value of money (TVM) functions (i.e., N, I/Y, PV, PMT, and FV). In this video, CEO David Harper shows you how to use the set of TVM to quickly find the price or yield of a bond. Notice that the approach is: input four, solve for the fifth. Maybe the most important first step is to simply decide on the length of each period, is it one year, six months (aka, semi-annual), quarterly, or daily? Then remember your output will solve in the same “periodicity.” In general, we want to keep the defaults of P/Y = C/Y = 1. Finally, realize that you are implicitly using discounted cash flow (DCF) here, so the bond’s returned price is the full (aka, cash) price, not its flat price. *

**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. 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.

**3. 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.

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