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 our CEO, David Harper, posts weekly. This week, we’ve included our newest FRM practice questions discussing country risk and the ISDA Master Agreement, new YouTube videos covering fixed income and a TI BA II+ tutorial, helpful FRM forum discussions, and more! Have a great week!
1. Valuation & Risk Models: P1.T4.914. The components of country risk include political, legal and economic structure (Damodaran) https://trtl.bz/2Gb72x1
2. Credit Risk Measurement & Management: P2.T6.905. ISDA Master Agreement and credit support annex (Gregory Ch.6) https://trtl.bz/2GaCDik These questions continue a long slog through a fresh pass of Jon Gregory’s counterparty credit risk (CCR) super-cluster. Personally, I have two criticisms: first, per previous feedback to GARP, I believe Gregory is over-assigned. I just mean that, while the topic, of course, is important, there are just too many learning objectives (LOs). There are almost three pages of LOs! Second, and not unrelated, while Gregory is the authority on CCR, even this latest third edition suffers some disorganization: many of the sub-topics are effectively spread out in multiple places, and consequently repeat. In any case, here are three new questions about collateral. In particular, I wanted to help reinforce your understanding of the (one-way? two-way) credit support annex (CSA) and the valuation agent. Details, to be sure, but real-world details!
1. Valuation & Risk Models: Fixed Income: Arbitrage to exploit violation of law of one price (FRM T4-24) https://trtl.bz/2GbJMyR This arbitrage is from Tuckman’s first introductory chapter, so most readers are taken aback by the apparent complexity. To exploit a mid-priced bond here requires four positions, for a grand profit of less than seven cents. It barely seems worth it until Tuckman reminds us “while a 6.5-cent profit may seem small, the trade can be scaled up: for $500 million face of the 3/4s, which would not be an abnormally large position, the riskless profit increases $500,000,000 * 0.065% or $325,000.” But to me, the importance of the exercise is that it really cements our understanding of the Law of One Price.
2. Calculator Tutorial: TI BA II+: How to compute future and present value with different compound frequencies (TIBA2-04) https://trtl.bz/2G99MuO I hope this video helps clarify compound frequency. Discount factors are exact (“they never lie”) but we can’t exactly retrieve the present value of a cash flow if we are told to (eg) discount at 8.0% over three years: the answer varies based on the compound frequency. Fluency with compounding forward and discounting back is an essential tool in the analyst’s toolkit
1. When is it optimal to early exercise? David Kim found a problem with one of my question’s choices (here at https://trtl.bz/2GcAnr2) about the optimality of early option exercise. Our forum has discussed this interesting dilemma for years; ie., when exactly is it optimal to exercise?. The feature can be viewed as an option embedded in an option. As is so often the case, precise language is important. The thread includes a small model that our CEO, David Harper, built that quantifies the trade-off. In the case of an American call on a dividend-paying stock, the choice is between the exercising early to collect dividends versus the value of waiting. The value of waiting is classic finance: Strike minus PV(Strike) = K*[1-exp(rT)].
2. Convexity: We had a couple of conversations above convexity, including Malz’s characterization of a securitization’s equity tranche as positively convex, a senior bond tranche as negatively convex, and the mezzanine tranche as mixed. See https://trtl.bz/2Gc1vGD. In the context of the vanilla bond asset class, forum member, abhinavkhanna, and CEO, David Harper, had a clarifying conversation about convexity https://trtl.bz/2Ggksru. Convexity is a second derivative such that positive convexity is when the first derivative (aka, slope of the tangent line) is increasing. Hopefully, you can visualize, per the curvature of the classic price/factor relationship, how vanilla bonds (i.e., bonds with embedded options) and options exhibit positive convexity. The slope of the bond’s tangent (to the price/yield curve) is negative but increasing with yield; hence its positive convexity! This slope is mathematically simple: ∂P/∂Y = -D*P. If negate this, we get dollar duration = D*P. Then if we divided dollar duration by the number of basis points in one unit (100.0%), we get DV01 = D*P/10,000.
3. Credit value adjustment (CVA): Forum member, nansverma, asked some good questions about Jon Gregory’s credit value adjustment (CVA): https://trtl.bz/2UELCm7 Did you know Jon Gregory is a forum member? There were some superficial formula changes between his second and third edition, with respect to CVA. But it should not throw off a fundamental understanding of CVA, which translates the fundamental expected loss formula, EL = EAD*PD*LGD, into an expression over time. Per one of the good questions, the default probability in the expression in unconditional. We were early to understand this feature: we informed an edit to one of GARP’s practice exam questions on CVA.
1. Consolidated Basel Framework: The Basel Committee has collected its global banking standards into one “consolidated” sub-site at https://www.bis.org/basel_framework/. For those of us who have studied the regulations over the years, this is an overdue but welcome development. Previously, to look up regulations (in order to answer technical subscriber questions), CEO, David Harper, often had to link-jump through a chain of consecutive standards. BIS even recorded a YouTube video explainer at https://www.bis.org/bcbs/publ/d462.htm. (yes, that’s correct, BIS has a YouTube channel, so, um, anything is possible?).
2. Stationarity explained: On the knowledge area of Time Series Analysis, the FRM assigns four chapters from Diebold. These are notoriously difficult because they lack scaffolding: ideally, you should read the four first unassigned chapters in order to follow some of the terminology. In particular, the definitions of stationarity in Chapter 7 assume prerequisites. Last week, Shay Palachy of Toward Data Science wrote one of the better introductions to stationarity that we’ve read: https://trtl.bz/2GiKHgT e.g., “In the most intuitive sense, stationarity means that the statistical properties of a process generating a time series do not change over time. It does not mean that the series does not change over time, just that the way it changes does not itself change over time.” His simple images, in particular, Figure 6, are really helpful.
3. Who is hedging climate change and disrupting insurance: Finally, we wanted to share two provocative articles from Sunday’s New York Times: How Big Business is Hedging Against the Apocalypse https://trtl.bz/2GbsXnO and: A.I. Is Changing Insurance https://trtl.bz/2GfxwgY.