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Hi @nickkl Since we do have so much reference material already on Mac vs. modified duratoin, per Nicole's help, I don't want to repeat too much now. But briefly this may help: Macaulay duration is the bond's weighted average maturity, where the weights are PV cash flows as a % of price (itself...

@tattoo yea, it's confusing because the (t) has different roles: the exponent should be 2*Δt = 2*0.5 = 1.0, where Δt = 2.5 - 2.0; or the exponent can just be omitted altogether because it is just 1.0 in this case were we are retrieving a six-month forward rate under semi-annual compounding (our...

Hi @tattoo The final cash flow includes two components, the $100.00 par plus the coupon. The PV of the final cash flow is given by (100 + 100 × 0.75%/2) × 0.99135; i.e., the final (FV) cash flow is return of the $100.00 plus the coupon amount of 0.75%/2*100. However the formula nevertheless...

Hi @Matthew Graves great points and advice, thank you! Like you, I find the exponentiation of x/2*4 above confusing. I used this example in a recent LinkedIn post (here https://www.linkedin.com/posts/bionicturtle_frm-riskmanagement-frm-activity-6595354453270949888-jgzr) to illustrate the...

Hi @FutureFRM We have already much discussion on this topic of implied forward rates (e.g, this may be helpful https://forum.bionicturtle.com/threads/shortcut-to-forward-rates-if-you-have-bond-prices.4927). There is only one concept here (ie, the rollover comparison at the top of your post...

@tattoo (cc: @Nicole Seaman ) 1. You and @Sixcarbs are correct, thank you! There is a typo in the R27 Study Note, page 6, in the 3rd paragraph, instead of "(p = 0.6523)" it should read "(p = 0.5503)" to match the exhibit, as follows: 2. In your binomial, it looks like you are discounting with...

I don't know that i've ever seen it explicitly explained why maintenance margins are typically 70% to 80% of initial margins, but maybe the reason is just operational: if maintenance were 100% of initial, then you only need a price drop (assuming a long position) in the first day to immediately...

Hi @akrushn2 You should know the formula that determines binomial up/down as a function of volatility, but the phrase "The stock price can go up or down by 20% each period" is a very common way to describe the (alternative) binomial step pattern; e.g., it's used 2 or 3 times in GARP's 2019...

Hi @anisapassfrm I think 100*0.06-90*0.07 = -0.3 is the expected change in surplus, ΔS, such that 10 surplus - 0.3 = +9.7 is the expected surplus. Thanks,

Hi @isagasta It's what i wrote above. Consider the example CF implied by a 20-year 2% semi-annual pay coupon bond will have a CF of somewhere around = -PV (6%/2, 20*2, $100*2%/2, 100) = $53.77 = about 0.5377. The short's motivation is simply to buy the cheapest bond and deliver it (getting...

Hi @isagasta By "more responsive" I think I simply meant "higher duration" and by "higher duration" I meant to summarize "low-coupon, long maturity" bonds. Below is what Hull says but my annotations [] are inserted: otherwise, the basic idea is articulated above in detail at...

Hi @diemhuongpham Interesting. The question requires that we make an assumption (it makes the assumption) that if the bonds have the same rating, then the must have the same yield (aka, yield to maturity). It's important to understand why equivalent ratings do not (necessarily) imply equivalent...

@Nicole Seaman The difference is "to a long position" in choice (b): "b. The roll return (roll yield) is profitable to a long position during an inverted (backwardation) futures market" .... most people haven't noticed! Thank you,

Hi @tattoo Yes, you are correct about question 4 on page 37 of R19 (cc @Nicole Seaman ): it had already been spotted and fixed in the source (see https://forum.bionicturtle.com/threads/l1-t3-147-normal-versus-inverted-futures-market-hull.4396/ ) i.e., ... but we did neglect to update the...

Hi @hp97 The OP question above is from the FRM handbook and it is approximately 15 years old. In my opinion, it is not a good question for the "modern" FRM. I located it in the FRM handbook and below is a copy of the answer: ... so you can see how the answer seems to be arguing that our first...

Hi @akrushn2 Here is an example using exaggerated numbers. Assume EMWA's lambda, λ = 0.80 (which is just a weight) and the prior variance estimate (because volatility was 10.0%) is 10%^2 = 0.010 If the return is higher at 15.0%, then squared return is 15.0%^2 and the updated EWMA variance...

Hi @danghara I just added thee sheets to the XLS above (http://trtl.bz/2trHMzs): backward-baseline, backward-unexp strengthen, and backward-unexp weakening. Of course, outcome is the same: under unexpected strengthening, the net cost increases; under unexpected weakening, the net cost decreases...

Hi @tattoo Yes, thank you so much, all of the above are required corrections. Thank you! cc @Nicole Seaman Please note in regard to the R19 Study Note: Page 37-38 (Question and corresponding Answers to Hull's Chapter 2): The Question labelled 708.2 actually should be drawn from 142.5 (see...

HI @tattoo (cc @Nicole Seaman ) Oh geez, we did not properly fixed that paragraph, I apologize. Page 34 should read: So @tattoo It should read as above, because: the more typical scenario (#2) is the coffee producer who plans to sell in the future but has not contractual arrangement with those...

@tattoo Yes, that typo has been fixed (for a while I think); page 34 now reads as below. The second scenario is the classic (aka, typical) case of a commodity seller (e.g., farmer) who plans to sell in the future at the then-prevailing but currently unknown (unknowable) price, whose risk is...