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Hi @ptf Thank you truly for that realistic (i.e., Bloomberg, trading desk!) and informative feedback. I happen to be currently updating the Tuckman notes (including an OAS model) and I will try to get this into my XLS update. A few thoughts: As a practical matter, we (an FRM EPP) can't vary the...

Hi @Amierul Mutually exclusive events cannot be independent, they must be dependent. Our independence rule is that P(A∩B) = P(A)*P(B), but when the events are mutually exclusive the probability that both occur is zero, P(A∩B) = 0. I'm a big fan of the contrapositive (see...

Hi Camille (@bollengc ) I hear you re: removing the formula but it's in GARP's notes so I've tagged the note for some improvement explanation (the extra work GARP creates for us, yay!). So both formulas are okay, if we understand how to use the first one in percentage terms, to your point. Using...

Hi @tinacheung128 pre and post-multiply simply refer to matrix (aka, dot product) multiplication; although there are probably many better illustrations of matrix multiplication, the wikipedia entry is decent at https://en.wikipedia.org/wiki/Dot_product We have two vectors and a matrix. The...

Hi @Amierul No, sorry, I do not know: I am getting the same $3,769.35 when I omit the PV keystroke (because when reset/cleared the default for PV should already be zero). However, I never run the solution this way. I always input four variables, and solve for the 5th. I don't see the value in...

Hi @novenagates Thank you. The carry-roll-down is the component of the price change due to the passage of time, and it does depend on which of the three scenarios is assumed. In the case of my YouTube video above, the initial state is a 1.5 year bond (i.e., three six-month periods) with an...

Hi @FRM_STUDY GARP had MANY of errors in the 2020 print, and that was one of them. Given betas of -1, 0 and 1, your solution WOULD correct! However, I don't think there was even a basis for determining those betas in the prior question. But for some unexplained reason they assumed betas of -1...

Hi @v.modaher Yes, the "(0.50)" is meant to convey a negative beta, otherwise denoted "-0.50" such that the unexpected return is given by (emphasis mine) the expression: 0.80*(2.0 - 1.0%) + (-0.50)*(1.0% - 1.0%) + 1.30*(1.5% - 0.5%). Thanks, David

Hi @Amierul I think weight is just implicit in the (right-hand) CML where the slope of the CML is the Sharpe ratio of the market portfolio, [E(Rm) - Rf]/σ(M). So, the implicitly the weight to the market portfolio is σ(P)/σ(M); e.g., if σ(P)/σ(M) = 0.70 then 70% weight to market portfolio and...

Hi @Amierul Because the SML is effectively a straight line in the slope-intercept form, y = mx + b where the constant slope is the market's excess return, E(Rm) - Rf, and the X-axis is beta, β. So just to map to this more-familiar y = mx + b --> [E(Rm) - Rf] = m and β = x. If the correlation...

Hi @Randy Moon In the lognormal formula P(t-1) is simply the price base and it can be included/excluded (like any VaR) depending on whether we seek the return (%) or the dollar ($) VaR. In the example, where μ = 10% and σ = 20%, we can say that the 95% lognormal VaR is given by 1 - exp(10% -...

Hi @Amierul In the MPV/PPC/CAPM worksheet, any negative values are weights (e.g., volatilities must be positive) and the weight of an asset (in the PPC) or the weight allocated to the risk-free rate (in the CML) can be negative. For an asset, negative signifies that we are shorting the asset...

Thanks, but the words about mathematics are imprecise, and is why I often use a numerical illustration (e.g., what is the mathematical meaning "absolute"? Well, it depends on the context). And mathematics is not the only domain. I'm trained in data science which relies on statistics and...

HI @mreshko Oh okay, I did not realize that's what you meant originally. I don't mean to suggest that "normal VaR" comports with a good stochastic model for asset prices. (lognormal VaR matches one of your examples, of course). You probably know more than me in this regard. We define normal...

Nah it was just an typo, like i said, an obvious typo. Back in the day, we used to call P1/P0 the "wealth ratio," then take LN(.) of the vector of "wealth ratios," when computing volatility; and another column that (. - 1) to the wealth ratio vector to give the simple returns. Or, really, wealth...

@mreshko In haste to reply to you (and get to my lunch), I simply misplaced the "-1", obviously. Fixed above. Simple return versus geometric (aka, continuously compounded) return, is the difference. But thank you for the dramatic "never seen"s, lol :) Next time I'll just refer you to the video.

Hi @mreshko Thank you. No, the assumption of arithmetic returns does not imply that drift and standard deviation are expressed in dollar (money) units. Your question contains a few different terms, I will use Kevin Dowd's (aka, GARP's since he is their longstanding author for this) terms: The...

Hi @bollengc Yes, I've included your recommendation in our PM (see below). Thank you for taking the time to offer such a specific recommendation!

Hi @superturtle "time-weighted discrete default rate" has never been a term in the FRM. It sounds like a lazy mashup of De Laurentis's default rate (itself already redundantly discrete; i.e., what would continuous imply in this context? But that author has errors we've already submitted) and...

Sure thing, after i posted, I found this (at CME group) because (to be honest) I just wanted to confirm that wrt to the ED vs FRA convexity bias, that it is the FRA that has slight convexity bias (this bias is much smaller than the typical convexity we observe in bonds)...