Hi David Hope you are well. Appreciate if you could explain below example taken from Qbank. I couldn't understand the relation btwn PVBP and VAR? Thanks Imad Question 11 - #29487 The price value of a basis point (PVBP) of a $20 million bond portfolio is $25,000. Interest rate changes over the next one year are summarized below: Change in Interest rates Probability>+2.50% 1%+2.00-2.49% 4%0.00-1.99% 50%-0.99-0.00% 45%<-1.00% 5%Compute VAR for the bond portfolio at 95 percent confidence level. A) $2,500,000. B) $2,750,000. C) $5,000,000. D) $12,500. The correct answer was C) $5,000,000. At 5% probability level change in interest rates is 2.00% or higher.Change in Portfolio value for 200 bps change in interest rate = 200*$25,000VAR = $5,000,000.
Hi Imad, The question assumes that an adverse change to the value of the (long) bond portfolio is a increase in the interest rate (higher rate --> lower bond price), such that the worst expected 95/5% outcome is the +2% increase in the rate (e.g., the 99% worst would be the +2.5% increase). I find it easier to be flexible w.r.t 5% or 95% and just focus on: we want the adverse tail (causing a drop in value) and we can perceive the adverse tail as either 95% or 5%, which is here an (presumed!) increase in the rate (although notice a better question would specify the portfolio is long; if it were short, the worst expected 5%/95% would be a 1% rate drop.) I don't know why the probabilities don't appear to sum to 1.0 (part of the definition of a prob distribution is summation to 1.0) finally, PVBP (which is more commonly referred to as DV01 in the FRM, but they are the same) is the dollar increase associated with a one basis point decline (so it's approx equal to dollar decrease associated with a one basis point increase). There are 200 basis point in +2%. So answer is +2% * 100 bps/% * $25,000 change/bps. Thanks,
Just another example of why Bionic Turtle is superior in terms of practice questions: 1) Correct answer 2) More insightful and well thought through questions 3) Rapid response, with an intuitive, easy-to-understand answer.
