 # duration estimatation problems?

which is most likely to be correct, duration underestimates for a convex bond: a) price increase far more than price decreases b) equally, both price increases and price decreases as its a linear estimation c) price decreases far more than the price increases d) underestimation by duration is likely to depend on the convexity of the bond in question. Guys i’ve made this question up, so prone to error, but if you think its good, let me know… i’ll continue to work on making new problems. and do not ask for answer as myself dont have F*ING CLUE!!

A- duration OVERestimates price decreases (look at a price-yield diagram and draw a tangent line for duration) imo the most correct answer is A.

a, b, c all depend on the yield. Answer = d.

if it is convex, how can a price decrease ever be underestimated by duration? the tangent/secant line will end up under the curve and thus always overestimate the price decrease

supersharpshooter Wrote: ------------------------------------------------------- > if it is convex, how can a price decrease ever be > underestimated by duration? > > the tangent/secant line will end up under the > curve and thus always overestimate the price > decrease very nice. so i should refphare my question.

as i said i made this up to clear some concepts. rephrasing the question. a) price increase far more than price decreases b) equally, both price increases and price decreases as its a linear estimation c) price decreases far more than the price increases d) underestimation by duration is likely to depend on the convexity of the bond in question. e) overestimation of price decrease is greater than the underestimation of price increase.

imo the answer is still ‘A’ because a price increase will always be underestimated, and a price decrease will always be overestimated, by drawing a tangent line to a price-yield curve that is convex towards the origin

B

anyone interested in explaining the answers to this one? since I am sort of still unsure. I should make this question, “comment on each of them” as opposed to picking the right one.

pos convexity for option free bond will increase faster (rates drop) vs. when rates rise. Therefore duration will be overestimated. Sharp, are you sure it’s the same from when there is a decrease in price?

i think it’s A BTW

pepp Wrote: ------------------------------------------------------- > anyone interested in explaining the answers to > this one? since I am sort of still unsure. Pepps, depends on the change in interest rate (if increase of decrease). Consider that the convexity is the sensitivity of the bond price at variation of the interest rates.

yeah i’m working under the assumption the bond is option-free with a positive convexity maybe i should draw up a diagram

yeah, same here. I just thought it was only greater for when rates drop vs when rates rise? posative convexity Price rises at an increasing rate Duration is higher at lower rates vs higher rates —just looked in SS

here is my rationale for why it’s A for an option-free bond with positive convexity http://i29.tinypic.com/x51qpi.jpg

Summary: For a positive convexity, prices rise faster than they fall, hence duration underestimates prices rises far more than over estimating the price declines. For a negative convexity, prices decline faster than they rise, hence duration overestimates declines far more than underestimates rises? AM I RIGHT?!! THIS IS NOT SIMPLE TO GRASP.

wouldnt duration overestimate price increase because it increases faster?

I don’t think any of us have any solid understanding on this! price increases are always underestimated!

From the book: positive convexity: large change in int. rates, amt of price appreciation is greater than amount of price depreciation negative convexity: price apprecation is less than amt of price depreciation Duration underestimates new price whether yld is increaed or decreased If convexity adjustment is positive, the gain is greater than the loss for large change in rates. If it is negative, the opposite happens. I cannot find anything on if there is a bigger change for positive vs. negative convexity in regards to duration in the book.

it certainly underestimates the price, but the question is whether it underestimates the change in price - to which i answer, only when we’re dealing with a price increase, otherwise, with a price decrease, the change is overestimated check out the diagram maybe we can’t agree on an answer because we’re all talking about a different problem