Duration and Convexity Question..

A certain agency bond has a duration of 8.73 years and a convexity of 61.33: A. If market yields increase significantly, the price of the bond falls by more than the amount indicated by duration alone. B. If market yields decrease significantly (e.g., by 250 basis points), the price of the bond increases by less than the amount indicated by the convexity measure alone. C. If market yields decrease significantly, the price of the bond increases by less than the amount indicated by duration alone. D. If market yields increase significantly (e.g., rates increase by 250 basis points), the price of the bond falls by less than the amount indicated by duration alone. From Passmaster… - Dinesh S

D. The numbers there are red herrings except that they are both positive. Positive convexity is completely to the benefit of the bond owner. If interest rates go up, they don’t get hurt as bad. If interest rates go down, they benefit more. Negative convexity is a bad thing for a bond owner in a similar way. BTW - If you are talking about risk under 250 basis point moves in interest rates, duration and convexity are not especially useful since they are both local measures and 250 basis points moves you out of your neighborhood. Edit: So I bet I can make an agency bond with those characteristics for which D isn’t true. Make a really well-supported PAC bond and then drop the prepayment rate to 0 by raising interest rates 250 bp so the life of the PAC tranche gets extended until forever. That 250 bp number is too big for the point they are making.

I would think B is the right answer here. B – Duration amount would be less than that indicated by Convexity alone -De * delta r + ce * delta r^2 which would be higher than (-de * delta r) Duration figure would be say +10, Convexity figure = +11 D – yields increase significantly (e.g., rates increase by 250 basis points), the price of the bond falls by less than the amount indicated by duration alone. -De * delta r (will be a -ve number which is -10 and convexity would be -9.5 e.g. and -9.5 > -10

Forget the math. Think of convexity as curvature of the price (y-axis) vs interest rates (x-axis). Positive convexity means that it is “concave up” (holds water). Positive convexity is always a good thing for the bond owner and the more you can get the better. Answer B doesn’t even make sense. You can’t predict the change in price of a bond using just the convexity measure. You need a duration measure.

D is the correct answer, as that is what is “convexity” all about… Price increses more when a yield falls than it decreases when the yield rises… And yes, B does not make sense… we could make use of duration measure alone to calculate the price sensitivity if the Price-Yield curve was flat i.e no-curvature, no-convexity but convexity alone is of no use in price-sensitivity calculation under any circumstances, Instead adding convexity to the duration would make a real close approximation of the price change. - Dinesh S

its D. I think the choices are confusingly worded.

dinesh.sundrani Wrote: ------------------------------------------------------- >Instead > adding convexity to the duration would make a real > close approximation of the price change. > Not usually for a 250 bp point. Using duration alone says the p/Y curve is a line. Using duration and convesity alone says its a parabola.

Lets suppose…that an instrument has +ve convexity…and zero duration…no matter how rates move (up or down)…the price of the instrument will always increase.

And the million dollar question is what kind of security would that be or how could you create one? (There are lots of ways and, of course, they would all cost money upfront).

A and C are false statements. B could’ve potentially been the correct answer if D was a false statement (for example, if market yield increases, bond prices go up). However, in the original example D was a much better choice than B.

No - B doesn’t make any sense. Give me any convexity and I can give you a security with any duration . Knowing the convexity alone doesn’t help anything.

A certain agency bond has a duration of 8.73 years and a convexity of 61.33:

maratikus, duration is the true measure of the price sensitivity, with convexity just being an error-corrector that accounts for the curvature of the P-Y curve. Flatter the PY profile, the more useless, the convexity measure gets… So knowing just the convexity of the security is of little to no use… - Dinesh S

Maratikus knows that… I see the point. Since they gave you the duration, the interpretation of B could include that duration. Got it. We agree that D is the right answer.