Bond convexity

Just as (Macaulay) duration is weighted average maturity of bond, convexity is weighted average of maturity-squares of a bond (where weights are PV of bond cash flows). Dollar convexity is also the second derivative (d^2P/dy^2); i.e., the rate of change of dollar duration.
Note: the corresponding blog entry at our website contains the downloadable spreadsheet I used here.

Category:

Education

Tags:

• Bond
• convexity
• duration

[mizlinkp]

Like your videos - I just wish you would not enunciate each word as if talking to retards....one just lose interest....

[bionicturtledotcom]

@mizlinkp but retards are my target audience, I resent you don't appreciate their importance (teasing!) ... thanks for the feedback, I will give consideration to less careful enunciation, maybe slurring(?), i agree enunciation is overrated (teasing again!) ... to be finally sincere, if I slow down sometimes, it's probably b/c some of this stuff is hard for me and sometimes i myself feel like a retard, begin careful is sometimes a coping mechanism.

[Jakers2009]

i think your videos are great - i also resolved my past confussion regarding the duration and the 1st derivative. I realised that the 1st derivative is the gradient function and that if you take the 1st derviative of any function and then substitute the values of the x-axis at any point on that function then you would get the gradient at that point.

[bionicturtledotcom]

@Jakers2009 thanks! Just one clarification that is common source of confusion: the gradient (slope) at x is the "dollar duration" rather than duration (note i am careful to say dollar duration when referring to slope of tangent line). b/c duration = dy/dx*-1/P; i.e., "infected" by price. So, above, the gradient is actually -436.95, i.e., -$436 per 100% (1 unit) or ~$4.36 per 1% (rise/run)

[bionicturtledotcom]

@Jakers2009 Actually, technical correction to my previous reply: the gradient (slope) of the above tangent line at x = 5% is -426.3. That is the "dollar duration" such that the (modified) "duration" = -426 * -1/Price = ~4.458.

And modified duration 4.458 = Mac duration / 1 + (y/k) = 4.57 / (1+5%/2); see @4:05

[Jakers2009]

hi david your still doing the bond videos

[bionicturtledotcom]

@Jakers2009 Yes, i hadn't tackled convexity yet....hard to do quickly, hope you like?

[Paata02]

It's Great, thanks..I understood more than on lecture

[dajieda0]

thanks! very helpful!