Convexity adjustment.

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Hi David

On excel sheet 4.c7 as well as on video 4.c. The example did convexity adjustment as C*(dy^2), but the formula I see on hand book as well as on the same video it's 0.5*C*(dy^2) Could you please clarify a little? Thanks.

 

[David Harper CFA FRM]

Hi chugangc,

It always gets to the same place, the issue (unassigned Fabozzi explains this best) is that the convexity measure doesn't matter. I copied 4.c.7. below.

http://learn.bionicturtle.com/images/forum/1118_convexity.png

The convexity measure can be fairly calculated either:
Convexity measure = [Price(+shock) + Price(-shock) - 2*Price]/[2*Price(0)*shock^2] = 118.09 (purple).
Then, modeling a +1% yield change, the convexity adjustment:
Convexity adjustment = 118.09*1%^2 = 0.0118

Or, the convexity measure can be calculated without the (2) in the denominator:
Convexity measure = [Price(+shock) + Price(-shock) - 2*Price]/[Price(0)*shock^2] = 236.18
Then, modeling a +1% yield change, the correct convexity adjustment:
Convexity adjustment = 0.5*236.18*1%^2 = 0.0118

… see how it doesn't matter (Fabozzi: "the convexity measure has no meaning")? if the convexity measure omits the (2) in the denominator, then the adjustment does require the 0.5 "scaling factor." If the measure includes the (2), no 0.5 scaling factor is warranted.

Thanks, David

 

[[email protected]]

Thanks a lot, got it, it does need to divided by 2, just where you do it is different. Although I likely still do it on later step as it's more intuitive since it's the same as Taylor.

 

[David Harper CFA FRM]

that's a good point (i all but forgot this is just Taylor) ... I like yours better (plus it fits with the 236.18 based on dollar durations, for the same reason: true 2nd derivative) - David