Bond convexity.

[abbas_sukhsorwala]

To calculate the return impact of a change in yield spread, why is convexity taken as 1/2?

 

[S2000magician]

Convexity isn’t taken as ½.
What makes you think that it is?

 

[abbas_sukhsorwala]

it says so in the formula -> Change in bond price = -annual modified duration (ΔYTM) + 1/2 convexity (ΔYTM)2

 

[cpk123]

if you consider a Δr change in rate on either side of r
Convexity = [P(r-Δr) - P(r+Δr)]/ (2 * P * Δr^2)
or ΔP/(2*P*Δr^2) = Convexity
So ΔP/ P = Δr^2 * Convexity / 2

 

[S2000magician]

abbas_sukhsorwala wrote:it says so in the formula -> Change in bond price = -annual modified duration (ΔYTM) + 1/2 convexity (ΔYTM)2

I see: it’s not that the convexity is ½; it’s that you multiply the convexity by ½.
I wrote an article about convexity that addresses this: http://financialexamhelp123.com/convexity/