Convexity Adjustment Bond Price

[rainerh]

Hi,
I’m a litte confused about the definition for the Convexity Effect/Adjustment when calculating the price change when interest rates change.
The approximation of the Bond Value is nothing more than a second order Taylor Approximation and therefore the adjustment should be: -Duration x delta_y+1/2*convexity*delta_y^2
But in the EOC and the EOC in schwester the adjustment is calculated with -Duration x delta_y+convexity*delta_y^2.What about the 1/2? Why don’t they consider it?
Thank you very much.

 

[alpha668]

In CFAI curriculum, the adjustment is : - Duration x delta_y + convexity*delta_y^2

 

[alpha668]

I think it is the definition of convexity that differs and the convexity in Taylor Approximation = the convexity in CFAI curriculum x 2.

 

[rainerh]

alpha668 wrote:
In CFAI curriculum, the adjustment is : - Duration x delta_y + convexity*delta_y^2

yes, I saw that but I wonder where the 1/2 got lost? I’m pretty sure that the 1/2 is necessary..

 

[S2000magician]

rainerh wrote:

alpha668 wrote:In CFAI curriculum, the adjustment is : - Duration x delta_y + convexity*delta_y^2

yes, I saw that but I wonder where the 1/2 got lost? I’m pretty sure that the 1/2 is necessary..

The ½ is necessary, as you say. What CFA Institute doesn’t tell you at Level I is that it’s included in the convexity coefficient.
At Level II you’ll learn that the calculation of (effective) convexity is:
Ceff = [(P-) + (P+) – 2 × (P0)] / (2 × P0 × Δy)
Do not bother with this formula now; just know how to use the convexity term in the (percentage) price change calculation.

 

[breadmaker]

rainerh wrote:
…
The approximation of the Bond Value is nothing more than a second order Taylor Approximation and therefore the adjustment should be: -Duration x delta_y+1/2*convexity*delta_y^2
…

It put a smile on my face when I saw that calculus is not lost on you young people.

 

[alpha668]

S2000magician]</p> <p>

wrote:

alpha668 wrote:In CFAI curriculum, the adjustment is : - Duration x delta_y + convexity*delta_y^2

Att Level II you’ll learn that the calculation of (effective) convexity is:
Ceff = [(P-) + (P+) – 2 × (P0)] / (2 × P0 × Δy)

This formula is in L1 curriculum, and the Ceff is actually called ”convexity”. I think this is purely an inssue of definition. The convexity in Taylor’s formula shall = [(P-) + (P+) – 2 × (P0)] / (P0 × Δy). It does not matter that a constant is multiplied as long as we know its definition.

 

[S2000magician]

alpha668]

wrote:

rainerh wrote:

alpha668 wrote:In CFAI curriculum, the adjustment is : - Duration * delta_y + convexity * delta_y^2

Att Level II you’ll learn that the calculation of (effective) convexity is:
Ceff = [(P-) + (P+) – 2 × (P0)] / (2 × P0 × Δy)

This formula is in L1 curriculum, and the Ceff is actually called “convexity”. I think this is purely an issue of definition. The convexity in Taylor’s formula shall = [(P-) + (P+) – 2 × (P0)] / (P0 × Δy). It does not matter that a constant is multiplied as long as we know its definition.

I’d forgotten that it was in the Level I curriculum. In any case, the ½ is in there, so go forth and calculate with confidence!

 

[rainerh]

Thank you, I didn’t found it in the curriculum, probably need to look closer . But anyways thank you for your answers, it confirmed my suspicion that it’s in the definiton.