Duration&Convexity formular

CFA Level I
#1

Hi,

Seems the duration&convexity formular can be:

-duration* change of y + 0.5 * convexity * change of y * 100

or

-duration* change of y + convexity * change of y * 100

or

-duration* change of y + convexity * change of y

???

I’m confused. Can somebody explain? Thanks

#2

Effective Duration = (v_-v+)/2V0 (delta y)

Convexity adjustment = + Convexity (delta y)^2

#3

Howdy.

It’s no wonder you’re confused. Part of the problem is that finance people haven’t agreed on the proper calculation of convexity.

The most common formula is:

%ΔP = -duration × Δy + convexity × (Δy)²

In the reading on credit analysis , the formula they have is:

%ΔP = -duration × Δy + ½ × convexity × (Δy)²

The reason for the disagreement in the formulae is that some finance people think that the “½” should be part of the convexity number itself, and others don’t. That’s unfortunate, but we have to live with that. I wouldn’t think that it’s likely that you’ll be doing a duration/convexity calculation in a credit analysis question.

As for the formulae that multiply by 100, that should be “100%”; i.e., you’re multiplying by 1. Ignore the “100”.

You’re welcome.

#4

The magician is quickly becoming my favourite AF contributor.

Thanks, I was going nuts because of these two versions of convexity…

#5

Awwwww . . . .

My pleasure.

You weren’t alone.