COnvexity question

[wrongsaidfred]

Hi David,

I saw a great article you wrote about how effective convexity can be defined as having a 2 in the denominator, in which case the convexity adjustment is just C*(delta y)^2, or without a 2 in the denominator and then the convexity adjustment would be 0.5*C*(delta y)^2.

Tuckman uses the latter form of the adjustment in chapter 5. Does this mean that this is the equation we should use on the exam and that we should assume that if we are given convexity it is being calculated using the formula without the 2 in the denominator?

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

Yes, that is exactly correct (in the next version of the study notes I am going to drop the alternative presentation, I think it is no longer useful).

GARP (Jorion) has tended to follow Tuckman in preserving the approach that more directly recognizes duration + convexity as a Taylor Series expansion; i.e.,
f(a) + f'(a)*(x-a) + 0.5*f''(a)*(x-a)^2 + .... ; see http://en.wikipedia.org/wiki/Taylor_series
... where the partial second derivative is multiplied by 1/2

and this (Tuckman's) method allows convexity (C) to represent the more succinct 1/P* d^2P/dy^2

Although Fabozzi (unassigned) has written that it's irrelevant which is used, saying the convexity measure is itself meaningless, I have come to disagree because the other advantage of Tuckman's usage of convexity is that it can be referred to as, for example, "80 years-squared" but I don't think you could say the same about the convexity of "40" if you were going to omit the 0.5 in the adjustment. I find Tuckman's approach winning because it matches Jorion's and Taylor series directly and gives us a convexity (80 instead of 40) that can be referred to as "years-squared."

That said, I may be wrong, but I cannot recall if GARP has ever quizzed the convexity as a quantitative adjustment. It definitely has appeared qualitatively ...

Thanks, David