Convexity effect - the logic behind it

CFA Level I Fixed Income
#1

Hi Team,

I am wondering if someone could explain to me why does convexity effect has to hold - the logic behind it? For example, the inverse effect is simple - if we increase the denominator, without changing the numerator, the result (PV) will be lower. I am having trouble figuring out the same logic for the convexity effect?

#2

The easiest way to see it is by looking at a graph of y = 1/x. For positive x, if you move to the left the graph gets steeper, and if you move to the right it gets flatter. If you want to see a proof that the percentage change is greater when x decreases than when it increases, I can produce one, but I’m not sure that you’re interested in that level of detail.

1 Like
#3

Thanks for reaching out and the explanation - that is a great catch! Yea, I was proving it right now using y=1/x and the change is l>0. You end with: 1/(x-l)>1/(x+l) which is always true for l>0. I had to do it since I come from a math colleague and was embarrassed for not catching that. :smiley: Thanks again! :slight_smile:

#4

My pleasure.

My background’s maths as well.