Calculate Convexity from Macaulay duration

CFA Level III Fixed Income
#1

I don’t know where this formula comes from

Convexity = (MacD2 + MacD + dispersion) / (1 + periodIRR)

or … we must just learn it by heart?

#2

The footnote points to external book. Denominator squared, btw.

#3

This formula seems to be “invented” by one of the authors of this the Reading 22 Donald J. Smith in this article Bond portfolio duration, cash flow dispersion and convexity in 2010 and presented in his book Bond Math: The Theory behind the Formulas.

I may try to see how he got this formula, but apparently the article above has only 2 citations (WTF, the author thinks he is Black or Scholes with this formula?). I hate to think that I must learn something useless.

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