# FRM vs CFA convexity

I am doing the 2018 GARP practice exam and convexity estimation is given by the formula [(P_{-}) -2(P_{0}) + (P_{+})] / (P_{0}) * Δy^{2}.

However, in the CFA curriculum, the denominator of the formula is 2*(P_{0}) * Δy^{2}.

Which one is correct?

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The formula for convexity is controversial.

Hatfields & McCoys controversial.

Some think that the “2” belongs in the denominator for the convexity calculation, and that the formula for using it should be:

%ΔP ≈ Dur

_{eff}× Δy+ Conv_{eff}× (Δy)^{2}Others think that the “2” does not belong in the denominator for the convexity calculation, and that the formula for using it should be:

%ΔP ≈ Dur

_{eff}× Δy+ ½Conv_{eff}× (Δy)^{2}Both formulations appear in the literature.

Sorry.

Simplify the complicated side; don't complify the simplicated side.

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Got back here after seeing David Herper’s (BT) post.

This is my take.

I think from mathematical standpoint FRM is correct, however from intuitive understanding let’s say If I try to understand Convexity impact for 1BP change the natural inclination would be to adjust Convexity*(1BP)

^{2}than 1/2*Convexity*(1BP)^{2}a typical tussle between mathematicians and finance experts. :D

Conclusion: Do as per your respective exams

Edit: I just checked in CFA LI & LII old book, in the denominator there is

NO 2 in convexity formulaMagina, the Antimage II Never ever give up!!

That’s a recent change: last couple of years.

Historically, the 2 has been in the formula, probably because that’s how it appears on Fabozzi.

Simplify the complicated side; don't complify the simplicated side.

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