 # FRM vs CFA convexity

I am doing the 2018 GARP practice exam and convexity estimation is given by the formula [(P-) -2(P0) + (P+)] / (P0) * Δy2.

However, in the CFA curriculum, the denominator of the formula is 2*(P0) * Δy2.

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 ≈ Dureff × Δ_y_ + Conveff × (Δ_y_)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 ≈ Dureff × Δ_y_ + ½Conveff × (Δ_y_)2

Both formulations appear in the literature.

Sorry.

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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. 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 formula

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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.

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I remember long ago, Schweser used to flag this because there were conflicting definitions in the texts. The definitions differ by the factor of 2.
It’s from the Taylor series expansion
f(x) approx f(0)+x f’(0)+x^2 f’’(0)/2+…