Confusion about annual modified duration

[therealoneZX]

I’ve come across this equation alot on the topic of Duration:

AnnualModDur = AnnualMacDur / ( 1+ YTM/m)

My question is why is the numerator stated on an annual basis, but the denominator seems to be stated on a basis of m periods? I understand this is the resulting form of stating both numerator and denominator on a period basis, and then annualising that amount… but it doesn’t make sense to me why just straight away stating both on an annual basis is wrong ; AnnualModDur = AnnualMacDur / ( 1+ YTM)

[PreDRaR66]

Macdur/[1+r]

[S2000magician]

@therealoneZX

I’ve come across this equation alot on the topic of Duration:

AnnualModDur = AnnualMacDur / ( 1+ YTM/m)

My question is why is the numerator stated on an annual basis, but the denominator seems to be stated on a basis of m periods? I understand this is the resulting form of stating both numerator and denominator on a period basis, and then annualising that amount… but it doesn’t make sense to me why just straight away stating both on an annual basis is wrong ; AnnualModDur = AnnualMacDur / ( 1+ YTM)

Do you want to see the calculus?