What are is the difference between the 2 formulas for modifying duration for a bond portfolio?

CFA Level III Fixed Income
#1

I have noticed there are two formuals, one in the FI curriculum and one in Derivatives. Obviously, depending on what info we get, we will know what formula to use, but could anybody provide more background for the two different formulas?

  1. [(Dt-Dp)P]/(DctdPctd) x Conversion factor

  2. [(MDt-MDp)/MDf] x (Vp/Pf*multiplier) x yield beta

#2

Exactly no difference. I cannot explain the link between those cause I’m not a math expert. You should learn both and first one you should apply under FI session, second under Derivatives session.

#3

if the bond and futures yields do not change one-for-one, we use yield beta in the formula.