connection in fixed income formula

In Fixed Income : DD (dollar duration) target = DD p (existing portfolio) + DD f (future) x number In Risk Management : number = ( (D target - D p) / MD future ) x ( Portfolio value / Futre principal) just found that 2 are the same formula and surprised. Am I the only one who didnt know this? And… hedge ratio = DD p /(DD t - DD p) = DDp / DD f = conversion Factor x ( DDp / DD ctd) this is also the same one as above 2 But actually the 2nd formula includes yield beta yield beta x ((D target - D p) / MD future ) x ( Portfolio value / Futre principal) And sometimes 1st & 3rd formula also has yield beta. Could you explain if there is mis understanding above ? & when should we include yield beta when calculating?

You only use yield beta when you’re making an imperfect hedge, e.g. hedging a corporate bond position with treasury futures.

Two yield beta threads that I am aware of: http://www.analystforum.com/phorums/read.php?13,1259388 Will lead you to: http://www.analystforum.com/phorums/read.php?13,1143043