# dollar duration question

schweser book 3 pg. 109 #9: with a current dollar duration of \$487,500 per 25 basis points, an investor fears a 25 bps rise in rates and wants to hedge. the dollar duration of the ctd issue is \$4,750 and the conversion factor is 0.917. how do you hedge the position? a. sell 94 contracts b. buy 94 contracts c. sell 112 contracts answer: A i know you sell contracts because you want to decrease dollar duration. the impending rise in rates will hurt the portfolio so you want to bring down duration, or the sensitivity of portfolio value due to changes in rates. now plug in: # of contracts = (dd target - dd portfolio) / (dd futures), where dd futures = dd ctd / conversion factor the answer calcs -487500 / (4750/0.917) = -94, which suggests that dd target = 0 in writing all this out i think i answered all my question but will post anyway. obviously to properly hedge you want the target dollar duration to be 0 so that the portfolio is unaffected by changes in interest rates. so always plug in 0 for dd target when calcing the number of contracts used to hedge?

your understanding is right. the key is to have the net duration impact to be zero, so that the portfolio is not affected by the potential IR increase.