What is the distinction for when we should use each of the below 2 formulas? I am getting confused since both are used when we are trying to achieve a target duration.
[((duration target - duration of portfolio) x portfolio value)/ (duration of CTD x price CTD)] x CTD conversion
((target modified duration – portfolio modified duration)/futures modified duration) x (value of portfolio / price of future) x (yield beta).
When you’re given a conversion factor and a CTD bond, use formula #1. When you’re given futures data and a yield beta, use formula #2.
For formula 1, what type of duration should be used? Modified duration?
Thank you.
Unless the exam writer is really mean, I don’t think they’re going to be so picky with duration meaning (i.e. give you Macaulay duration in the portfolio and modified in the hedge, or something). The reality is that duration is linear, so as long as the duration metric you’re using is consistent, this should work.
Use modified or effective duration.
The vignette will tell you.
Thank you both!