When the bond portfolio is fully hedged, is the hedge ratio equal to 1? Is there any relationship between full hedging and full immunization? Thanks!

Hedge ratio is used to minimize basis risk on duration hedging. In cross hedge, underlying bonds in futures contract is not identical to the asset being hedged. Basis can change unexpectedly due to difference in underlying bond and futures contract. Hedge ratio = 1 when DD(futures) = DD(portfolio) assume yield beta = 0. Immunization is to minimize interest rate risk ie. lock in the bond return regardless of interest rate change.

Sorry, typo assume yield beta = 1 hedge ratio = DD(portfolio)/DD(futures) or hedge ratio = {DD(portfolio)/DD(CTD)}*CF

So is immuization a duration hedging? Is fully hedged bond portfolio same as saying “duration is 0”? What does hedge ratio=1 mean intuitively? Thanks!

Yes, here is the text in the textbook. In the case of immunization, the use of duration is critical. The matching of the portfolio duration to the duration of liabilities to be funded by the portfolio is a form of hedging. Offsetting(reducing) the interest rate exposure of a cash position in a portfolio is also a form of hedging. Whenever an interest rate exposure must be reduced, futures can be used to accomplish the hedge.

hedge ratio = 1 when factor exposure of bond to be hedged = factor exposures of futures. Bond portfolio is fully immunized when DUR(asset)-DUR(liab) = 0. (and other immunization assumption works. e.g. parallel yield curve shift, PVa =PVliab…etc)

To summarize. Fully hedged when $DUR(asset)=$DUR(futures) Fully immunized when DUR(asset) = DUR(liability), PV(portfolio) = PV(liability) and other immunization assumption works.