All,
I’m trying to understand the concept behind the hedge ratio and its relation to the formula on the number of contracts required to reach a target dollar duration.
During that previous formula to find the number of contracts, did we assume the future contract is perfectly correlated to the bond portfolio?
What is the relationship between both formulas/concepts?
The formula is nearly the same, but the formula on hedge ratio does not consider the difference between Dt and Dp, it only considers Dp.
Also, they give us an example:
“If it was determined that 100 futures contracts would be needed to hedge a bond porfolio and the manager subsequentlyestimates that the hedge ratio is 1.2, the bond portfolio should be hedged with 120 contracts”.
Doesn’t the initial 100 future contracts calculated already take into accoung the hedge ratio?
I’m really confused between these 2 concepts/formulas!
Hedging ratio is a broad concept that has applications in many areas.
A bond has many risk factors and interest rate risk is one of them. The instrument used to hedge this specific type of risk is a futures contract. The interest rate risk exposure of a bond is measured using dollar duration. The hedge ratio is the ratio of exposure of the bond to the exposure of the hedging instrument (futures in this case).
In the case of dollar duration adjustment, the bond (portfolio) was initially purchased to satisfy a liability (target) - specifically the duration of a liability. But as time passed the exposures of the liability and the bond (portfolio) diverged. We then need to make the small adjustment to the asset’s exposure to match that of the liability again (target). Dt-Dp is used for that small adjustment. You are welcome to think of Dt-Dp as a whole new Dp that need to be hedged fully.