The formula for the duration hedge ratio for interest rate futures (to protect against interest rate risk) is :
>
> H = (PP* DP)/ (PF * DF)
>
> Where:
>
> PP is the forward value the fixed-income portfolio being hedged (at
> the maturity date of the hedge)
>
> DP is the duration of the portfolio at the maturity date of the hedge
>
> PF is the futures contract price
>
> DF is the duration of the asset underlying the futures contract at the
> maturity date of the contract
For example
Lets say the investor owns a $2 million portfolio of bonds
They use an interest rate futures hedging tool against fluctuations against interest rate risk (lets say by X contracts of $100,000 bond futures, where the futures contract is due for delivery in 8 months)
My question is why is why in the denominator of the formula is the duration of the $100,000 bond underlying the futures contract used in DF rather than the duration of the $100,000 bond underlying asset plus the 8 months?
Thank you for your assistance
PS. The following website https://au.mathworks.com/help/fininst/examples/managing-interest-rate-risk-with-bond-futures.html
suggests "Since bond futures derive their value from the underlying instrument, the duration of a bond futures contract is related to the duration of the underlying bond." but I don't understand why this is the case
