Duration hedge ratio for interest rate futures

[alimik]

The formula for the duration hedge ratio for interest rate futures 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

My question is why is the duration of the asset underlying the futures contract used in DF rather than the duration of the underlying asset plus the term to maturity for the futures contract?

Thank you for your assistance