A pay-fixed, receive-floating interest rate swap is the appropriate hedge.

Why

• The portfolio manager is long 10-year Treasury Notes, so the position has positive duration and will generally lose value when interest rates rise.
• A pay-fixed swap has negative duration from the payer’s perspective, meaning it tends to gain value when rates rise.
• Therefore, it offsets the bond position’s exposure to rising rates.

Why the others are wrong

• B receive-fixed/pay-floating: this is a long duration position and would make the exposure to rising rates worse.
• C long Treasury Note futures: a long futures position benefits from rising bond prices, which is the opposite of what is needed.
• D buy a call on Treasury Note futures: a call would benefit from rising futures prices, again not the desired hedge.

Key takeaway

To hedge a long fixed-income position against rising rates, you generally want a position with negative duration, such as a pay-fixed swap or a suitable short futures hedge.