Explanation

To hedge the interest rate risk from the two swap positions, we need to calculate the net dollar duration of the portfolio and then determine the appropriate Eurodollar futures position.

Step 1: Calculate Dollar Duration for Each Swap

5-year pay fixed swap:

• Notional: $420 million
• Duration: 4.433
• Dollar Duration = Notional × Duration × 0.01 = $420M × 4.433 × 0.01 = $18,618,600

10-year receive fixed swap:

• Notional: $385 million
• Duration: 7.581
• Dollar Duration = $385M × 7.581 × 0.01 = $29,186,850

Step 2: Calculate Net Dollar Duration

Since the trader is:

• Paying fixed in the 5-year swap (short position - benefits from rising rates)
• Receiving fixed in the 10-year swap (long position - benefits from falling rates)

The net dollar duration = Dollar Duration of 10-year swap - Dollar Duration of 5-year swap = $29,186,850 - $18,618,600 = $10,568,250

This positive net dollar duration means the portfolio has net long exposure to interest rates (benefits from falling rates).

Step 3: Calculate Eurodollar Futures Hedge

Each Eurodollar futures contract has a notional value of $1 million and a duration of 0.25 (since they represent 3-month LIBOR).

Dollar duration per contract = $1M × 0.25 × 0.01 = $2,500

Number of contracts needed = Net Dollar Duration / Dollar Duration per contract = $10,568,250 / $2,500 = 4,227.3 ≈ 4,227 contracts

Step 4: Determine Hedge Direction

Since the portfolio has positive dollar duration (net long), the trader needs to sell Eurodollar futures to hedge. Selling Eurodollar futures creates a short position that profits when rates rise, offsetting the portfolio's losses when rates rise.

Therefore, the trader should sell 4,227 Eurodollar contracts.

Answer: B