Please show all work, calculations, and formula used

13* [4 Points) Your bond portfolio is worth $300,000,000. You expect the interest rates to increase by 1.5% (i.e., Ay = 0.015). The futures price for a Treasury note futures contract is 105 (per 100) and each contract is for the delivery of bonds with a face value of $100.000. On the delivery date the duration of the futures is 6.5 years and the duration of the portfolio will be 4 years. a. How many contracts are necessary for hedging the portfolio? [1 Point] (short/long?). b. What are gain/losses on the portfolio? [1 Point] c. What are gain/losses on the futures? [1 Point] d. What are gain/losses on the hedged (combined) position? [1 Point). 13* [4 Points) Your bond portfolio is worth $300,000,000. You expect the interest rates to increase by 1.5% (i.e., Ay = 0.015). The futures price for a Treasury note futures contract is 105 (per 100) and each contract is for the delivery of bonds with a face value of $100.000. On the delivery date the duration of the futures is 6.5 years and the duration of the portfolio will be 4 years. a. How many contracts are necessary for hedging the portfolio? [1 Point] (short/long?). b. What are gain/losses on the portfolio? [1 Point] c. What are gain/losses on the futures? [1 Point] d. What are gain/losses on the hedged (combined) position? [1 Point)