15. A bank has a LADG of 3.5 and assets of 200M. The bank wishes to hedge by shorting futures contracts that have a face value of $100,000 and a price of $98,000. The duration of the bond underlying the futures contract is 9 years. How many contracts should the bank short? 16. A put option has a strike price of 98. The underlying bond trades at par with a coupon of 5%. The modified duration of the bond is 4. What is the interest rate that would make the option become at the money? 17. Consider the following Fed Funds rates below and the price of the Fed Funds futures contract that expires on April 30. What is the likely price of the contract on April 1?: Apr 1 3.00% Apr 18 3.00% Apr 23.00% Apr 19 3.00% Apr 33.00% April 20 3.00% Apr 4 3.00% April 21 3.00% Apr 5 3.00% April 22 2.75% Apr 6 3.00% April 23 2.76% Apr 7 3.00% April 24 2.76% Apr 8 3.00% April 25 2.73% Apr 9 3.00% April 26 2.75% Apr 10 3.00% April 27 2.75% Apr 11 3.00% April 28 2.75% Apr 12 3.00% April 29 2.75% Apr 13 3.00% April 30 2.75% Apr 14 3.00% Apr 15 3.00% Apr 16 3.00% Apr 17 3.00%