Suppose that a 5 year coupon bond of face value $ 100 and coupon rate 3% sells for $ 98 dollars, and that a 5 year coupon bond of face value $100 and coupon rate 7 % sells for $ 102. Both bonds pay coupons annually.

(a) What portfolio composed of these two dierent bonds replicates the payouts of a 5 year coupon bond of face value $ 100 and coupon rate 5%?

(b) If there is no arbitrage, what would be the price of this 5 % coupon bond?

(c) Suppose this 5 % coupon bond sold for a price of $ 99. What arbitrage trade could you make to get a riskless profit today in exchange for nothing in the future?