Consider an 1-year US Treasury zero and a 5-year US Treasury zero currently trading in the market. The term structure is flat at 5% per annum. All bonds pay their coupons annually and they are denominated at $100 face value per contract.

(i) Suppose that we are currently managing a liability portfolio consisting of 3 payments of 100,000 each, to be paid at the end of every year over the next 3 years. We would like to fund our liability portfolio by investing in 1-year zeros and 5-year zeros. Describe the quantities of each zero that we need to buy/sell in order to create this funding portfolio

(ii) Suppose that a 3-month forward contract with the 1-year zero as the underlying asset is currently trading in the market. Compute the theoretical forward price and discuss how much it would cost to buy this forward contract.

(iii) Briefly discuss the forward price computed in (ii) in the context of the cost-of-carry

(iv) Suppose that the forward contract in (ii) is quoted at a forward price of 98. Discuss how we can construct an arbitrage strategy to exploit this discrepancy.