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Required: i. Determine the number of futures contract that Fredrick Aloo should sell. ii. Suppose that the yield on the bond has decreased by 20 basis points at the horizon date, the bond portfolio has increased in value by 1.5% and the futures price has increased to Sh. 121,200. Determine the overall gain on the portfolio and the ex-post modified duration as a result of the futures transaction.a) Discuss the following terms as used in the swaps market: i. Index amortising swap. ii. Arrears swap. iii. Index differential swap. iv . Overnight index swap. b) A two year swap with semi-annual payments pays a floating rate and receives a fixed rate. The term structure at the beginning of the swap is as follows: Lo (180) = 0.0583 L. (360) = 0.0616 Lo (540) = 0.0680 Lo (720) = 0.0705 Where Li (m) is the m-day LIBOR on day i. In order to mitigate credit risk of the parties engaged in the swap, the swap will be marked to market in 180 days. Suppose it is now 180 days later and the swap is being marked to market. The new term structure is as follows: L18o (180) = 0.0429 L18o (360) = 0.0538 LISO (540) = 0.0618 Required: i. The market value of the swap per Sh.1 notional principal. Indicate the amount paid by each party. ii. The new fixed rate on the swap at which the swap would proceed after marking to market. c) Fredrick Aloo offers fixed income portfolio management services to institutional investors. He would like to execute a duration changing strategy for a Sh.100 million bond portfolio for a particular client. This portfolio has a modified duration of 7.2. Fredrick plans to change the modified duration of the portfolio to 5.0 by using a futures contract priced at Sh.120,000 which has an implied modified duration of 6.25 and a yield beta of 1.15