QUESTION FOUR a) Although the expectations of increases in future interest rates can result in an upward sloping yield curve; an upward sloping yield curve does not in and of itself imply the expectations of higher future interest rates. Explain. (6 marks) b) Suppose that all investors expect that interest rates for the 4 years will be as follows: i) What is the price of a 3-year zero coupon bond with a par value of Kshs.1,000,000? (2 marks) ii) If you have just purchased a 4-year zero coupon bond, what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value Kshs.1,000,000). 1000,000 (2 marks) iii) What is the price of a 2-year maturity bond with a 10% coupon rate paid Answer the following questions that relate to bonds with a face value of Kshs. 1,000,000. i) A 2-year zero coupon bond is selling for Kshs.890,000. What is the yield to maturity of this bond? (1+5%)(1+7%)21=6% (2 marks) ii) The price of a 1-year zero coupon bond is Kshs.931,970. What is the yield to maturity of this bond? iii) Calculate the forward interest rate for the second year. (2 marks) i.) How can you construct a synthetic one-year forward loan (i.e. you are agreeing now to a loan in one year)? State the strategy and show the corresponding cashflows. Assume that you can purchase and sell fractional portions of bonds. Show all your calculations and explain the meaning of the transactions. ( 5 marks)