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5 Explain what is meant by the following theories of the shape of the yield curve: (a) market segmentation theory (b) liquidity preference theory. [4] Short-term, one-year annual effective interest rates are currently 6%; they are expected to be 5% in one year's time; 4% in two years' time and 3% in three years' time. (ii) Calculate the gross redemption yields from one-year, two-year, three-year and four-year zero-coupon bonds using the above expected interest rates. [4] The price of a coupon-paying bond is calculated by discounting individual payments from the bond at the zero-coupon yields in part (ii). (iii) Calculate the gross redemption yield of a bond that pays a coupon of 4% per annum annually in arrears and is redeemed at 110% in exactly four years. [5] (iv) Explain why the gross redemption yield of a bond that pays a coupon of 8% per annum annually in arrears and is redeemed at par would be greater than that calculated in part (iii). [2] The government introduces regulations that require banks to hold more government bonds with very short terms to redemption. (v) Explain, with reference to market segmentation theory, the likely effect of this regulation on the pattern of spot rates calculated in part (ii). [2] [Total 17] 6 Consider a fixed-interest security that pays coupons of 10% at the end of each year and is redeemable at par at the end of the third year. Calculate, using an effective interest rate of 8% pa, the: (i) volatility of the cashflows (ii) discounted mean term of the cashflows (iii) convexity of the cashflows. 7 Consider the three 20-year annuities described below: (i) level payments of E1,000 payable annually in arrears (ii) increasing payments made annually in arrears, where the first payment is f1,000 and the payments increase by 10% po compound each year thereafter (iti) continuous payments at the rate of f1,000 pa over the 20 years. Calculate the discounted mean term of each annuity using an interest rate of 10% pa effective