Answer the following questions

An index-linked zero-coupon bond was issued on 1 January 2003 for redemption at par on 31 December 2007. The redemption payment was linked to a price inflation index with a 6-month time lag. Calculate the average money and real rates of return obtained by an investor who purchased $10,000 nominal of the stock on 1 January 2005 for (10,250 and held it until redemption. You are given the following values for the price index: Date Index Date Index 01.01.02 144 01.01.06 181 01.07.02 148 01.07.06 182 01.01.03 155 01.01.07 188 01.07.03 160 01.07.07 193 01.01.04 162 01.01.08 201 01.07.04 168 01.01.05 175 01.07.05 177 [4]An insurance company has liabilities of $10 million due in 10 years time and $20 million due in 15 years time, and assets consisting of two zero-coupon bonds, one paying $7.404 million in 2 years time and the other paying $31.834 million in 25 years time. The current interest rate is 7% per annum effective. (i) Show that Redington's first two conditions for immunisation against small changes in the rate of interest are satisfied for this insurance company. [S] (ii) Determine the profit or loss, expressed as a present value, that the insurance company will make if the interest rate increases immediately to 7.5% per annum effective. [2] (iii) Explain how you might have anticipated, before making the calculation in (ii), whether the result would be a profit or loss. [2] [Total 9]An institution has a liability to pay f15,000 per annum, half-yearly in arrears, forever. (i) Calculate the present value and volatility of the liability at 8% pa effective. [6] (ii) Calculate the duration of the liability at 8% pa effective. [1] The following two stocks are available for investment: (A) A special 5-year stock, redeemable at par, that pays a coupon of 5 per 100 nominal at the end of the first year rising, by 2% pa compound, to 5x 1.02# at the end of the fifth year. (B) Ann-year zero-coupon bond, redeemable at par. The institution chooses to invest equal amounts of cash in Stock A and Stock B. (iii) If the institution requires that the duration of the assets must equal the duration of the liabilities, show that n, the term of the zero-coupon bond, must equal 22 years if interest rates are 8% pa effective. [8] (iv) Without doing any further calculations, explain whether the institution has managed to implement an immunisation strategy. [2] [Total 17]