Provide solutions to the following attachments.

().6) A company is adopting a particular investment strategy such that the expected annual effective rate of return from investments is 7% and the standard deviation of annual returns is 9%. Annual returns are independent and (1 + i) is lognormally distributed where it is the return in the (" year. The company has received a premium of Rs.1,000/- and will pay the policyholder Rs.1,400/- after 10 years. Page 4 of 5 ASI CT1 1006 (1) Calculate the expected value and standard deviation of an investment of Rs.1,000/- over 10 years, deriving all formulae that you use. (9) (ii) Calculate the probability that the accumulation of the investment will be less than 50% of its expected value in ten years time. (8)(.5) (i) for is the forward rate applicable over the period t to t + r. it is the spot rate over the period 0 to t. The gross redemption yield from a one year bond with a 6% annual coupon is 6% per annum effective; the gross redemption yield from a two year bond with a 6% annual coupon is 6.3% per annum effective; and the gross redemption yield from a three year bond with a 6% annual coupon is 6.6% per annum effective. All the bonds are redeemed at par and are exactly one year from the next coupon payment. (a) Calculate i, i and i; assuming no arbitrage. (5) (b) Calculate 6,1 , fi,1 and f 2, 1 assuming no arbitrage. (5) (ii) Explain why the forward rates increase more rapidly with term than the spot rates. (2) (iii) You are given the following term structure of spot interest rates: Term (in years) Spot interest rate 5.00% 2 5.75% 6.25% 6.50% A three-year annuity- immediate will be issued a year from now with annual payments of Rs.5000/-. Using the forward rates, calculate the present value of this annuity a year from now. (3) [15]Q.3) An institution has a liability to pay Rs.15,000/ 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: Stock A: A special 5-year stock that pays a coupon of Rs.5/- per Rs.100/- nominal at the end of the first year rising, by 2% pa compound, to 5 x 1.02 ^* at the end of the fifth year. Stock B: An n- year zero-coupon bond. 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) Do you think that the institution has managed to implement an immunization strategy? Give reasons, but not any calculations, to support your answer. (2)Q.2) (i) What are the different types of loans? Describe in brief. (3) (ii) A loan is being repaid with 25 annual payments of Rs.300/ each. With the 10" payment, the borrower pays an extra Rs. 1000/-, and then repays the balance over 10 years with a revised annual payment. The effective rate of interest is 8%. Calculate the amount of the revised annual payment. (3) (iii) An investor borrows an amount at an annual effective interest rate of 5% and will repay all interest and principal in a lump sum at the end of 10 years. She uses the amount borrowed to purchase a Rs.1000/- par value 10-year bond with 8% semiannual coupons bought to yield 6% convertible semiannually. All coupon payments are reinvested at a nominal rate of 4% convertible semiannually Calculate the net gain to the investor at the end of 10 years after the loan is repaid. (4) (iv) A loan is repaid with level annual payments based on an annual effective interest rate of 7%. The 8th payment consists of Rs.789/- of interest and Rs.211/- of principal. Calculate the amount of interest paid in the 18" payment. (5) (v) Define the characteristics of government index linked bonds. Explain in practice why most index linked securities carry some inflation risk in practice. (3) [18]