Problem 3 (8 points): Assume the term structure of interest rates is flat and consider a 1-factor model with the factor equal to that interest rate. Assume also that the current interest rate is 10%. You currently own 1000 of 20-year 12% coupon bonds. a) (3 points) If you want to hedge your portfolio with 20-year 8% coupon bonds, how many bonds do you need to sell? b) (3 points) By how much the value of your hedged portfolio will change if the interest rate increases by 0.4% from 10% to 10.4% c) (2 points) You just found a nice risk-free security trading on the market - a perpetuity with $100 face value and 12% annual coupon rate (paid semi-annually). How many of such perpetuities do you need to sell to hedge your original portfolio?