Problem 4 (15 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 the current interest rate is 10%. Your portfolio consists of $100,000 investment in 5-year zero-coupon bonds and $200,000 investment in 8-year zero-coupon bonds a) (2 points) Find the Duration of your portfolio b) (2 points) If you want to hedge your portfolio with 15-year zero-coupon bonds, what will be the total dollar value of the 15-year bonds that you will sell? c) (2 points) If you want to hedge your portfolio with perpetuities that pay semi-annual payments, what will be the total dollar value of the perpetuities that you will sell? d) (4 points) If you want to hedge your portfolio using both 15-year zero-coupon bonds and perpetuities, what is the dollar value of 15-year zero-coupon bonds and perpetuities you need to buy/sell? e) Assume the interest rate increases by 1% from 10% 11% e.1) (1 point) What will be the change in the value of your unhedged portfolio? e.2) (1 point) What will be the change in the value of your hedged portfolio if you used only 15- year bonds for hedging? e.3) (1 point) What will be the change in the value of your hedged portfolio if you used only perpetuities for hedging? e.4) (1 point) What will be the change in the value of your hedged portfolio if you used both 15- year bonds and perpetuities for hedging? f) (1 point) Assume you have a hedged portfolio that you were supposed to find in part (d). Assume you held this portfolio for 6 months and liquidated it at that time right after all coupons are paid. Assume also that the interest rate remains at the same level of 10%. What is your realized holding period percentage return? Express your holding period return as an annual return with semi-annual compounding.