1. You have a liability of $100,000 that is due in four years. In order to hedge against interest rate risk, you must use a portfolio with a similar duration using a 5-year zero-coupon bond and a 3-year 8% annual coupon bond with a yield to maturity of 10% (face value of $1,000).

a) What is the duration of your liability?

b) How much of the portfolio value (in percent) would you need to invest in the zero-coupon bond?

c) Assuming that the yield has not changed, do you have to rebalance your portfolio in one year? If yes, in which direction? No calculations are needed but you should explain the intuition for your answers.