Problem 6: Consider two bonds (i) a 3-year bond with zero coupons, and (ii) 3-year bond with 5% annual coupon. Assume the yield curve is flat at 5.5%. 1. Calculate the price and duration of each bond. Suppose the yield curve shift up by 0.1%. what are the new prices of each bond? Check that the % change is close to D times the yield change 2. 3. Suppose the yield curve shifts up by 2%. Is the approximation still good? Discuss 4. You have $10 million and invested 40% of them in the zero-coupon bond and 60% in the 5-year coupon bond. what is the duration of your portfolio