1. (20 points) Assume you have a portfolio zero coupon bonds. The first bond is 15 year bond with yield of 3.5% and the other bond is 5 year bond with a yield of 2.8%. Assume that the current market value of the first bond is 100,000,000 and the second bond is shorted and has a market value of 300,000,000.

a. (6 points) What is the duration and convexity of the portfolio?

b. (7 points) Assume that the yield moves down 75 bps. Calculate portfolio return through duration convexity formula.

c. (7 points) Now calculate portfolio return directly using the bond price formula in the continuous model. Do you see a good fit?