Use the table on p27 in the Lecture 06: Convexity and the following two portfolios:

(i) Bullet portfolio: $100,000 par of 20-year zeros

(ii) Barbell portfolio: $25174 par value of the 10-year zero and $91898 par value of

the 30-year zero.

1. a)Assuming all rates shift by the same amount, how much the rates have to move so that barbell and bullet portfolios have the same price today?
2. b)Assuming all rates shift by the same amount in a year (from -3% to 3% with an increment of 0.5%), what are the portfolio values of the barbell and bullet portfolios?
3. c)Assuming NONparallel shifts in rates, how much rates have to move so that barbell and bullet portfolios have the same price today?
4. d)Assuming NONparallel shifts in rates, what are the values of the barbell and bullet portfolios in a year (assuming the shift in the rate of the bullet portfolio is random, and the 10 and 30 year zero rates move down (up) by 25 bp for the barbell portfolio?