Bond Return and Convexity.

Consider a self-financed convexity trade.

Three zero couple bonds: i. 2Y zero at 1.00%; ii. 10Y zero at 2.50%; iii. 30Y zero at 3.50%

a. Calculate duration and convexity for all three

b. If you want to combine 2Y and 30Y zero to match the $100M bullet in 10Y zero for dollar duration, what is percentage weights in 2Y and 30Y respectively? (note: combined value in 2Y and 30Y is also $100M, ie weights sum up to 100%)

c. The combination of 2Y and 30Y is a barbell. 10Y only position is a bullet. What are the daily interest accruals of $100M portfolio in long barbell portfolio, and $100M in long bullet, respectively ?

d. What is the DOLLAR convexity of a dollar duration neutral that is LONG barbell and SHORT bullet (LONG $100M of barbell and SHORT $100M of bullet)?

e. What is the total PnL for a 1 bps upward parallel movement of yield curve due to convexity effect?

f. What is the breakeven level of single day parallel yield change for the long-short portfolio? (hint: breakeven level is achieved when convexity profit is offset by daily interest cost)