Q2 Bond Return and Convexity

Consider a self-financed convexity trade.

Three zero coupon bonds: i. 2Y zero at 1.60%; ii. 10Y zero at 1.85%; iii. 30Y zero at 2.30%

a. Calculate duration and convexity for all three bonds.

b. If you want to combine 2Y and 30Y zero to match the $100M bullet in 10Y zero for dollar duration, what are the percentage weights in 2Y and 30Y respectively? (note: combined value in 2Y and 30Y is also $100M, i.e. 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 (4 points)?

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 10 bps upward parallel movement of yield curve?

f. What is the total PnL for a 2 bps downward parallel movement of yield curve?

g. 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)