Q2. Consider three zero coupon bonds: 5Y yielding 3%, 10Y yielding 4.25%, and 30Y yielding 4%. Q2a Calculate duration and convexity for all three (4 points)

Q2b If you want to construct a 100M portfolio of 5Y and 30Y to match the dollar duration of 100M position in 10Y, what is the weight in 5Y and 30Y respectively?

Q2c What is the $convexity for shorting 100M of 10Y zero? What is $convexity for long 100M portfolio of 5Y and 30Y as constructed in Q2b?

Q2d. What is the 1-day net interest payment (ie carry) for the long-short duration-neutral portfolio above in Q2c?

Q2e. If yields moved up or down by 10 bps for ALL THREE bonds in a single day, what is the long-short portfolios duration and convexity PnL?

Bonus: Q2f. What is the break-even amount of parallel movement in yield curve in a single day (breakeven means the convexity pnl will offset daily interest payment)

Please show all work and equations used.