Q3. A Barbell

Q3a. what is the weight in 10Y and 30Y if you combine them in a way that matches the $dur of the 100M long 20Y position? This is known as a barbell position.

Q3b. what is the $dur and $convexity for a long 100M 20Y and short barbell position?

Q3c. what is the pnl for the following rotational move of the yld curve based on duration effect? 10Y 1.50% =>1.60%; 20Y 2.00% =>2.00%; 30Y 2.25% =>2.15%

Q3d. what is the pnl for the following belly flattening move of the yld curve based on duration effect? 10Y 1.50% =>1.60%; 20Y 2.00% =>2.05%; 30Y 2.25% =>2.35%