pawn

A. price/par value * duration * par value * 0.01 = price * duration * 0.01
= price change for a 1% change in interest rate.
B. denominator = price * 0.01 * duration = price change of 10 year bond for a 1% price change.
if the $ duration has to be the same -
A must be equal to B * How much of B should be bought (B_Val).
so how much of B should be bought?
B_Val = Numerator / denominator