Which of the following is NOT true?

A. The longer the duration, the greater the price sensitivity.

B. The price of a new security (such as a coupon bond) predicted using duration always underestimates its true new price

C. Duration is often thought of an average time to maturity. Therefore, it is impossible for duration to be negative

D. Convexity refers to the fact that a fixed income security's price yield relationship is not linear (plots as a straight line) but rather is curved.