The convexity of shorter-term coupon bonds is generally less than the convexity of longer-term bonds. That is because convexity increases with the square of maturity.

A barbell strategy is where a manager uses bonds with short and long maturities—forgoing any intermediate-term bonds. A bullet strategy is when managers buy bonds concentrated in the intermediate maturity range. Therefore, the barbell will tend to have the greater convexity due to the exponential (squared) influence of the longer-term bonds.

Since duration is linearly related to maturity, it is possible for a bullet and a barbell strategy to have the same duration.