Convexity in Barbell and Bullet
I have a question.
For bonds convexity is supposed to be a positive thing as when the Yields fall the bond with higher convexity rises more in price than a bond with lower convexity and likewise falls less when there is an increase in yield.
Barbell structure has higher convexity (dispersion) than a bullet structure portfolio.
now my question is when the slope of the yield curve increase the price decrease of a barbell portfolio is more than that of a bullet portfolio because the longer term bonds fall more in value than the increase in value of short term bonds in a barbell (due to the fact that Duration of Long term bonds in Barbell is greater than the short term bond’s duration in a barbell). Which makes sense.
But now in terms of convexity, shouldn’t the Barbell portfolio’s value decrease less than the bullet because of its higher convexity when the yield curve’s slope increase?
I hope i am able to explain my question well.