Bullets/Barbells and convexity

I’ve noticed in the book they say that barbell has more convexity but don’t explain why. I understand barbells perform better when yield is flattening.

I’ve also can see that the barbell is shown to be more convex but they don’t seem to give an explanation as well. They SHOW in exhibit 9 and 1 that a barbell has more convexity but it’s not explained in layman’s terms.

Can somebody explain to me why it has more convexity?

You should create some bonds in Excel and compute their durations and convexities, then compare the convexity of a bullet portfolio with that of a barbell portfolio with the same duration. You’ll learn a lot more by doing that than you will by reading an answer here.

Yeah, that’s what I figured. Was looking for the easy way out. Thanks

Longer the maturity of bonds, higher their convexity (I think because rise in yield, will affect these bonds for longer time - longer time investor has to take lower coupon, so their price will drop more than shorter duration bonds). Since Barbell has these bonds along with shorter duration bonds, while Bullet has only intermediate duration bond, Barbells have more convexity.

The way I remember this is the barbell has the weight at the extreme ends so benefits most when the entire curve moves. It suffers when just one end moves the wrong way. The bullet is very narrowly focussed application of force, the barbell spreads the application of force out over the entire width of the yield spread. So when the entire curve goes up or down the even distribution (barbell) outperforms.

For the flattening / steepening I physically anchor my flashcard at the right (long duration) end and move the short duration up or down, up for flattening, down for steepening. Same for more or less curvature, you can just bend the flashcard to see that the bullet is affected the most. Finally for volatility it is down to mass distribution, the barbell has lots of mass evenly distributed so is more stable in high volatility. The bullet has less mass (but obviously more velocity) so it could be affected by extremely high volatility (high winds for instance) more than the barbell which is obviously balanced more evenly on the ground.

You could just bend/manipulate your exam booklet during the exam if you got desperate.

Flashcards for the win.

Just search for Bullet or Barbell, you can just memorize too. Sometimes the answer is just to memorize the damn flashcard.