Extreme Bullet & Less extreme barbell vs. laddered benchmark portfolio

CFA Level III Fixed Income
#1
  1. For a parallel shift, why does extreme bullet (7 and 10 year bonds) underperform a laddered bond portfolio (2, 3, 5, 7, 10, 30 year bonds) for a parallel + 100 bps shift? This is from section 5.4 Chapter 23.

Is it because of the convexity of the laddered portfolio?

  1. A less extreme barbell outperforms a laddered benchmark portfolio when the yield curve becomes less curved (less curvature).

An extreme barbell underperforms a laddered benchmark portfolio when the yield curve becomes less curved (less curvature).

In both cases, barbelled version has higher convexity than the benchmark laddered portfolio. Numbers from the curriculum are Less extreme barbell has a convexity of 1.183 vs 1.134 of benchmark laddered portfolio. The extreme barbell has a convexity of 1.578 vs 1.134. Again, in both cases barbelled (extreme and less extreme) have higher convexity. Why does extreme underperform the benchmark while less extreme outperforms the same bench mark with less curvature?

#2

Anyone?

#3
  1. For a parallel shift, why does extreme bullet (7 and 10 year bonds) underperform a laddered bond portfolio (2, 3, 5, 7, 10, 30 year bonds) for a parallel + 100 bps shift? This is from section 5.4 Chapter 23.

Is it because of the convexity of the laddered portfolio?

Correct, for a given duration and parallel shift, the bond with higher convexity outperforms bond with lower convexity.

So, Laddered>Barbell>Bullet

For #2 below, you need to move beyond convexity statistic analysis, since curvature is a non-parallel yield curve movement.

Less curvature means, the intermediate yields (10 yr) have gone down or 2/30 yields have gone up or a combination of both.

  1. A less extreme barbell outperforms a laddered benchmark portfolio when the yield curve becomes less curved (less curvature).

As the curriculum mentions: “the less extreme barbell portfolio has more “participation” in the middle part of the yield curve”

Less extreme barbell has exposure to intermediate maturities (3/10 yr)- see Exhibit 50.

So the loss in portfolio value from increase in 2/30 yr is atleast partially offset by gain in value from drop in 10 yr yields

An extreme barbell underperforms a laddered benchmark portfolio when the yield curve becomes less curved (less curvature).

Extreme barbell has No exposure to intermediate maturities (such as 3/10 yr)- see Exhibit 46

So as the curvature goes down (i.e. 2/30 yr yield goes up) this portfolio underperformes (or does not get to benefit from drop in intermediate maturities)

Laddered portfolio on other hand, is diversified across the yield curve- so intermediate maturities gain in value and others lose value, but these would overall perform better than Extreme barbell

In both cases, barbelled version has higher convexity than the benchmark laddered portfolio. Numbers from the curriculum are Less extreme barbell has a convexity of 1.183 vs 1.134 of benchmark laddered portfolio. The extreme barbell has a convexity of 1.578 vs 1.134. Again, in both cases barbelled (extreme and less extreme) have higher convexity. Why does extreme underperform the benchmark while less extreme outperforms the same bench mark with less curvature?

#4
#5

Thank you!

That is an amazing answer!

I was just thrown off because I was trying to create a heuristic - any version of barbell out performs a ladder when there is less curvature.

Obviously, that’s not going to work.

Again, thank you for a detailed response!

#6

[quote=“cfa2014”]

#7

[quote=“bazz”]

[quote=“cfa2014”]

Shouldn’t this be Barbell > Laddered > Bullet given that Barbell has the highest convexity?

#8

Yes