Impact of curvature changes on a barbell portfolio

Hey guys,

I have one question regarding reading 20, exhibit 65. In this part of the reading, we compare a “less extreme” barbell portfolio to a laddered portfolio and change the yield curve in order to see how the performance of those portfolios reacts.

In general, my understanding was that a barbell portfolio outperforms if curvature increases. This is consistent with the summary in exhibit 67. Anyways, in exhibit 65 the opposite is the case. Can someone explain why, please?

Thank you very much in advance!

Is there a way you can paste a screen shot of the exhibit? I only have last year’s books so I can’t look it up.

Yes, please find the exhibit here:

Exhibit 65

I expected the opposite sign for “Return Difference” in the last two rows…

Yeah that is weird. If the benchmark portfolio is laddered while the other one is a barbell, the barbell should outperform when curvature increases as it does not have positions in the middle of the yield curve. Maybe the return difference is an error ? I checked the errata and there’s a bunch of mistakes in reading 20.

That was my understanding as well. I reported it to CFAI, let’s see what happens. The errata is indeed quite long already…

Anyways, thank you very much for your time and help!

No problem, let us know what CFAI says when they get back to you.

Ok guys, I got the following response from CFAI:

“Thank you for contacting us about the CFA Program curriculum. The text is correct. Exhibit 65 cannot be compared to Exhibit 67. Exhibit 65 compares the less extreme barbell to a laddered portfolio. Exhibit 67 compares a barbell and a bullet. The signs on the “return difference” are correct as shown.”

I thought that the performance of a laddered portfolio would always be somewhere between the performance of a barbell and a bullet portfolio. Given the response stated above, this is incorrect. Unfortunately, I still do not understand why this is the case.

To make the approach of the chapter a bit clearer: We first compare an extreme barbell portfolio to a laddered one. The extreme barbell outperforms when curvature increases. Then we compare a less extreme barbell to the same laddered portfolio. Now, the less extreme barbell underperforms when curvature increases. So the laddered portfolio’s performance is somewhere in between?!

Why that? What am I missing here?

If you are hell bent upon mugging the text , then of course it becomes difficult to get the underlying concept and the reasoning thereof.

  1. An extreme barbelled has all the mass at the extreme maturities thus reaps the maximum curvature benefit because of the higher convexity. ( I presume you know that convexity is a fn. of Duration and Duration for all practical purposes is the maturity. Convexity is the 2nd order derivative of the curvature ). This when compared to a similar Bullet or Laddered portfolio ( same in all other aspects )

  2. A less extreme barbelled has not all masses concentrated at the extrnee maturities and ends somewhat before that although it still is a barbelled portfolio. This when compared to the similar laddreed is naturally at disadvantage as the Laddered portfolio has the masses evenly distributed across the maturities and thus extends well beyond the less extreme barbelled’s two ends.

Higher mass at extreme end maturity means higher convexity means higher curvature benefit.

Rest of the things should be easy to grasp.

Are you sure a less extreme barbell does not have any positions at the extreme ends? I’ve never heard of this before. To me (assume a 1,3,5,15,30 yr ladder) extreme barbell : positions split about 50/50 between the 1yr and the 30yr. Less extreme barbell: largest positions on 1yr and 30yr while smaller positions in 3yr,5yr and 15yr.

And why should that be a surprise ?

Did I say that the WAC or the Dur. differ ?

And if they don’t differ the only point of difference is the convexity. The less extreme barbelled portfolio is naturally disadvantaged here wrt to the Laddered one. BTW, in all fairness, I am not sure if your example of 1 yr, 30 yr., 3 yr., 15 yr. actually qualifies for a less extreme barbelled portfolio. May be, portfolio comprising of 3 yr. And 25 yr. Significantly weighted at these maturities do qualify. Now you may compare this with a Laddered one you hypothesised. I think rest of it should be easy.

i’m reading this right now, where does it show the opposite?