# Postivie butterfly twist and - definition of short term as well as 'humped' convexity

CFA Mock 2011 #11

They give you the following data (please excuse the formatting):

key rate, portfolio A, portfolio B, portfolio C 3m, .3, .2, .9 2yr, .4, .2, .9 5yr .3, 2.3, 1.1 10yr, 3.6, .3, .9 20yr, .5, .3, 1.0 30yr, .4, 2.3, .8

Some dude expects the yield curve to experience positive butterfly twist (i.e. Short-term and Long-term rates to increase)

The answer is portfolio B although I think that this question is very tricky. I literally took the 3m to 2yr to mean short term, 5 to 10yr to be medium term and 20 to 30 year to be long term. If you go by those parameters then portfolio A is clearly out of the running.

So you are left with portfolio B whose key rate durations for the short-term add up to .4 (I know that this method is not necessarily correct but roughly speaking it is correct) and whose long-term key rate durations add up to 2.6.

For portfolio C, short-term key rate durations add up to 1.8 and long-term add up to 1.8. I would lean toward saying that portfolio C would be most affected by the positive butterfly twist unless:

1. the 5yr key rate duration is considered short-term (thus tilting in favor of portfolio B) OR 2. my method is off. I’m pretty sure that I’m not off and that the problems should allow you to use this logic to determine the portfolio most likely to be affected by this scenario.

So, any suggestions? Is there a guideline for what is short, medium and long term?

Lastly, while looking for an answer I ran into a bunch of posts. Is the term ‘humped’ in CFAland equivalent to ‘negative convexity’ (‘u’ being convex and ‘n’ being negative convex)? Also, with a positive butterfly twist a ‘normal’ term structure (usually slightly negatively convex) would become less so, ultimately reducing curvature and leading to a term structure that is less humped, no?

Conversely, a negative butterfly twist would increase negative convexity thus leading to more humped, right?

Just checking.

Note also that if you were to consider 3m to 5yrs to be short-term and 10yr to 30yr, then in the short-term case portfolio C beats portfolio B by .2 key rate durations, i.e. 2.9 vs 2.7. While portfolio B in the long-term case beats C by .2 key rate durations (.3+.3+2.3)=2.9 vs (.9+1.0+.8)=2.7.

They seem way too close. I just need to make sure my logic is somewhat sound…

It says he expects interest rates to rise materially over the next 6 months so I think they are using that and only looking at the 3m one not the 2 yr. That is how I looked at it.