The CFA material says that in case of parallel shift of a yield curve, barbell outperforms bullet. Could someone please explain this?
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If the duration of barbell strategy is equal to the duration of bullet strategy, under a parallel shift (up or down), barbell strategy outperforms because its convexity is greater than the convexity of bullet
Note that after the shift, the strategies will no longer be duration matched.
shift up or down?? In case its a downshift, (since you’re long the Short and Long end of the curve, you’ll gain the most appreciation on your high duration Long-Term Bonds) A bullet will have a modest gain since its concentrated in the mid range of the curve and thus has lower duration than the Long Bond.
The assumption is that the portfolios have the same (effective) duration.
In that case, the barbell portfolio should gain with a parallel shift either up or down.
Thank you!
You’re welcome.
Will you be able to explain why for a parallel down-shift a barbell portfolio will outperform a bullet portfolio? To me, it makes sense for a (parallel) downward shift but I am having hard time to understand why a barbel portfolio will outperform a bullet one even for an upward shift?
Thanks
convexity is a measure of dispersion…it’s a second order effect of price changes due to yield changes (duration being the first). Convexity is always positive if you own it- it will magnify increases in price due to yield drops, and will mitigate price losses due to rising yields. Therefore, it is always beneficial to have (and expensive). Barbell portfolios are more dispersed than bullets and therefore carry more convexity- so given identical effective durations, the barbell will always do better during parallel yield shifts for this reason (in ANY direction, for the reason stated above). If the yield curve moves in different ways (curvature, steepness change) it gets more complicated.
hope this helps
If you’re saying that owning a bond means that you always have positive convexity, you’re mistaken.
Lots of bonds have _ negative _ convexity in some region of their price/yield curve, notably callable bonds and prepayable bonds (e.g., mortgage-backed securities).
This is why I love the Magician. Thank you sir for clearing up any misconceptions
My pleasure.
Hi, i think we may need more information on the question at hand -
I think Schweser Book 3, page 64 - Example 2 provides ONE discussion of what you are looking for (i see you are prepping with Schweser)
Also, there is no need to discuss effective duration if the bonds forming the bullet/barbell/ladder do not have embedded option - the modified duration should suffice (meaning modified and effective duration are the same).
It’s not merely a matter of having embedded options; any time cash flows might change when the yield changes you want to use effective duration, not modified duration. An example that doesn’t involve a bond with an embedded option is a floating-rate bond; for a floater, modified duration is a lousy measure of interest rate sensitivity, while effective duration is a good measure thereof.
Agree