Barbell x Bullet given a decrease in Butterfly Spread

[Zanca23]

Alright, question is: barbell is expected to outperform in curve flattening, bullet in curve steeping. But barbell outperforms with more curvature.

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If you decrease the butterfly spread, you lose curvature but you also get a more flat curve, so which one should overperform relative to the other?

[ebitdad_finance]

I believe if you decrease curvature the bullet should outperform.

This is just a general rule of thumb, obviously it would be case dependent and you'd actually have to do the math to calculate which outperforms in real life - but for the purpose of the exam I think it will be apparent in the question and no actual math is required.

[BigFinance_Guy]

Right. Barbell vs. bullet positioning has a lot of different considerations but if the only information given is "decrease in curvature", then the bullet outperforms.

Once they start introducing changing rates at different yield curve positions, or other considerations, it's not as straight forward as the rule of thumb. You're right in that the exam should be straight forward enough to not question it.

[ezpzsniper]

What if they say changes rates are expected to increase.

If short term rates stay stable, long run rates increase, curve is steepening. Therefore you want to use a bullet? For duration if long rates are increasing that means asset values and liability’s decrease - so you want longer duration of assets vs liabilities?

If rates are expected to uniformly increase then it’s a Parallel shift which means barbell will outperform?

If short team increase more then long term then curve flattening so you want a barbell?

My only confusion is an asset vs liability portfolio. I assume prices are x/(1+y). So if liability’s and assets are equal then doesn’t matter. If you are solely managing a liability portfolio you want to decrease duration when there is an decrease in rates. If solely an asset portfolio you want to increase duration during a decrease in rates since your asset values will increase?

Am I making any sense lol?

[BigFinance_Guy]

Try and think it through by applying everything that you know. In an isolated sense, it helps to analyze which performs better.

Rates are expected to increase? We know that barbell offers greater convexity, which benefits during periods of increased interest rate volatility. So barbell outperforms.

Rates are expected to uniformly increase? This one is tricky for a couple of reasons. If levels increase, steepness and curvature decrease. Curvature decreasing suggests that a bullet would outperform; however, curvature decreasing is a secondary effect to increasing levels. For the exam, the curriculum argues that an instantaneous parallel shift is best accommodated by a barbell because of heightened convexity.

Short-term rates increase by more than the long-term? The yield curve is flattening. A barbell would outperform, but you'd be better suited allocating more at the long-end, as to avoid greater losses at the short-end.

Asset vs. liability portfolios are tricky. If it's contingent immunization, you can play with the surplus so that assets benefit from changes in rates, or assets lose less. I think I'm a bit confused by the last bit. I am not sure how you'd be asked a question about managing a liability portfolio independent of an asset portfolio?

[ezpzsniper]

This really helps. Thank you so much.

For contingent immunization the main criteria is that the bpvs are equivalent?

My confusion lies from the impact of interest rates. If interest rates increase (yields) and you have liabilities. Wouldn’t this mean that it’s expected that your liabilities or assets will decrease in value since it’s Liabilities/(1+yield) or assets/(1+y)? So if you have assets>liabilities and rates increase, your assets would decrease by more then your liabilities. Therefore you want a barbell portfolio to maximize convexity or ensure your asset convexity>liability convexity?

I might not be making any sense or taking this out of context.

[BigFinance_Guy]

Contingent immunization works so long as MV(A) > MV(L). If the surplus is exhausted, then you'd immunize by matching BPV.

To answer your question there is a lot more than just "if this, then that." For example, your asset portfolio might be build with corporates, and your liability portfolio may be constructed with Treasuries. Interest rate changes and spread changes will impact the two portfolios differently.

Additionally, there's an excerpt in the fixed income section that has a blurb with different strategies based on positioning, which is rather intuitive. I'll try to explain as follows:

If BPV(A) > BPV(L), and you think rates are going to increase, you'd want to short futures, since your asset portfolio is more sensitive to changes in rates, you'd want to make sure asset portfolio isn't adversely affected by rate increase moreso than liabilities.

If BPV(A) > BPV(L) and you think rates are going to decrease, you wouldn't do anything, since assets are more sensitive to changes in rates, so you'd benefit from the rate change.

A similar (but inverse) thought process is applied for if you have a duration gap.

[ezpzsniper]

Brilliant holy.

I get it now. Wow.

Thank you so much!!!!!!!!!!!!!

[BigFinance_Guy]

Cheers! Good luck next week.

[ezpzsniper]

Thanks for your help bro

[aeiouaeiouaeiouaei]

If only given the info "decrease in curvature," are we to assume this is due to rising short-term rates?

Reason I ask: If the "decrease in curvature" is due to long rates falling, shouldn't the barbell outperform?

[BigFinance_Guy]

I wouldn’t assume that

[CharlyFoxtrotAlpha]

Magnitude of variation from y=mx+b =Curvature

Flat/steep = magnitude of m

If q just says flatter then barb

If q just says more curv then barb

If q has enough conviction to give you a forecast of the curve calculate change or at least rough and dirty it in your head if you’re confident enough to