Fixed Income Return Attribution: Decomposition
If you like the Brinson-Hood-Beebower (BHB) model for equity return attribution, you should like fixed-income decomposition; it's sort of "BHB for bonds."
You can always estimate bond price changes using duration; what else is needed to estimate a duration-based price change?
Of course.
No, coupons don't change. It's the yield that changes, and based on this, duration is used to estimate a change in the price of the bond.
But if you want a more accurate price of a bond, you do a full repricing. Grab the spot rates from zero-coupon bonds and discount each cash flow according to the appropriate yield curve. How does this sound?
Not really. It's flexible and accurate, but fairly complex to get all of that data and process. Here's an example of a benchmark and portfolio so that attribution analysis can be performed:
Yes, it is. Here's an example of a benchmark and portfolio so that attribution analysis can be performed:
| | | | | | | | | |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| **Portfolio** | **Weights** ||| **Durations** |||||
| | Short | Mid | Long | **Total** | Short | Mid | Long | **Total** |
| Government | 10% | 10% | 20% | **40%** | 4.42 | 7.47 | 10.21 | **8.08** |
| Corporate | 10% | 20% | 30% | **60%** | 4.40 | 7.40 | 10.06 | **8.23** |
| | | | | | | | | |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| **Benchmark** | **Weights** ||| **Durations** |||||
| | Short | Mid | Long | **Total** | Short | Mid | Long | **Total** |
| Government | 20% | 20% | 15% | **55%** | 4.42 | 7.47 | 10.21 | **7.11** |
| Corporate | 15% | 15% | 15% | **45%** | 4.40 | 7.40 | 10.06 | **7.29** |
There's a lot to take in here. The duration totals are a weighted average of the three bond groups in each case. Based on what the manager chose, what would you assume about the manager's expectations for yield curve shifts?
There's really no reason to assume that based on her weighting here. Look at the portfolio weights compared to those of the benchmark for duration.
Exactly! The manager chose to overweight the long-duration bonds, leading to a portfolio duration of over 8 while the benchmark portfolio's duration is closer to 7.
Unlikely. If that was the case, the manager probably would have stayed with the portfolio weightings as far as durations are concerned.
What might you also infer about the manager's expectations of credit spreads, given other information here?
There's really no reason to assume that based on her weighting here. Look at the portfolio weights compared to those of the benchmark for government and corporate issues.
Yes! Just as the manager overweighted the long-duration bonds, the manager also chose to allocate more to corporate bonds than government issues. This will be a good plan if credit spreads narrow.
Unlikely. If that was the case, the manager probably would have stayed with the portfolio weightings as far as government vs. corporate issues are concerned.
Here's a quick snapshot of what happened, in terms of returns:
| | | | |
|:---:|:---:|:---:|:---:|
|| **Returns** |||
| | Short | Mid | Long |
| Government | -3.48% | -5.16% | -4.38% |
| Corporate | -4.33% | -6.14% | -5.42% |
How does it look like the manager did in terms of sector weighting?
It looks that way, yes. Corporate bonds performed worse than government bonds, so the manager lost there. And how about for duration weighting?
There's no evidence for that. Corporate bonds performed worse than government bonds, so the manager lost there. And how about for duration weighting?
What other yield curve change may the manager have been anticipating?
Absolutely. This is another good reason to overweight long-duration bonds, and this is what happened when you take a look at the attribution results:
| Duration Bucket | Duration Effect | Curve Effect | Total Interest Rate Allocation | Sector Allocation | Bond Selection | Total |
|---|:---:|:---:|:---:|:---:|:---:|:---:|
| Short | 0.40% | 0.12% | 0.52% | 0.04% | 0.00% | 0.56% |
| Mid | 0.23% | 0.03% | 0.26% | -0.05% | 0.00% | 0.21% |
| Long | -1.25% | 0.37% | -0.88% | -0.22% | 0.13% | -0.97% |
| **Total** | -0.62% | 0.52% | -0.10% | -0.23% | 0.13% | -0.20% |
Incorrect. That would mean a higher relative yield for longer-term bonds, which would work *against* the manager.
No, anticipation of an upward shift would make the manager want to reduce portfolio duration.
Right again!
Not really. The manager increased portfolio duration as bonds were about to lose value; that seems like a mistake.
There you go.
What change was the manager right about?
No, the manager lost 125 basis points on that in total.
That's right. The manager underperformed the portfolio by 20 basis points. You can see that this came from a 23-basis-point loss in sector selection, and the manager lost big on the yield increase. But the curve *did* flatten, gaining back 52 basis points of credit for the shape.
A lot of complexity, a lot of inputs, a lot of calculation, and a lot to digest. But when the decomposition is complete, that's a lot of good information to use for judging performance!
No, the manager lost 23 basis points in sector selection.
To summarize:
[[summary]]
A change in coupon
A change in yield
Simpler
More complex
The manager expects yields to rise
The manager expects yields to fall
The manager expects yields to remain unchanged
The manager expects credit spreads to widen
The manager expects credit spreads to narrow
The manager expects credit spreads to remain unchanged
Badly
Well
Upward shift
Flattening
Steepening
Badly
Well
Bad
Good
Yield shift
Curve shape
Credit spread
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