pybrinson 1.2.0

Portfolio return attribution in Python: Brinson-Hood-Beebower, Brinson-Fachler, and multi-period linking.

pybrinson

Portfolio return attribution in Python — with sources you can audit.

pybrinson decomposes a portfolio's excess return versus a benchmark into allocation, selection, and interaction effects, across any user-defined classification (sector, country, asset class). Every formula ships with its mathematical statement, an academic citation, and a clickable URL — readers can verify the math without leaving the file.

It targets the gap left by the existing Python finance stack: R has the pa package on CRAN and MATLAB ships brinsonAttribution, but no maintained PyPI package implements the Brinson family of models.

Status

v1.2 — adds Menchero (2000, 2004) optimised multi-period linking (patent US 7,249,082 B2 expired 2024-02-18), second-source literature fixtures from Frongello (2002), and a ppar cross-validation script for the Cariño coefficient. Also fixes the v1.1 Frongello implementation to match the published convention (prefix portfolio × suffix benchmark, per the recursion on pp. 4-5 of Frongello 2002).

Methods supported

	Method	Reference
Single-period	Brinson-Hood-Beebower (3-effect)	Brinson, Hood & Beebower (1986)
Single-period	Brinson-Fachler (3-effect)	Brinson & Fachler (1985)
Single-period	Multi-level hierarchical roll-up (any depth)	Bacon (2008), chap. 5
Multi-period linking	Cariño log-smoothing	Cariño (1999)
Multi-period linking	GRAP factors	GRAP (1997)
Multi-period linking	Frongello recursive	Frongello (2002)
Multi-period linking	Menchero optimised	Menchero (2000, 2004)
Multi-period linking	Geometric (Bacon)	Bacon (2008), chap. 6

Deferred to v1.3+: currency attribution (Karnosky-Singer), pandas / polars adapters, fixed-income (Campisi) attribution. See docs/implementation-v1.3.md.

Install

pip install pybrinson

pybrinson has zero runtime dependencies — just the Python standard library. Requires Python 3.14+.

Quickstart

from pybrinson import Segment, bhb

segments = [
    Segment("UK Equity", portfolio_weight=0.40, benchmark_weight=0.40,
            portfolio_return=0.20, benchmark_return=0.10),
    Segment("Japan Equity", portfolio_weight=0.30, benchmark_weight=0.20,
            portfolio_return=-0.05, benchmark_return=-0.04),
    Segment("US Equity", portfolio_weight=0.30, benchmark_weight=0.40,
            portfolio_return=0.06, benchmark_return=0.08),
]

result = bhb(segments, period="2024-Q1")
print(result)

BHB attribution — period 2024-Q1
  R_p = 8.3000%   R_b = 6.4000%   excess = 1.9000%

Segment       Allocation  Selection  Interaction     Total
------------  ----------  ---------  -----------  --------
UK Equity        0.0000%    4.0000%      0.0000%   4.0000%
Japan Equity    -0.4000%   -0.2000%     -0.1000%  -0.7000%
US Equity       -0.8000%   -0.8000%      0.2000%  -1.4000%
Total           -1.2000%    3.0000%      0.1000%   1.9000%

The identity allocation + selection + interaction == excess_return holds within 1e-9 by construction; pybrinson raises AttributionError rather than storing a silent residual when it fails.

Multi-period linking

from pybrinson import bhb, link_carino, Segment

period_attrs = [
    bhb([Segment("Equities", 0.6, 0.5, 0.10, 0.05),
         Segment("Bonds",    0.4, 0.5, 0.05, 0.10)], period="P1"),
    bhb([Segment("Equities", 0.5, 0.5, 0.20, 0.10),
         Segment("Bonds",    0.5, 0.5, 0.05, 0.10)], period="P2"),
]

print(link_carino(period_attrs))

See examples/ for runnable scripts covering BHB, Brinson-Fachler, and Cariño / GRAP / Frongello / geometric linking.

Multi-level hierarchies (v1.1+)

Each Segment may declare an immediate parent label. For chains deeper than one level, pass a parents={parent: grandparent} mapping to bhb() / fachler():

from pybrinson import Segment, bhb

leaves = [
    Segment("UK",      0.20, 0.25,  0.10,  0.08, parent="Europe"),
    Segment("Germany", 0.25, 0.20,  0.05,  0.06, parent="Europe"),
    Segment("US",      0.30, 0.35,  0.12,  0.10, parent="Americas"),
    Segment("Brazil",  0.25, 0.20, -0.04, -0.02, parent="Americas"),
]
result = bhb(leaves, parents={"Europe": "Equity", "Americas": "Equity", "Equity": None})

Allocation, selection and interaction roll up additively at every level: each parent equals the sum of its descendants, and the root parent equals the period total.

Reusable cited fixtures (v1.1+)

from pybrinson import bhb
from pybrinson.fixtures import bacon_2008_ch5_bhb

segments, expected = bacon_2008_ch5_bhb()
result = bhb(segments)
assert abs(result.excess_return - expected["excess_return"]) < 1e-12

The same fixtures back the test suite — there is one source of truth.

Design principles

• Pure Python first. Zero runtime dependencies. Realistic attribution inputs are small (≤1k segments × ≤1k periods); a NumPy dependency would not pay for itself.
• Specification-driven, externally verified. Every function carries its formula, an academic citation, and a clickable URL. The math is cross-checked against published worked examples.
• No silent residuals. Identity failures raise. Bad inputs raise. pybrinson never imputes, rescales or swallows residuals.
• Typed and tested. Public API is fully type-annotated; ships py.typed; tests cover both pinned worked examples and randomised identity checks.

Positioning vs ppar / fincore

	ppar	fincore	pybrinson
BHB	no	yes	yes
Brinson-Fachler 3-effect	2-effect only	no	yes
Cariño linking	yes	no	yes
GRAP linking	no	no	yes
Frongello linking	no	no	yes
Menchero linking	no	no	yes
Geometric linking	no	no	yes
Multi-level hierarchical roll-up	no	no	yes
Public fixture pack of cited examples	no	no	yes
Cross-method consistency suite	no	no	yes
Inline source citations	no	no	mandatory
Identity failure handling	n/a	silent residual	raises
Runtime dependencies	9	2	0

See docs/implementation-v1.md for the audited findings against pinned upstream commits.

Development

This project uses uv and targets Python 3.14.

uv sync                  # install deps, fetch Python 3.14 if needed
uv run pytest            # full test suite
uv run pytest -k bhb     # subset
uv build                 # sdist + wheel into dist/

References

Primary papers cited in the source:

• Brinson, G. P., Hood, L. R., & Beebower, G. L. (1986). "Determinants of Portfolio Performance." Financial Analysts Journal, 42(4). DOI
• Brinson, G. P., & Fachler, N. (1985). "Measuring Non-U.S. Equity Portfolio Performance." Journal of Portfolio Management, 11(3). DOI
• Cariño, D. R. (1999). "Combining Attribution Effects Over Time." Journal of Performance Measurement, 3(4).
• Groupe de Recherche en Attribution de Performance (1997). Synthèse des modèles d'attribution de performance.
• Frongello, A. (2002). "Linking Single Period Attribution Results." Journal of Performance Measurement, 6(3).
• Frongello, A. (2002). "Attribution Linking: Proofed and Clarified." Journal of Performance Measurement, 7(1). Author PDF
• Menchero, J. (2000). "An Optimized Approach to Linking Attribution Effects Over Time." Journal of Performance Measurement, 5(1).
• Menchero, J. (2004). "Multiperiod Arithmetic Attribution." Financial Analysts Journal, 60(4). DOI
• Bacon, C. R. (2008). Practical Portfolio Performance Measurement and Attribution, 2nd ed., Wiley. Wiley page
• Bacon, C. R. (2019). Performance Attribution: History and Progress. CFA Institute Research Foundation. Free PDF

License

MIT — see LICENSE.