Home / Financial Tools / Portfolio Performance Attribution & Multi-Factor Risk Decomposition Engine

Graduate-Level Modeling · Institutional Asset Management

Portfolio Performance Attribution & Multi-Factor Risk Decomposition Engine

Beating the benchmark and understanding why you beat it are two different skills. This tool forces both answers out into the open, sector by sector, factor by factor.

How To Use This Model

Reading This Tool

Enter portfolio and benchmark weights and returns across six sectors for a full Brinson-Fachler attribution, then set six factor exposures for a Barra-style risk decomposition.

Attribution explains why you beat or missed the benchmark, allocation, selection or the interaction between them, sector by sector. The factor model explains where your risk actually comes from, decomposed all the way down to a single factor's contribution to total portfolio variance, using the same Euler decomposition institutional risk systems run in production.

Brinson-Fachler Attribution Inputs (%)

Sector	Port. Wt	Bench. Wt	Port. Ret	Bench. Ret
Technology
Financials
Healthcare
Energy
Cons. Disc.
Industrials

Portfolio and benchmark weights should each sum to roughly 100% across the six sectors for the attribution to be meaningful, the tool will still compute if they don't, but the interpretation gets murkier.

Multi-Factor Risk Model: Exposures (Betas)

Market Beta 1.05

SMB (Size) Beta 0.30

HML (Value) Beta -0.15

RMW (Profitability) Beta 0.20

CMA (Investment) Beta 0.10

Momentum Beta 0.25

Factor Volatilities (Annualized)

Market Vol 16%

SMB Vol 10%

HML Vol 9%

RMW Vol 7%

CMA Vol 6%

Momentum Vol 12%

Risk Model Structure

Average Pairwise Factor Correlation 15%

Specific (Idiosyncratic) Risk 8%

Brinson-Fachler Attribution Summary

Portfolio Return

Benchmark Return

Active Return

Largest Single Effect

Attribution Bridge: Benchmark To Portfolio Return

Allocation, Selection & Interaction By Sector

AllocationSelectionInteraction

Institutional Performance Attribution & Risk Management

The Core Formulas

Allocation_i = (w_P,i − w_B,i)(r_B,i − r_B,total)
Selection_i = w_B,i(r_P,i − r_B,i)
Interaction_i = (w_P,i − w_B,i)(r_P,i − r_B,i)
Factor Variance = β′Σβ, Risk Contribution_i = β_i·(Σβ)_i (Euler decomposition, sums exactly to factor variance)

When To Actually Use This Model

Teaching institutional performance attribution and factor risk modeling in an asset management or quantitative investment course.
Preparing a client-facing quarterly attribution report that separates genuine sector-selection skill from lucky or unlucky allocation timing.
Diagnosing where a portfolio's risk actually concentrates before a factor tilt becomes an unpleasant surprise in a drawdown.

Key Assumptions & Limitations

This tool uses a single uniform pairwise correlation across all factor pairs for tractability, real factor risk models (Barra, Axioma) estimate a full empirical factor covariance matrix from historical returns.
The "Information Ratio" shown is a simplified proxy using total portfolio volatility rather than a properly modeled tracking error against the specific benchmark, treat it as directional, not a precise IR.
Brinson-Fachler attribution is a single-period model, multi-period attribution requires geometric linking across periods to avoid compounding distortions.

Foundational References

Brinson, G. P., Hood, L. R., & Beebower, G. L. (1986). Determinants of Portfolio Performance. Financial Analysts Journal, 42(4), 39-44.

Fama, E. F., & French, K. R. (2015). A Five-Factor Asset Pricing Model. Journal of Financial Economics, 116(1), 1-22.

Grinold, R. C., & Kahn, R. N. Active Portfolio Management. McGraw-Hill.

Want the single-factor CAPM version of this too?

Open The Fama-French Regression Estimator →