Brinson Factor Attribution

Brinson attribution decomposes a portfolio's realised return into contributions from each factor exposure. The framework, introduced by Brinson, Hood & Beebower (1986) and refined by Brinson, Singer & Beebower (1991), lets you answer: "My strategy returned +18% — how much came from value exposure, how much from quality, and how much from neither?"

The decomposition

For a portfolio held over one period, define:

• w_i: portfolio weight on factor i
• r_i: realised return of the long-short version of factor i over the period
• r_p: realised return of the actual portfolio
• r_s: specific (idiosyncratic) return — the part not explained by factor exposures

The decomposition is:

In FM103, the factor exposures are inferred from the configured factor weights (e.g., 25/25/25/25 V/Q/M/G if the user set a uniform multifactor strategy). The per-factor realised returns are computed from the schema-v2 factor_return_series per period: top-quintile minus bottom-quintile spread for each factor in each period. The specific return is the residual.

Why this decomposition matters

Without attribution, a +18% return is just a number. With attribution, you might find:

• Value contributed +6% (consistent with the value factor's realised spread)
• Momentum contributed +9% (the period had unusually strong momentum returns)
• Quality contributed +1% (factor barely moved)
• Growth contributed −1% (factor was a drag)
• Specific return: +3% (stock selection within the factor scores added a bit)

This is a very different read than "my strategy works." The strategy worked because momentum was on a tear in the period — not because the factor blend is robust. The next period's momentum return is the headline risk. Without attribution, you don't know this is a single-factor bet dressed up as a multi-factor blend.

Hit rate and t-statistic

For each factor, attribution also computes:

• Hit rate: fraction of periods where the factor contributed positively to portfolio return. A 65% hit rate is solid; below 55% the factor is essentially noise.
• t-statistic of the average per-period contribution. A t-stat below 1.5 means the factor's contribution is statistically indistinguishable from zero across the sample.

Specific return interpretation

Specific return is the part of the strategy's performance that the named factor model does not explain. Three readings, all important:

• Small specific return (< 10% of total): The strategy really is a factor strategy. The factor exposures explain almost everything.
• Moderate specific return (10–30%): The strategy has factor exposure plus some stock-selection content. Reasonable for a quant strategy with intelligent stock screening on top of factors.
• Large specific return (> 50%): The strategy is barely a factor strategy. Most of the return is unexplained by factors — either you're a skilled stock picker, or you have a hidden factor (sector, country, currency) that the model doesn't name.

See Specific Return for the deeper treatment.

Limitations of single-period attribution

Brinson attribution is exact within a period but doesn't compound cleanly across periods (the cross-product terms accumulate). Menchero & Poduri (2008) extend the framework with multi-period linking that preserves the property "sum of contributions = total return." FM103 applies the simpler single-period decomposition then sums — small linking error remains in the multi-period aggregate. For a 20-period backtest the linking error is typically < 1%.

The "best factor / worst factor" headline

The attribution sub-pill surfaces:

• Best factor: the factor with the largest cumulative contribution across the backtest.
• Worst factor: the factor with the most negative cumulative contribution (or smallest if all positive).

If best and worst are not the same as the highest- and lowest-weighted factors, the strategy is benefiting from factor stretches not aligned with the configured weights. This is information for re-weighting.

How to use attribution in practice

1. Sanity-check the strategy thesis. If your strategy is "multi-factor value + quality," confirm that value + quality together contribute the bulk of return. If momentum is the actual contributor, the strategy is mis-described.
2. Identify single-factor bets in disguise. A multi-factor strategy with one factor contributing > 70% is not really diversified.
3. Tune weights based on per-factor t-stats. Factors with high t-stats deserve higher weight; factors with t-stats near 0 deserve less or none.
4. Cross-reference with hit rate. A factor with high cumulative contribution and low hit rate (e.g., +12% from 3 huge wins out of 20 periods) is unreliable.