What is performance attribution?

Performance attribution explains why a portfolio's return differed from its benchmark's. It splits the difference — the active return — into the decisions that caused it. The best-known method, the Brinson model, separates two kinds of decision:

Allocation: how much was put into each segment — each asset class, sector or region — compared with the benchmark.
Selection: which investments were chosen within each segment, and how they did compared with that segment of the benchmark.

The formulas

For each segment $k$ , let $w_k$ and $b_k$ be the weights in the portfolio and in the benchmark, $R_k$ and $B_k$ the returns of the segment in the portfolio and in the benchmark, and $B$ the benchmark's total return:

\text{Allocation}_k = (w_k - b_k) \times (B_k - B)

\text{Selection}_k = w_k \times (R_k - B_k)

This version folds the original model's separate "interaction" effect into selection. Together, the effects of all segments add up exactly to the active return:

R_p - B = \sum_k \text{Allocation}_k + \sum_k \text{Selection}_k

A simple illustration

A portfolio and its benchmark both hold only stocks and bonds:

	Portfolio weight	Benchmark weight	Portfolio return	Benchmark return
Stocks	80%	60%	+12	+15
Bonds	20%	40%	+2	+2
Total			+10.0	+9.8

The portfolio beat its benchmark by 0.2 points. Attribution shows two opposite stories behind that small number:

\text{Allocation} = 0.2 \times (15\% - 9.8\%) + (-0.2) \times (2\% - 9.8\%) = +2.6\%

\text{Selection} = 0.8 \times (12\% - 15\%) + 0.2 \times (2\% - 2\%) = -2.4\%

Holding more stocks than the benchmark in a year in which stocks did well added 2.6 points; the particular stocks chosen lagged the stock market and cost 2.4 points. A strong allocation decision and weak stock picking almost cancelled out.

How to read it

Allocation effects reward being over-weight in segments that beat the benchmark as a whole, and under-weight in those that lagged.
Selection effects reward choosing investments that beat their own segment of the benchmark.
Allocation usually dominates. Studies of pension funds have found that most of the variation in their returns over time is explained by their asset allocation rather than by security selection.

Limits

It depends on the segments chosen. Attributing by sector tells a different story than attributing by country.
It adds up exactly only for a single period. Over several periods, the effects must be linked with special methods to match the total.
It explains, it does not predict. A strong selection effect in one year says little about skill without a longer record.

A worked example

Worked through on a sample portfolio. The figures below are that portfolio’s, not yours.

How much of my return came from asset allocation vs security selection?

I don't have an allocation-vs-selection attribution already computed for your portfolio. Your portfolio's total return is +94,58%.

What an attribution needs and what I already have

Required to run the split: the period to analyse, portfolio weights and returns by asset (available), and benchmark returns per asset class or per security (not present).
What I already have from your data: current weights and holding returns, asset-class weights and portfolio period returns (so I can compute security contributions). I need the reference returns (benchmarks) to separate pure allocation effects from security selection and interaction.

If you want the decomposition I can run it for any period you choose. I will report: allocation effect, selection effect and interaction effect, and show which asset classes and securities drove each term.

See these numbers for your own portfolio

Floreo works out every figure on this page from your own holdings — returns, risk, allocation, currencies — and the assistant explains them the way this page does. Import from your broker, or try it on the sample portfolio first.

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