Contribution to Return

A stock doubling in price sounds like the headline of the year — until you learn it was 1% of the portfolio, while a boring 5% gain in the position that made up 40% of the book did more than ten times as much for the bottom line. A position's return tells you how it performed on its own money. Its contribution to return tells you how much of the portfolio's actual return it was responsible for, and those are frequently very different rankings.

Weighting the return by the position size

$$\text{Contribution}_i = w_i \times r_i, \qquad \sum_i \text{Contribution}_i = R_{\text{portfolio}} .$$

In words: multiply each position's weight $w_i$ (its share of the portfolio's total value at the start of the period) by its own return $r_i$. Add up every position's contribution and, for a single period with no cash flows during it, the sum comes out to exactly the portfolio's total return — no rounding, no residual. That identity is what makes contribution useful: it's a clean, additive decomposition of exactly where the portfolio's return came from.

Worked example 1 — three positions, one total

A portfolio holds three positions: Stock A at 50% weight returning $4\%$, Stock B at 30% weight returning $-6\%$, and Stock C at 20% weight returning $15\%$. Contributions: A, $0.50 \times 4\% = 2.0\%$; B, $0.30 \times -6\% = -1.8\%$; C, $0.20 \times 15\% = 3.0\%$. Sum: $2.0 - 1.8 + 3.0 = 3.2\%$ — the portfolio's total return, built entirely from these three numbers.

Worked example 2 — return rank versus contribution rank

By raw return, Stock C's $15\%$ is the best performer, comfortably ahead of A's $4\%$. But by contribution, A added $2.0\%$ and C added $3.0\%$ — C is still the bigger contributor, but the gap has narrowed sharply once weight is accounted for. If C's weight had instead been only 5% (with A's raised to 65% to compensate), C's contribution would fall to $0.05 \times 15\% = 0.75\%$ — suddenly the worst contributor of the three, despite still posting the best individual return, purely because so little capital was behind it.

What this means in practice

A performance review that only lists each position's own return can send a manager chasing the wrong lesson — praising a tiny position's lucky double, or overlooking that the portfolio's single largest holding quietly did most of the real work. Contribution reports are what performance and risk teams actually read in a post-mortem, because they answer "where did the money come from" rather than "which stock happened to move the most."