What is contribution to return?

Contribution to return is the part of a portfolio's return that comes from a single holding. It combines two things: how well the holding performed, and how much of the portfolio it made up. A holding that doubled contributes little if it was a tiny position; a large position with a modest loss can pull the whole portfolio down.

The formula

For one period, the contribution of holding $i$ is its weight at the start multiplied by its return:

c_i = w_i \times r_i

where $w_i$ is the holding's share of the portfolio's value at the start of the period and $r_i$ its return over the period. The contributions of all holdings add up to the portfolio's return:

r_{\text{portfolio}} = \sum_{i} w_i \, r_i

Contributions are measured in percentage points, not percent: a holding that contributes 1.5 points raised the portfolio's return by 1.5 points.

A simple illustration

Holding	Weight	Return	Contribution
World ETF	60%	+8	+4.8
Tech stock	5%	+40	+2.0
Bank stock	25%	-10	-2.5
Cash	10%	0	0.0
Portfolio	100%		+4.3

The tech stock had by far the best return, yet the world ETF contributed more than twice as much, simply because it was twelve times larger. And the bank stock's loss took away more than the tech stock's gain added.

Over longer periods

Weights change as prices move and as money is added or withdrawn. Over longer periods, contributions are therefore calculated for each short period — a day or a month — and then linked together. Multiplying the average weight by the total return only gives an approximation, and those approximations no longer add up exactly to the portfolio's return.

How to read it

Where the result came from. If most of the return comes from one or two holdings, the portfolio's result depends on them, whatever the number of positions it holds.
Size matters as much as performance. Contribution answers what drove the portfolio's result; return answers which investment performed best. They are different questions, and the answers are often different holdings.
Negative contributions are normal. In a diversified portfolio some holdings almost always detract. The question to ask is whether one of them detracts out of proportion to its weight.

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