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# Risk Premium Contribution

The risk premium for an individual asset is computed from the factor prices and factor loadings of a company. See "The cross section of factor prices" for more details.

The marginal contribution of a factor f to the risk premium of an asset j, $//$, is the difference between $//$ and the risk premium computed with $//$ set to 0 (or equivalent). We are essentially computing the premium without the effect of factor f to see the impact that it has.

The marginal contribution of a factor f for an index is the weighted average of the asset marginal contributions.

This can be expressed as a percentage of the total factor marginal contributions as per the below. This is a measure of how much a given factor drives the risk premium of an index relative to other factors.

Note on contribution signs

Risk factors can have a positive or negative contribution to the risk premia: e.g. the profit factor has a negative effect because more profitable infrastructure companies tend to have lower risk premia. Conversely, the leverage factor has a positive effect: higher leverage leads to higher risk premia ceteris paribus.