Contribution to Risk (Component Risk)

the contribution to risk is the metric used for true risk budgeting and attribution it provides an additive decomposition of the total portfolio risk metric principle contribution to volatility the money/percentage share of the total portfolio volatility attributable to the category contribution to var the additive portion of the total portfolio var attributable to the category contribution to cvar the additive portion of the total portfolio cvar (expected shortfall) attributable to the category calculation the contribution for any coherent risk measure (volatility and cvar) is derived from the marginal risk , which measures the sensitivity of the total portfolio risk to a small change in the category's weight \text{contribution to risk} i = \text{weight} i \times \frac{\partial \text{risk} {\text{portfolio}}}{\partial \text{weight} i} interpretation this value directly answers the question "how much of the total portfolio's risk is this category genuinely responsible for?" this is the most accurate measure for risk management positive contribution the category is actively increasing the overall portfolio risk (e g , high beta or highly volatile assets) negative contribution a negative contribution indicates that the category is providing a powerful diversification benefit to the total portfolio this means the asset's losses tend to occur at different times or with less severity than the rest of the portfolio's losses, making it an effective hedge or risk reducing component the additive principle the crucial feature of the contribution to risk is the euler decomposition principle this ensures that the sum of the contribution to risk across all categories is exactly equal to the total risk measure of the portfolio \text{total portfolio risk} = \sum {\text{all categories}} \text{contribution to risk} {\text{category}} this perfect additivity is what makes this measure ideal for risk budgeting, allowing a manager to allocate a specific risk budget to each part of the portfolio, regardless of whether the measure is volatility (based on variance/covariance) or a tail measure like cvar