MCR measures each holding's share of total portfolio volatility. Holdings with MCR greater than their portfolio weight are contributing disproportionately to risk.
Formula
MCRᵢ = wᵢ × (Σⱼ wⱼσᵢσⱼρᵢⱼ) / σₚMethodology
Marginal Contribution to Risk (MCR) is a powerful tool for understanding risk sources in a portfolio. It decomposes total portfolio volatility into contributions from each holding.
The key insight is the Euler decomposition property: the sum of all MCRs equals exactly the portfolio volatility. This allows us to attribute 100% of portfolio risk to individual holdings.
MCR accounts for both: 1. The holding's own volatility 2. How it correlates with other holdings
A high-volatility stock that's uncorrelated with the rest of your portfolio may contribute less risk than a medium-volatility stock that's highly correlated with other holdings.
The risk-to-value ratio (MCR weight ÷ portfolio weight) identifies inefficient holdings: - Ratio > 1.3: Disproportionate risk contributor - Ratio < 0.8: Risk-efficient holding - Ratio ≈ 1.0: Proportional risk contribution
How to Interpret
| Range | Label | Meaning |
|---|---|---|
| ≥ 1.3 | Inefficient | Contributing disproportionately more risk than value |
| 0.8 to 1.3 | Proportional | Risk contribution roughly matches portfolio weight |
| < 0.8 | Efficient | Providing diversification benefits relative to weight |
Data Source
Calculated using Euler decomposition of portfolio variance. Uses sector correlations as a proxy for individual stock correlations.
Reference
Roncalli, T. (2013). Introduction to Risk Parity and Budgeting. Chapman & Hall/CRC Financial Mathematics Series
Limitations
Uses sector-level correlations rather than individual stock correlations. Correlation estimates are based on historical data and may change.
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For Educational Purposes Only
This analysis is not investment advice. Results are based on simplified models using historical data. Past performance does not guarantee future results. All investments carry risk of loss. Consult a qualified financial advisor before making investment decisions.