--- title: "Marginal Contribution to Risk: Formula" description: "Marginal contribution to risk (MCTR) is how much portfolio volatility changes for a small increase in one asset's weight. It is the partial derivative of..." canonical: https://www.getswoopr.com/indicators/portfolio-and-risk/marginal-contribution-to-risk/ source: "Swoopr Investment: https://www.getswoopr.com" --- ## Direct Answer > Marginal contribution to risk (MCTR) is how much portfolio volatility changes for a small increase in one asset's weight. It is the partial derivative of portfolio volatility with respect to that weight. It is a per-unit-weight rate: assets with a high MCTR add the most volatility at the margin, assets with a low or negative MCTR dilute it. # Marginal Contribution to Risk: Formula, Meaning, Signals, Examples and How to Use It ## How Is Marginal Contribution to Risk Calculated? Marginal contribution to risk (MCTR) is how much portfolio volatility changes for a small increase in one asset's weight. It is the partial derivative of portfolio volatility with respect to that weight. **Formula:** `MCTR_i = d sigma_p / d w_i = (Sigma w)_i / sigma_p = cov(r_i, r_p) / sigma_p` **Inputs:** - Covariance matrix of asset returns - Portfolio weights - Portfolio volatility sigma_p **Worked example.** An asset whose return covariance with the portfolio is 0.018, in a portfolio with 12% volatility, has a marginal contribution to risk of 15.0%. The inputs are illustrative numbers, not market data. **Reading it.** It is a per-unit-weight rate: assets with a high MCTR add the most volatility at the margin, assets with a low or negative MCTR dilute it. Multiplying by the weight gives the asset's volatility contribution. **Limits.** It is a local, first-order measure that holds only for small weight changes, and it relies on a noisy covariance estimate. It does not say how large the position's total effect is until multiplied by its weight. ## What is Marginal Contribution to Risk? Marginal contribution to risk (MCTR) is how much portfolio volatility changes for a small increase in one asset's weight. It is the partial derivative of portfolio volatility with respect to that weight. ## How to use Marginal Contribution to Risk It is a per-unit-weight rate: assets with a high MCTR add the most volatility at the margin, assets with a low or negative MCTR dilute it. Multiplying by the weight gives the asset's volatility contribution. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime. ## Strengths - The derivative with respect to a weight shows which holding adds the most volatility per unit of capital at the margin. - It can be computed from a covariance matrix and weights alone, so no return forecast is needed. - Reproducible when the formula and data convention are fixed. ## Weaknesses and limitations - A negative value says increasing the weight lowers volatility, but that holds only while correlations stay as estimated. - Because it is a derivative of the whole portfolio, it changes whenever any other weight changes, so a stored value goes stale after rebalancing. - Correlated indicators can create false confidence by repeating the same underlying information. ## Editorial and risk note This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance. ## Frequently Asked Questions Is Marginal Contribution to Risk a buy or sell signal? No. It is a per-unit-weight rate: assets with a high MCTR add the most volatility at the margin, assets with a low or negative MCTR dilute it. It is a local, first-order measure that holds only for small weight changes, and it relies on a noisy covariance estimate. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions. What is the best setting for Marginal Contribution to Risk? Marginal Contribution to Risk is computed from covariance matrix of asset returns; portfolio weights; portfolio volatility sigma_p, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner. Can Marginal Contribution to Risk be used by itself? It is a local, first-order measure that holds only for small weight changes, and it relies on a noisy covariance estimate. It does not say how large the position's total effect is until multiplied by its weight. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone. Does Marginal Contribution to Risk work on every timeframe? The calculation (MCTR_i = d sigma_p / d w_i = (Sigma w)_i / sigma_p = cov(r_i, r_p) / sigma_p) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it. Why does Marginal Contribution to Risk give false signals? A negative value says increasing the weight lowers volatility, but that holds only while correlations stay as estimated. Because it is a derivative of the whole portfolio, it changes whenever any other weight changes, so a stored value goes stale after rebalancing. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated. How should Marginal Contribution to Risk be backtested? Rebuild Marginal Contribution to Risk from covariance matrix of asset returns using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline. S Swoopr Editorial Team The Swoopr Editorial Team produces independent investment education, research, and tools for understanding markets, evaluating opportunities, and managing risk. All content is educational only and does not constitute personalized investment advice. 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