# Risk Contribution and Risk Decomposition

> Risk contribution shows how much each position adds to total portfolio risk, including correlations. Learn marginal and total contributions with a worked example.

Source: https://learn.tradelabsai.com/portfolio/risk-contribution/  
Track: Portfolio and Performance · Level: Advanced · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Risk Contribution and Risk Decomposition", https://learn.tradelabsai.com/portfolio/risk-contribution/

Knowing each position's weight tells you where your money is. Knowing each position's risk contribution tells you where your risk is, and the two can be very different. A position with a small weight but high volatility and high correlation to the rest of the portfolio can drive most of the swings, while a large position in a diversifying asset may barely register. Risk decomposition breaks total portfolio risk into the parts contributed by each position, sector or factor, so you can see what really drives results.

## Key measures

| Measure | Meaning |
|---|---|
| Marginal contribution to risk (MCR) | How much portfolio volatility changes for a small increase in a position |
| Total risk contribution (RC) | Weight times marginal contribution; the position's share of portfolio volatility |
| Percentage contribution | Risk contribution divided by total portfolio volatility |

The total risk contributions of all positions add up exactly to total portfolio volatility. This additivity makes decomposition useful for budgeting. See [Risk Budgeting and Risk Parity](https://learn.tradelabsai.com/portfolio/risk-budgeting-and-risk-parity/).

```
Risk contribution of asset i = w_i × (Covariance matrix × w)_i / Portfolio volatility
```

## A worked example

**Example: Decomposing a 60/40 portfolio**
Stocks have 15% volatility, bonds 5%, and their correlation is 0.2. Weights are 60% and 40%. Portfolio variance is 0.36 times 0.0225, plus 0.16 times 0.0025, plus 2 times 0.6 times 0.4 times 0.2 times 0.15 times 0.05, which is 0.0081 plus 0.0004 plus 0.00072, or 0.00922. Portfolio volatility is about 9.6%. Stocks' contribution to variance is 0.6 times (0.0225 times 0.6 plus 0.0015 times 0.4), which is 0.6 times 0.0141, or 0.00846, about 92% of the total. Bonds contribute 0.4 times (0.0015 times 0.6 plus 0.0025 times 0.4), which is 0.4 times 0.0019, or 0.00076, about 8%. In volatility terms, stocks contribute about 8.8 points and bonds about 0.8 points of the 9.6%. Holding 40% in bonds does not mean 40% of the risk.

## Why correlation matters

A position's risk contribution depends on how it moves with everything else. A volatile asset that is negatively correlated with the portfolio can have a negative risk contribution: adding a little of it reduces total risk. That is how hedges work. See [Hedging](https://learn.tradelabsai.com/markets/hedging/) and [Correlation Management](https://learn.tradelabsai.com/portfolio/correlation-management/).

## Decomposition by group or factor

| Level | Example question |
|---|---|
| Position | Which three holdings drive half the risk? |
| Sector or asset class | Is technology more than 40% of risk? |
| Factor | How much risk comes from market beta, momentum or interest rates? See [Factor Models](https://learn.tradelabsai.com/portfolio/factor-models/) |
| Strategy | Which strategy dominates the fund's volatility? |

Factor decomposition often reveals that a portfolio thought to be diversified is mostly one bet, such as exposure to the overall market or to falling interest rates.

## Tail risk contributions

The same idea applies to value at risk and expected shortfall: component VaR shows how much each position adds to the portfolio's VaR, highlighting which holdings would drive losses in a bad day. See [Value at Risk (VaR)](https://learn.tradelabsai.com/portfolio/value-at-risk/) and [Expected Shortfall (CVaR)](https://learn.tradelabsai.com/portfolio/expected-shortfall/).

## Using risk decomposition

1. **Compare risk shares with intentions:** if one idea is 70% of risk, is that deliberate?
2. **Set risk budgets** and adjust weights to match them.
3. **Identify hedges:** positions with negative contributions.
4. **Watch changes over time:** rising volatility or correlation shifts risk without any trades. See [Concentration Risk](https://learn.tradelabsai.com/risk/concentration-risk/).

## Frequently asked questions

### What is risk contribution?

The share of total portfolio risk attributable to a position, accounting for its weight, volatility and correlation with the rest of the portfolio.

### Why is risk contribution different from weight?

Volatile assets and assets that move with the rest of the portfolio contribute more risk than their weight suggests, while diversifying assets contribute less.

### Can a risk contribution be negative?

Yes. An asset negatively correlated with the portfolio can reduce total risk, giving it a negative contribution.

Next, weigh up active and passive approaches in [Active vs Passive Investing](https://learn.tradelabsai.com/portfolio/active-vs-passive-investing/).

## Continue learning

- Next lesson: [Active vs Passive Investing](https://learn.tradelabsai.com/portfolio/active-vs-passive-investing/)
- Previous lesson: [Portfolio Optimization](https://learn.tradelabsai.com/portfolio/portfolio-optimization/)
- Related: [Portfolio Optimization](https://learn.tradelabsai.com/portfolio/portfolio-optimization/): Portfolio optimisation uses maths to choose weights that best meet a goal. Learn mean variance, minimum variance, constraints and how to handle estimation error.
- Related: [Risk Budgeting and Risk Parity](https://learn.tradelabsai.com/portfolio/risk-budgeting-and-risk-parity/): Risk parity balances how much risk each asset contributes instead of how much money it holds. Learn risk budgeting, a worked example, leverage and drawbacks.
- Related: [Correlation Management](https://learn.tradelabsai.com/portfolio/correlation-management/): Correlation management keeps a portfolio from turning into one big bet. Learn to measure correlations, combine correlated risks and set sensible limits.
- Related: [Factor Models](https://learn.tradelabsai.com/portfolio/factor-models/): Factor models explain asset returns with common drivers such as the market, size, value and momentum. Learn CAPM, Fama French and how to run a factor regression.
- Related: [Value at Risk (VaR)](https://learn.tradelabsai.com/portfolio/value-at-risk/): Value at risk estimates the loss a portfolio should not exceed with a given confidence over a set period. Learn the three methods, an example and the limits.
- Related: [Concentration Risk](https://learn.tradelabsai.com/risk/concentration-risk/): Concentration risk is the danger of having too much exposure to one asset, sector or idea. Learn how it hides in portfolios, how to measure it and how to limit it.