Risk Contribution and Risk Decomposition

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#

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.

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

A worked example#

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 and Correlation Management.

Decomposition by group or factor#

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) and Expected Shortfall (CVaR).

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.

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.