Who this is for — Anyone moving from single-position controls to the right portfolio question: what risk does the whole portfolio produce, under which assumptions, and with which contributions?
Aggregate risk is a risk measure calculated over a common scope: included positions, strategies, accounts or entities; valuation time; currency; horizon; scenarios; and method. It is not a universal number, and values with different units or definitions cannot be added into one.
Portfolio value changes are additive:
ΔVₚ = ∑ᵢ ΔVᵢIt does not follow that the volatilities, VaR, Expected Shortfall, drawdowns or margin of individual components can be added in the same way. Each metric has its own aggregation rule and depends on relationships among positions.
The linear volatility case
For linear returns, coherent weights and an estimated covariance matrix, the portfolio identity is:
σₚ² = wᵀ × Σ × w = ∑ᵢ∑ⱼ (wᵢ × wⱼ × σᵢ × σⱼ × ρᵢⱼ)The formula shows why weights, volatilities and covariances matter together. It is not a universal formula for every risk: options and other nonlinear payoffs may require full revaluation or sensitivities, while liquidity, funding, operations and counterparty risk require additional measures and scenarios.
When the chosen measure is homogeneous of degree one, as volatility is in the
linear formulation, component i's Euler contribution can be written as:
RCᵢ = wᵢ × (Σw)ᵢ / σₚ; ∑ᵢ RCᵢ = σₚContribution therefore depends on both standalone risk and covariance with the rest of the portfolio. A risk budget is an allocation target; it is not an observed risk measure and should not be confused with invested capital or gross exposure.
Aggregate without changing units
| Object | Coherent aggregation | What not to do |
|---|---|---|
| P&L / value | same currency and valuation time | add unconverted amounts |
| Exposure | same convention: market value, notional or sensitivity | call every total “risk” |
| Volatility | weights and covariance on aligned data | add individual volatilities |
| VaR / ES | same horizon, level, dataset and method; joint model | add desks with incompatible assumptions |
| Scenario / stress | one coherent shock revalued across all positions | mix scenarios or dates |
| Drawdown | the actually aggregated portfolio series | add historical maximum drawdowns |
Gross exposure and net exposure diagnose scale and direction; they are not automatic substitutes for a loss measure. Arithmetic offsetting also does not remove basis, convexity, liquidity or counterparty risk.
Operational control
- Fix the entity, portfolio, currency, date and horizon.
- Reconcile positions, prices, collateral and factor mappings.
- Calculate each metric with a stated methodology and time-aligned data.
- Decompose contributions and concentrations instead of stopping at the total.
- Add severe scenarios, liquidity and unmodelled vulnerabilities to distribution-based measures.
- Set escalation and actions for the mandate; there is no threshold that fits every portfolio.
Common mistake — Displaying VaR, gross exposure, drawdown and a risk budget as four versions of the same number. They are different objects and must retain their definition, unit and horizon.
Sources
- Harry Markowitz, Portfolio Selection, The Journal of Finance (1952) — the original portfolio-selection formulation using returns, variances and covariances.
- Basel Committee on Banking Supervision, Principles for effective risk data aggregation and risk reporting — BCBS 239 — accuracy, completeness, timeliness, adaptability and governance in risk-data aggregation.
- Basel Committee on Banking Supervision, MAR10 — Market risk terminology — institutional scope and terminology for market-risk exposures and risk factors.
- U.S. Securities and Exchange Commission, Division of Economic and Risk Analysis, Use of Derivatives by Registered Investment Companies — limitations of notional-based measures and the need for risk-sensitive metrics when comparing different instruments.