Risk budgeting: allocating capital by risk contribution rather than by weight

Capital weight and risk contribution are not the same thing. A portfolio that allocates 60% of its dollars to equities and 40% to bonds typically allocates 90%+ of its risk to equities, because equities are several times more volatile than bonds. Risk budgeting is the framework for choosing capital weights with explicit attention to the risk allocation that results.

What risk budgeting is

Risk budgeting is a portfolio-construction framework in which each asset (or asset class) is assigned a target share of total portfolio risk—a risk budget—rather than a target share of capital. The capital weights are then chosen so that each asset's contribution to portfolio volatility matches its assigned budget.

The key concept is the marginal risk contribution: the change in portfolio volatility produced by a small increase in the weight of a given asset. Multiplied by the asset's weight, it gives the total risk contribution of that asset, and the sum across all assets equals the portfolio volatility. Risk budgeting solves backwards: given a target distribution of risk contributions, find the capital weights that produce it.

Risk parity—the approach in which every asset contributes equally to portfolio risk—is the special case of risk budgeting in which the target distribution is uniform. Other budgets are equally well-defined: an investor might assign 50% of risk to equities, 30% to fixed income, 10% to commodities, and 10% to alternatives, and let the optimisation solve for the corresponding capital weights.

How it works

The mechanics depend on the covariance matrix of asset returns. For a portfolio with weights w and asset return covariance Σ, portfolio variance is wᵀΣw, and the marginal risk contribution of asset i is (Σw)ᵢ / √(wᵀΣw). Asset i's total risk contribution is wᵢ × (Σw)ᵢ / √(wᵀΣw). Setting these contributions equal to a target distribution and solving for w yields the risk-budget portfolio.

For a 60/40 stock-bond portfolio with annualised stock volatility of 16%, bond volatility of 5%, and stock-bond correlation of 0.0, portfolio variance is 0.6² × 0.16² + 0.4² × 0.05² = 0.00922, giving a portfolio volatility of approximately 9.6%. The risk contribution of stocks is approximately 9.4 percentage points; the risk contribution of bonds is approximately 0.2 percentage points. The dollar split is 60/40; the risk split is approximately 98/2.

To produce an equal risk contribution—50/50 risk—the same two assets require dollar weights of approximately 24% stocks and 76% bonds, assuming the same covariance inputs. The same total volatility target can be reached with very different capital weights depending on the desired risk allocation.

What the evidence shows

Risk-budgeted portfolios tend to underweight high-volatility assets relative to capital-weighted portfolios with the same nominal allocation, and to overweight low-volatility assets. Maillard, Roncalli, and Teïletche (2010) document the structural property: equal risk contribution portfolios sit between the equal-weight and minimum variance portfolios in terms of their risk profile, and tend to outperform both on a risk-adjusted basis when the covariance matrix is reasonably stable.

The strongest empirical case for risk budgeting is in multi-asset contexts where the volatility differential between asset classes is large. Bridgewater's All-Weather strategy, popularised by Ray Dalio, is a high-profile implementation of equal risk contribution at the asset-class level, and similar approaches have been adopted in pension and endowment portfolios. Asness, Frazzini, and Pedersen (2012) extend the analysis to leveraged risk-parity strategies, showing they have historically outperformed the unlevered benchmark on Sharpe-ratio terms over multi-decade evaluation windows.

The performance is not unconditional. Risk-parity portfolios with substantial bond allocations underperformed cap-weighted alternatives in 2022 because the bond drawdown was deeper than the historical correlation structure suggested. The same vulnerability applies to any portfolio whose construction relies on assumptions that hold in normal regimes and break in tail regimes.

Limitations and trade-offs

Risk budgeting requires an estimate of the covariance matrix, which is subject to estimation error. The same noise that affects mean-variance optimisation affects risk budgeting, though typically with smaller consequences because the optimisation does not depend on expected return estimates—the most error-prone input in mean-variance.

The framework is silent on what the target risk budget should be. It provides the machinery to translate a budget into capital weights but offers no guidance on whether the budget itself is sensible. An equal risk contribution may be the right answer for an investor with no view on which asset class will perform best; an unequal contribution may be the right answer for an investor with a view. The framework does not adjudicate.

Risk budgeting also assumes the covariance structure is stable enough that the historical estimate is informative for the target horizon. In regimes where correlations shift materially—a flight-to-quality episode, for instance—the realised risk contributions can differ substantially from the targeted ones, even with the optimal capital weights based on historical inputs.

Risk budgeting in pfolio

pfolio's portfolio optimiser uses mean-variance optimisation by default, with Hierarchical Risk Parity and equal weight as alternatives. Risk budgeting at the asset class level is not specified ex ante; the implicit risk allocation across asset classes emerges from the optimiser's solution rather than from a pre-defined budget. The construction methodology is documented at how we build portfolios.

Related articles

• Risk parity investing: how to allocate by risk contribution rather than capital
• Hierarchical Risk Parity (HRP): a robust alternative to mean-variance optimisation
• Covariance estimation in portfolio optimisation: look-back periods, shrinkage, and stability
• Portfolio diversification: why spreading risk across asset classes beats spreading across stocks
• Tail risk parity: allocating by tail-risk contribution rather than volatility contribution
• Hierarchical Equal Risk Contribution (HERC): combining hierarchical clustering with equal risk allocation
• Risk contribution analysis: decomposing portfolio risk by asset