Risk contribution analysis: decomposing portfolio risk by asset

A 60/40 stock-bond portfolio's capital is split 60% / 40%, but its risk is closer to 90% / 10%—equities are several times more volatile than bonds, and the volatility differential dominates the portfolio's behaviour. Risk contribution analysis is the methodology that makes the gap between dollar weight and risk weight explicit, and that reveals where a portfolio's volatility actually comes from.

What risk contribution analysis is

Risk contribution analysis decomposes a portfolio's total risk—typically volatility, but the framework extends to other risk measures—into the additive contribution of each asset. The result is a set of numbers that sum to the portfolio's total risk, with each number representing how much of that risk is attributable to a specific asset given its weight, volatility, and covariance with the rest of the portfolio.

The framework is the analytical complement to portfolio construction. Construction methodologies (mean-variance, risk parity, equal weight) determine how to choose weights; risk contribution analysis tells the investor what those weights actually produce in terms of risk allocation. The two are linked but distinct: a portfolio constructed by equal weight produces a specific risk contribution decomposition that is not generally equal across assets.

How it works

For a portfolio with weights w and asset return covariance Σ, total portfolio variance is σₚ² = wᵀΣw, and total portfolio volatility is σₚ = √(wᵀΣw). The marginal contribution to risk for asset i is the partial derivative of portfolio volatility with respect to weight w_i: MCR_i = (Σw)_i / σₚ. The total risk contribution of asset i is its weight times the marginal contribution: RC_i = w_i × MCR_i. The sum across all assets equals total portfolio volatility: Σ RC_i = σₚ.

For the 60/40 example with stock volatility 16%, bond volatility 5%, stock-bond correlation 0, and weights 60% / 40%: portfolio variance is 0.6² × 0.16² + 0.4² × 0.05² = 0.00922, portfolio volatility is approximately 9.6%. Stock risk contribution is 0.6 × (0.6 × 0.16² + 0) / 0.096 ≈ 9.4 percentage points; bond risk contribution is 0.4 × (0.4 × 0.05² + 0) / 0.096 ≈ 0.2 percentage points. The 60/40 dollar split corresponds to a roughly 98% / 2% risk split.

Risk contribution can be expressed as a percentage of total risk: stock contribution = 9.4 / 9.6 = 97.9%; bond contribution = 0.2 / 9.6 = 2.1%. The percentage view makes the construction implication direct: the 60/40 portfolio is, from a risk perspective, almost entirely an equity position. Investors who want a more balanced risk profile must rebalance the dollar weights toward bonds, often substantially.

What the evidence shows

The 60/40 example is canonical because the stock-bond risk asymmetry has been known and documented for decades. Less obvious cases show similar patterns. A typical multi-asset portfolio with 50% equities, 30% fixed income, 10% commodities, and 10% alternatives will produce a risk decomposition heavily skewed toward equities—perhaps 75–85% of risk on equities depending on the precise correlation structure. The dollar weights distribute capital broadly; the risk weights concentrate it on the most volatile asset.

The asymmetry is the structural reason why risk parity strategies have gained adoption. By targeting equal risk contribution rather than equal capital weight, risk parity portfolios deliberately rebalance away from the volatility-concentration that capital-weighted multi-asset portfolios produce. The trade-off is that the resulting capital weights look unusual—typically heavy in fixed income, light in equities—but the risk profile is more balanced.

Risk contribution analysis is also useful as a diagnostic on portfolios that were not constructed with explicit risk allocation. Comparing intended diversification (the dollar weights the investor chose) to realised diversification (the risk weights that result) often reveals that the portfolio is much less diversified in risk terms than the dollar weights suggest. This is the most common application in retail portfolio review.

Limitations and trade-offs

Risk contribution depends on the covariance matrix, which is subject to estimation error. The same portfolio analysed with different covariance estimates will produce different risk contributions, and the choice of look-back window or shrinkage method matters. Comparisons across portfolios should use a consistent estimation approach.

The analysis is also backward-looking. The risk contributions reflect the historical covariance structure; future contributions depend on whether that structure is stable. In regimes where correlations shift materially—flight-to-quality episodes, for instance—the realised risk contributions can differ substantially from the historically-estimated ones.

Risk contribution decomposes total volatility but does not, on its own, address tail risk. A portfolio with the same volatility decomposition can have very different drawdown characteristics depending on the assets' joint distribution beyond second moments. Risk contribution analysis paired with stress testing and tail-risk metrics provides a more complete picture than the volatility decomposition alone.

Risk contribution analysis in pfolio

pfolio's portfolio analytics report risk metrics at the portfolio level—volatility, drawdown, Sharpe, and the rest. Risk contribution by asset is implicit in the optimiser's solution rather than reported as a standalone breakdown; users who want to decompose portfolio risk by asset can do so by combining the portfolio weights, asset volatilities, and the correlation matrix from pfolio Insights.

Related articles

• Risk budgeting: allocating capital by risk contribution rather than by weight
• Risk parity investing: how to allocate by risk contribution rather than capital
• Covariance estimation in portfolio optimisation: look-back periods, shrinkage, and stability
• Portfolio variance: understanding return dispersion and investment risk