Level III Core · Principles of Asset Allocation

Risk Budgeting and Risk Measures in Asset Allocation

Updated 8 October 2026 · Fact-checked

Risk budgeting decides how much total portfolio risk each asset class, factor or manager may use, instead of deciding how much capital each gets. You set a total risk limit, split it by risk contribution, then check that expected return per unit of risk is balanced across the parts.

Understand Risk Budgeting and Risk Measures in Allocation

Traditional allocation starts with capital: 60% in equities, 40% in bonds. Risk budgeting starts with risk. You first decide how much total risk the investor can bear. Then you divide that risk among asset classes, strategies, factors or managers.

The two views can differ a lot. A 60/40 portfolio holds 60% of capital in equities, but equities may produce 90% or more of the portfolio's volatility. The capital split looks balanced. The risk split is not. Risk budgeting shows this and lets you control it.

The key tool is risk contribution. An asset's contribution to portfolio risk depends on its weight, its own volatility and its correlation with the rest of the portfolio. Contributions add up to total risk. This is why they are used for budgets. A risk budget is a target share of total risk for each component. It can be set in volatility terms, or in terms of tracking risk (active risk) against a benchmark.

Factor-based allocation budgets risk to underlying return drivers, such as equity market, interest rate (duration), credit, inflation, value, momentum or liquidity. Asset classes often share the same factors. Two asset classes that look diversified by label can load on the same factor, so a factor view reveals hidden concentration. A related idea is risk parity, which sets each component's risk contribution to be equal. Risk parity ignores expected returns, so it is a risk-only rule and not a full optimisation. It often needs leverage to reach a return target, because it tilts toward low-volatility assets.

Risk measures matter because volatility treats gains and losses alike. Downside measures focus on losses. These include value at risk (VaR), conditional VaR (CVaR, the average loss beyond the VaR cutoff), shortfall risk and semi-deviation. They suit investors with a minimum return need, or when returns are skewed or fat-tailed. Always link the choice to the client: a pension fund with a funding target cares about shortfall, a foundation with a spending rule about drawdown and liquidity.

A well-run budget is optimal when the ratio of marginal excess return to marginal contribution to risk is equal across components. If one component offers more return per unit of risk, move risk toward it. Budgets also need monitoring, since correlations and volatilities change.

Key rules to remember

Portfolio variance (two assets): σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ12 σ1 σ2; Portfolio risk is σp = √σp². Weights are capital weights.
Marginal contribution to risk (MCTR): MCTRi = Cov(Ri, Rp) ÷ σp; Change in portfolio risk from a small increase in asset i's weight.
Contribution to risk (CTR): CTRi = wi × MCTRi = wi × Cov(Ri, Rp) ÷ σp; CTRs sum to σp. Percentage contribution = CTRi ÷ σp.
Equal-risk-contribution condition: w1 × MCTR1 = w2 × MCTR2 = …; Defines risk parity. It uses no expected returns.
Optimal risk budget condition: (E(Ri) − Rf) ÷ MCTRi equal for all i; Excess return per unit of marginal risk is equal across components at the optimum.
Parametric VaR (normal): VaR = (z × σ − μ) × portfolio value; z = 1.65 for 95% one-tail, 2.33 for 99%. Match μ and σ to the same horizon. Normality may understate tail risk.
Tracking risk (active risk): TE = standard deviation of (Rp − Rb); Used to budget active risk across managers or strategies.

How to solve Risk Budgeting and Risk Measures in Allocation questions

Use this order for any risk budgeting question. Tie each step to the client's objectives and constraints.

1Read the client's return objective, risk tolerance and constraints. Note the total risk limit and the risk measure given (volatility, tracking risk, VaR, shortfall).
2Identify what is asked: a risk contribution, a budget comparison, a factor exposure, a recommendation, or a choice of risk measure.
3Compute the needed inputs: portfolio volatility, and each component's covariance with the portfolio or its marginal contribution.
4Convert to contributions: CTR = weight × MCTR. Express as a percentage of total risk and compare with the capital weight.
5Compare with the budget or with return per unit of risk. Find which component is over or under budget.
6State the action: shift risk toward the component with higher excess return per unit of risk, or toward the target budget.
7Justify in one or two sentences using the client's needs, and note a limitation if the command word asks for it (for example, VaR assumes normality).

Quickest way: Percentage risk contribution shortcut

When to use it: Use for two-asset portfolios when asked for each asset's share of risk, or when a rough check is enough.

Compute portfolio variance once, then σp.
For asset 1 compute Cov(R1, Rp) = w1σ1² + w2ρσ1σ2.
Percentage risk share of asset 1 = w1 × Cov(R1, Rp) ÷ σp².
Asset 2's share = 1 − asset 1's share. Use this as a check.
If an asset's risk share far exceeds its capital weight, say it dominates risk and recommend reducing it.

Common mistakes in Risk Budgeting and Risk Measures in Allocation

Treating capital weights as risk weights.
Allocation tables show capital, so students assume risk is split the same way.
Fix: Always compute contribution = weight × marginal contribution. Compare it with the capital weight.
Adding standalone volatilities to get portfolio risk.
It feels like adding parts. Correlation is forgotten.
Fix: Use the variance formula with correlation. Only the contributions to risk add up, not standalone volatilities.
Saying risk parity maximises return or is mean-variance optimal.
Equal risk looks balanced, so it sounds efficient.
Fix: Say risk parity ignores expected returns. It is optimal only if all assets have equal Sharpe ratios and equal correlations.
Using VaR as if it gives the maximum loss.
The word 'value at risk' sounds like a worst case.
Fix: VaR is a loss threshold at a probability. Losses beyond it can be larger. CVaR measures the average loss beyond it.
Mixing time horizons in VaR, such as annual σ with a daily μ.
Inputs come from different parts of the vignette.
Fix: Convert both to the same horizon first. Scale σ by the square root of time and μ in proportion to time.
Calling assets diversified because the asset class labels differ.
Students stop at the label and skip the factor view.
Fix: Ask which factors drive each asset. Shared factors, such as equity beta in private equity and equities, mean concentration.

Worked examples

Example 1

A portfolio has 60% in equities (σ = 18%) and 40% in bonds (σ = 6%). The correlation is 0.20. Compute each asset class's percentage contribution to portfolio risk.

Show the solution

Variance terms: (0.6 × 0.18)² = 0.108² = 0.011664. (0.4 × 0.06)² = 0.024² = 0.000576.
Covariance term: 2 × 0.6 × 0.4 × 0.20 × 0.18 × 0.06 = 0.48 × 0.20 × 0.0108 = 0.0010368.
Portfolio variance = 0.011664 + 0.000576 + 0.0010368 = 0.0132768. σp = √0.0132768 = 0.11523, about 11.52%.
Equity covariance with portfolio = 0.6 × 0.0324 + 0.4 × 0.20 × 0.18 × 0.06 = 0.01944 + 0.000864 = 0.020304.
Equity risk share = 0.6 × 0.020304 ÷ 0.0132768 = 0.0121824 ÷ 0.0132768 = 0.9176, about 91.8%.
Bond risk share = 1 − 0.9176 = 8.2%. Check: bond covariance = 0.4 × 0.0036 + 0.6 × 0.00216 = 0.00144 + 0.001296 = 0.002736. Then 0.4 × 0.002736 ÷ 0.0132768 = 0.0824.

Answer: Equities contribute about 91.8% of risk on a 60% capital weight. Bonds contribute about 8.2% on a 40% weight. Portfolio volatility is about 11.52%. Risk is heavily concentrated in equities.

Example 2

A fund has excess returns and marginal contributions to risk (MCTR) as follows. Equities: excess return 5.0%, MCTR 0.16. Credit: excess return 2.4%, MCTR 0.06. Government bonds: excess return 0.5%, MCTR 0.02. The risk budget is otherwise unconstrained. Which component is most attractive for extra risk, and why?

Show the solution

Compute excess return ÷ MCTR for each component.
Equities: 5.0 ÷ 0.16 = 31.25.
Credit: 2.4 ÷ 0.06 = 40.0.
Government bonds: 0.5 ÷ 0.02 = 25.0.
At the optimum these ratios would be equal. They are not, so the portfolio is not optimal.
Credit has the highest ratio, so shifting risk to credit adds the most return per unit of risk. Government bonds have the lowest, so they are the source of the shift.

Answer: Credit is most attractive, with 40.0 of excess return per unit of marginal risk against 31.25 for equities and 25.0 for government bonds. Move risk budget from government bonds (and then equities) toward credit, subject to the client's constraints, until the ratios equalise.

Exam tips

When the command word is 'calculate', show the variance, covariance and share steps. A correct number alone earns credit, but shown work protects you if you slip.
For 'recommend' or 'justify', give the action and one reason tied to the client, such as a funding shortfall limit or a liquidity need.
For 'discuss limitations' of VaR, name two: assumes a distribution (often normal) and does not describe losses beyond the cutoff.
In item sets, check that the volatility and return inputs share the same time horizon before you compute anything.
Know the contrast cold: capital allocation sets how much money goes where, risk budgeting sets how much risk goes where.

Risk Budgeting and Risk Measures in Allocation in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Risk Budgeting and Risk Measures in Allocation: frequently asked questions

What is the difference between risk budgeting and capital allocation?

Capital allocation sets the share of money in each asset class. Risk budgeting sets the share of total portfolio risk each component may use. Two portfolios with the same capital weights can have very different risk budgets.

How do I calculate risk contribution in a portfolio?

Multiply the asset's weight by its marginal contribution to risk, which is its covariance with the portfolio divided by portfolio volatility. Divide by portfolio volatility again to get a percentage. The percentages across all assets sum to 100%.

What is factor-based asset allocation?

It allocates risk to underlying return drivers, such as equity market, duration, credit, value and inflation, instead of to asset class labels. It helps reveal concentration when different asset classes share the same factors.

Is risk parity the same as risk budgeting?

No. Risk parity is one special budget where every component contributes equally to risk. Risk budgeting allows any target split, which can reflect expected returns and client needs.