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CAIA Level II · Worked application

Risk Budgeting for Alternatives: Capital Weight versus Risk Share

A risk budget allocates a measured portfolio risk, not just invested capital. Under a covariance model, component contributions to volatility depend on weights, asset volatilities and co-movement with the whole portfolio.

The key decisions, at a glance

  • 1. Portfolio volatility

    Compute σp = √(w′Σw).

    Watch for: Weights alone do not determine volatility.

  • 2. Marginal contribution

    Use (Σw)i / σp for the local derivative of volatility.

    Watch for: Standalone asset volatility is not marginal portfolio risk.

  • 3. Component contribution

    Multiply marginal contribution by the asset weight.

    Watch for: Component contributions have volatility units, not dollar units.

  • 4. Risk share

    Divide component contribution by portfolio volatility.

    Watch for: The covariance model does not capture every liquidity or tail risk.

Original worked case

Half the capital carries 80% of the modeled risk

Given: Assets A and B each have 50% capital weight. Volatilities are 20% and 10%, and correlation is zero. Use a fixed covariance model.

  1. 01 Portfolio variance

    0.5² × 0.2² + 0.5² × 0.1² = 0.0125; σp = 11.18%.

  2. 02 Component volatility

    A: 0.0100 / 0.1118 ≈ 8.94 percentage points; B: 0.0025 / 0.1118 ≈ 2.24 points.

  3. 03 Risk shares

    A contributes 80% and B 20% of modeled portfolio volatility.

Answer and interpretation

Equal capital weights are not equal risk weights. The component contributions sum to portfolio volatility in this model.

Same capital weights, different risk shares

% share · scale 0 to 80

Same capital weights, different risk shares; % share
ScenarioValue
A capital50
B capital50
A volatility contribution80
B volatility contribution20

Illustrative covariance model. Capital shares and risk shares are two separate decompositions.

Change one assumption

Changing correlation changes both portfolio volatility and contributions. With negative covariances, an asset’s contribution can even be negative.

Independent teaching example with the stated assumptions. Not an official exam question, marking key or observed market trend.

Understand the method

Part 1

Build covariance before allocating volatility

For weights w and covariance matrix Σ, portfolio variance is w′Σw and volatility is its square root. Each covariance equals the product of the two asset volatilities and their correlation. The matrix must use compatible horizons, return definitions and valuation timing. Stale private marks can distort the estimated relationship even when the spreadsheet calculation is correct.

For two assets, expand the expression as wA²σA² + wB²σB² + 2wAwBρσAσB. The cross term is why adding weighted standalone volatilities generally does not give portfolio volatility. Begin with a small worked matrix and check symmetry and units before extending the calculation to many alternative strategies.

Part 2

Differentiate marginal risk from component risk

Holding the covariance matrix fixed, marginal contribution to volatility for asset i is (Σw)i / σp. Component contribution is wi times that marginal contribution. Component contributions sum to total portfolio volatility under this homogeneous model. Dividing each component by total volatility gives its percentage share of the volatility budget.

The derivative is an unconstrained weight sensitivity. If a portfolio must remain fully invested, increasing one weight requires reducing another; the relevant local change then depends on the difference between their marginal contributions. State the funding assumption before saying that adding 1% to an asset changes risk by a particular amount.

Part 3

Interpret negative and changing contributions carefully

A component contribution can be negative when an asset sufficiently offsets the rest of the portfolio under the estimated covariance. That does not mean the asset cannot lose money or that it is risk-free. It means its local effect in this particular portfolio and model reduces aggregate volatility. The result can reverse if correlations, volatilities or weights change.

Risk parity equalizes a chosen contribution measure, not capital weights or all forms of risk. A low-volatility asset may require a large allocation or leverage to reach an equal volatility contribution. Expected return, liquidity, tail behaviour and capacity still need separate assessment. Do not optimize a risk budget using only a covariance matrix and then assume the resulting alternative-asset commitments are fundable.

Part 4

Overlay cash access and tail scenarios on the statistical budget

Private commitments, margin and redemption restrictions are not fully represented by a standard return covariance. A strategy contributing little measured volatility may still dominate near-term cash needs. Combine the statistical budget with a dated liquidity forecast and a stress scenario in which reported correlations change and distributions slow.

Use the contribution calculation as one diagnostic within an allocation decision. Explain the data window, valuation conventions and sensitivity to alternative covariance assumptions. Compare capital weight, volatility contribution, scenario-loss contribution and funding requirement side by side. Each measures a different claim on the institution’s capacity to bear risk.

Two-asset risk budget: 60/40 weights, 10%/20% volatility, 0.25 correlation

A

Capital weight
60%
Marginal volatility
7.18%
Component volatility
4.31 percentage points
Share
38.71%

B

Capital weight
40%
Marginal volatility
17.06%
Component volatility
6.83 percentage points
Share
61.29%

Portfolio

Capital weight
100%
Marginal volatility
Not additive
Component volatility
11.14%
Share
100%

Rounded independently. Covariance is 0.10 × 0.20 × 0.25 = 0.005. Percent shares are calculated before rounding.

More worked practice

Original teaching cases. Use the stated assumptions; these are not official exam questions or marking keys.

Recalculate when correlation rises

Given: Keep the table’s 60/40 weights and 10%/20% volatilities, but raise correlation from 0.25 to 0.75. Use a fixed covariance within each scenario.

  1. 1At 0.25 correlation, variance is 0.0036 + 0.0064 + 0.0024 = 0.0124, so volatility is 11.14%.
  2. 2At 0.75 correlation, the cross term rises to 0.0072, giving variance 0.0172.
  3. 3Stress volatility is √0.0172 = 13.11%.

Interpretation: The capital allocation is unchanged, but its diversification benefit falls. Risk budgets must be recomputed when the covariance assumptions change, rather than carrying forward old component shares.

A diversifying asset can have a negative component

Given: Use 80% in A and 20% in B, volatilities of 10% and 20%, and correlation -0.75. Keep covariance fixed.

  1. 1Covariance is -0.015. The covariance-weight products are 0.005 for A and -0.004 for B.
  2. 2Variance is 0.8 × 0.005 + 0.2 × (-0.004) = 0.0032; volatility is 5.66%.
  3. 3Component contributions are 7.07 percentage points for A and -1.41 for B, or 125% and -25% of total volatility.

Interpretation: The signed contributions sum to portfolio volatility before rounding. B reduces this modelled portfolio volatility even though B has substantial standalone risk.

Check your understanding

Answer first, then open the explanation. These checks are original practice and do not generate an exam score.

1. Should weighted standalone volatilities sum to portfolio volatility?

Only in special cases such as perfectly positively correlated long positions. Normally the covariance terms change the result.

2. Can a negative component contribution guarantee a positive return in a crisis?

No. It describes a local volatility effect under estimated covariance, not every scenario or tail outcome.

3. What check catches a broken component-risk calculation?

The unrounded component contributions should sum to portfolio volatility under the stated model. Also check covariance units and funding assumptions.

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Common questions

Do risk shares always equal capital weights?

No. They depend on covariance with the portfolio. They coincide only under particular assumptions.

Does an 80% risk share predict 80% of the next loss?

No. It is a model decomposition of volatility, not attribution of a specific future scenario loss.

Sources and scope

The sources below establish their stated framework or subject context. Calculations and cases are our own teaching material; these sources do not endorse them or establish complete exam coverage.

By MiloPrep editorial team. Updated 10 October 2026. Independent study notes, not affiliated with or endorsed by CAIA Association. How we prepare our content.

Notes

  • * Study scope: Selected study concepts, not complete curriculum coverage. Match your sitting to the official exam-year materials; CAIA’s current resource page now links to 2027. ↩ Return to content