CAIA: Portfolio risk
Explanations, applications and practice for portfolio risk.
- Common mistakes
Taking absolute values of signed risk contributions
Keep the hedge effect in an additive Euler decomposition.
- Lessons
State the baseline for a diversification comparison
Name which risk quantity the portfolio is being compared with.
- Templates
Portfolio variance and contribution check
Download the original variance bridge and signed contribution reconciliation.
- Lessons
Build a two-asset covariance risk model
Match weights, return periods and covariance before aggregating risk.
- Concepts
Capital weights and risk shares
Read the decomposition before calling an allocation a risk budget.
- Practice
Signed risk contribution and model-domain checks
Test marginal versus weighted risk, zero denominators and joint coherence.
- Lessons
Decompose model volatility into weighted contributions
Distinguish a marginal derivative from its capital-weighted contribution.
- Common mistakes
Omitting the second covariance cross term
Recover the factor two from the variance expansion.
- Formulas
Weighted Euler volatility contribution
Apply the weight after deriving marginal volatility risk.
- Worked examples
Hedging contribution with positive capital weights
Preserve negative terms when interpreting a covariance decomposition.
- Templates
Portfolio risk input record
Download a record for weight, horizon, return definition and covariance assumptions.
- Tool guides
Interpreting the two-asset risk calculator
Keep units, baselines and signed contributions attached to the entered assumptions.
- Templates
Covariance model review record
Download a structured review record for symmetry, matched observations and matrix coherence.
- Worked examples
Incoherent three-asset correlation record
Show why valid-looking individual correlations can still form an invalid matrix.
- Formulas
Two-asset minimum-variance weight with long-only bounds
Separate the unconstrained stationary weight from a permitted long-only allocation.
- Concepts
Negative volatility contribution in a long-only pair
Distinguish a hedge effect from a negative capital holding.
- Worked examples
Perfect positive correlation and weighted volatility
Identify the condition under which the weighted sum is the portfolio standard deviation.
- Lessons
Keep risk-input periods and estimation bases compatible
Compare data definitions before putting dispersions and correlation into one model.
- Worked examples
Diversification below weighted risk but above the safer asset
Resolve two apparently conflicting diversification comparisons.
- Study plans
Covariance to risk contribution study sequence
Move from compatible input records to variance, baselines and signed decomposition.
- Worked examples
Capital share and volatility share reconciliation
Track an asset’s capital weight through covariance, marginal risk and weighted risk.
- Tools
Two-asset portfolio risk calculator
Calculate covariance, portfolio dispersion and signed weighted volatility contributions.
- Worked examples
Uncorrelated variables that are dependent
Check zero covariance without assuming independence.
- Concepts
Portfolio variance and volatility unit labels
Keep squared-return quantities distinct from return-scale quantities.
- Worked examples
Two-asset variance bridge
Reconcile asset terms, covariance and the square root in a complete original example.
- Formulas
Two-asset portfolio variance
Include the covariance term when aggregating a weighted pair.
- Practice
Portfolio variance and baseline checks
Test covariance aggregation, squared units and the diversification comparator.
- Common mistakes
Adding weighted standard deviations as portfolio risk
Restore the covariance term before labeling a weighted sum.
- Concepts
Zero total volatility and undefined risk shares
Avoid dividing by a vanished denominator in a contribution calculation.