Reference desk / edition 2026.10
Reference guides
The choices behind the formula: inputs, estimates, benchmarks and evidence.
Equal Weighting Starts With the Universe
A 1/N rule removes one weighting decision, but membership, counting units and rebalance timing still determine the portfolio.
Allocation referencesWhen Inverse Volatility Is, and Is Not, Risk Parity
Inverse-volatility weights equalize weighted standalone volatility. Equal portfolio risk contributions require correlation information except in special cases.
Allocation referencesTwo-Asset Minimum Variance Depends on the Feasible Weights
A closed-form minimum can imply shorting or leverage. Long-only and allocation bounds change the answer without changing the covariance inputs.
Statistical estimationCovariance Shrinkage Is a Choice of Target, Not Just Intensity
The same shrinkage intensity can preserve individual variances, pull them together or impose factor structure. Those choices produce different risk estimates and allocations.
Risk measurementComponent Risk Contributions Are Not Capital Weights
Volatility contributions allocate a portfolio-level estimate. They can be negative or exceed the total, even when every capital weight is positive.
Risk measurementVolatility Targeting Has Lags, Caps and Forecast Error
Scaling exposure by a volatility forecast targets a modeled risk level. Timing, leverage limits and changes in subsequent volatility prevent it from guaranteeing realized risk.
Statistical estimationEWMA Variance Needs a Seed and an Information Clock
The decay parameter alone does not define an EWMA variance series. Initialization, mean treatment, normalization and observation timing determine its early and subsequent values.
Risk measurementCovariance Units and Frequency Must Travel With the Matrix
Decimal versus percentage returns and daily versus annual horizons change covariance scales. Correct matrix multiplication cannot repair mismatched units or unsupported time aggregation.
Statistical estimationRegression fit is not forecast evidence
Separate least-squares estimation, conditional predictions and genuinely unseen forecast evaluation, including what a high fitted R-squared cannot establish.
Statistical estimationBeta depends on its window and benchmark
Interpret beta as an estimated slope with a specific return definition, benchmark and observation window, rather than a permanent label attached to an asset.
Risk measurementTracking error needs an explicit convention
Distinguish centered active-return volatility from tracking difference, root-mean-square deviation and forward risk estimates, with explicit sample and annualization choices.
Validation examplesThe denominator defines the information ratio
Keep active-return means and tracking error on compatible scales, and separate a large historical ratio from evidence about repeatable performance.
Validation examplesCompound returns and external cash flows
Distinguish chained investment returns, account balance growth and money-weighted experience using a fully specified hypothetical cash-flow timeline.
Risk measurementDrawdown depends on the observed path
Trace maximum drawdown through ordered wealth observations, distinguish depth from duration and show how coarser sampling can conceal a larger interim loss.
Validation examplesArithmetic tests are not empirical validation
Identify what deterministic fixtures can verify, what they leave untested and why correctly implemented statistics do not establish investment usefulness.
Validation examplesOut-of-sample evidence and multiple testing
Separate chronological evaluation from repeated model selection, and quantify how a hypothetical search across many null tests changes the chance of a false discovery.
Allocation referencesTurnover definitions: count the trades before comparing the number
Distinguish gross trading, half-turnover, cash movements and drift using a fully reconciled synthetic rebalance.
Allocation referencesTransaction cost units: from a quoted rate to portfolio drag
Reconcile basis points, trade notional, ticket fees and portfolio-level drag without confusing a cost assumption with observed execution.
Implementation contractsThe model card input contract: make valid inputs unambiguous
Specify shape, units, identity, numerical domains and rejection behavior before treating a mathematical example as reusable code.
Implementation contractsMissing data and alignment: decide what was actually observable
Keep missingness, stale observations, asynchronous timestamps and covariance sample selection visible in a calculation's input history.
Implementation contractsReproducible model artifacts: preserve the calculation, not just its answer
Build a checkable evidence bundle that distinguishes identical files, numerically equivalent outputs and independently verified arithmetic.
Implementation contractsModel version and change control: preserve what each result meant
Define compatibility for mathematical outputs, classify hypothetical changes and keep first-edition evidence distinct from proposed future releases.
Implementation contractsOpen source and data rights: separate the permissions in a reproduction kit
Inventory code, fixtures, documentation and external data separately, using primary licence texts rather than assuming public access grants redistribution rights.
Validation examplesChoosing a reference model: match the calculation to the question
Select an inspectable mathematical baseline by output, assumptions and input burden, not by treating a synthetic example as a performance ranking.