Reference desk / edition 2026.10
Risk measurement
Trace portfolio variance, risk contributions, volatility scaling and path-dependent loss measures.
Calculation references
Two-asset portfolio variance
Reconcile capital weights and covariance into a portfolio variance and volatility at the input frequency.
Euler volatility contributions
Attribute two-asset portfolio volatility to signed Euler contributions without equating risk share and capital share.
Capped volatility scaling
Translate a stated volatility estimate and target into a capped proportional exposure reference.
Observed-path maximum drawdown
Find the deepest peak-to-observation decline in a finite nonnegative wealth path.
Detailed guides
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.
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.
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.
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.