Equal risk contribution: let covariance change the answer

ERC uses the covariance matrix to make component volatility risk shares equal. Change correlations while standalone volatilities stay fixed, then compare the computed ERC result with the inverse-volatility baseline.

Teaching sequence

Choose a matrix, then step through the evidence and interpretation of the completed solve. Step does not replay individual CCD iterations.

1. Choosematrix and evidence
2. SolveCCD Eq. 7
3. Inspectshares and residual
4. Explainwhat covariance sees
5. Compareinverse-volatility baseline
Five-stage ERC teaching sequence The lab guides the learner from choosing a covariance matrix through solving, inspecting shares, explaining covariance, and comparing inverse volatility. ChooseSolveInspectExplainCompare

Stage 1 of 5: choose a tested matrix and evidence state.

Choose a synthetic matrix and check its input evidence before interpreting any allocation.

1. Choose the synthetic input

Risk unit: decimal simple return per daily synthetic period. The pure solver does not estimate returns or validate a provider.

canonical fixture

2. Computed result

The matrix is generated from the editable synthetic volatilities/correlations, then passed to the tested ERC module.

      

        
q = wᵀΣw
σp = √q
RCi = wi(Σw)i / σp
sharei = RCi / σp

        

      

    

    

      
ERC output versus inverse-volatility baseline
AssetERC weightInverse-vol. weightRCShareTargetShare bar

      
On a narrow screen, scroll this audit table horizontally; the page itself stays within the viewport.

    

    

  


  

    
3. Boundary card

    

      
Market value
Q × local mark × FX(base/local)
This is a base-currency market-value conversion, not cost basis and not a covariance estimate.

      
Return basis
(1 + rlocal)(1 + rFX) − 1
Local-return covariance and base-currency covariance are different estimands; the product term matters.

      
Evidence route
A stale quote, split mismatch, stale FX, or suspect quantity is upstream evidence. This lab blocks it instead of turning it into a zero return or invented rebalance.