Portfolio Diversification / Correlation mechanism

Model scope

The core two-asset variance and weighted-return formulas are standard and correct under the stated assumptions. Verdict is NEEDS_REVIEW because the spec does not define units, weight constraints, the minimum-variance or other meaning of the 'efficient-mix hint,' or the explicit square-root step for portfolio risk. The educational-only and non-advisory label is appropriate.

• The variance formula is standard for a fully specified two-asset portfolio, assuming σ1 and σ2 are standard deviations and ρ is their correlation.
• The advertised portfolio risk σ is not explicitly given by the supplied formulas; it must be computed as σp = sqrt(σp²).
• The 'efficient-mix hint' is undefined. If it means the minimum-variance fully invested mix, the instrument needs to specify w1* = (σ2² - σ1σ2ρ)/(σ1² + σ2² - 2σ1σ2ρ), with w2* = 1 - w1*, plus any long-only constraint.
• The return formula is correct for expected returns, but the inputs are labeled only 'asset returns'; the instrument must distinguish expected returns from realized or historical returns.
• The formulas require an explicit portfolio-weight constraint, normally w1 + w2 = 1. Whether short positions are allowed is unspecified.

Units and conventions

• Returns and standard deviations must use consistent units. The calculations below use decimal returns and decimal standard deviations unless an input explicitly states percent units.
• A return of 8% is represented as 0.08, and a standard deviation of 15% is represented as 0.15.
• Correlation ρ is dimensionless and must satisfy -1 ≤ ρ ≤ 1.
• Weights are dimensionless. For the portfolio interpretation, w1 + w2 = 1.
• Portfolio risk is the nonnegative square root of portfolio variance and is expressed in the same units as the standard deviations.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "w1": 0.6,
    "w2": 0.4,
    "R1": 0.08,
    "R2": 0.12,
    "sigma1": 0.15,
    "sigma2": 0.25,
    "rho": 0.2,
    "units": "decimal returns and decimal standard deviations"
  },
  "expected_outputs": {
    "portfolio_expected_return": 0.096,
    "portfolio_variance": 0.0217,
    "portfolio_risk_sigma": 0.1473091986,
    "plot_sample": {
      "x_portfolio_risk": 0.1473091986,
      "y_portfolio_return": 0.096
    }
  },
  "working": "Weights check: 0.6 + 0.4 = 1. Return: Rp = 0.6×0.08 + 0.4×0.12 = 0.048 + 0.048 = 0.096. Variance: σp² = 0.6²×0.15² + 0.4²×0.25² + 2×0.6×0.4×0.15×0.25×0.2 = 0.36×0.0225 + 0.16×0.0625 + 0.0036 = 0.0081 + 0.0100 + 0.0036 = 0.0217. Risk: σp = sqrt(0.0217) = 0.1473091986."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Inputs outside the correlation domain can produce a negative portfolio variance and an undefined square root. The instrument must validate rho in [-1,1] and reject any case where the computed variance is negative instead of returning NaN or an invalid risk value.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json