Portfolio Diversification / Correlation

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Finance, Economics & Business (educational only — never individualized investment, tax, or legal advice)

Tranche

tranche-6

Evidence ID

t6-051

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

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