Source: https://guthlabs.ai/docs/instruments/portfolio-diversification-correlation/
instrument / verified-clean
# Portfolio Diversification / Correlation
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## 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`