Source: https://guthlabs.ai/docs/instruments/capm-expected-return/mechanism/

instrument mechanism / verified-clean

# CAPM Expected Return mechanism

The inspectable method record for CAPM Expected Return, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The formula E(R)=Rf+β(Rm−Rf) is the standard single-factor CAPM expected-return formula. The specification is otherwise correct, but it is ambiguous whether rate inputs are decimal fractions or percentage points, so the panel needs an explicit unit convention and conversion/display rule. The honest educational-model label is appropriate; CAPM output is a model-implied expected return, not a guaranteed forecast.

No additional formula finding is recorded.

## Units and conventions

- Rf and Rm must be expressed in the same units, either decimal fractions or percentage points; beta is dimensionless.

- The numeric input format is unspecified: for example, 0.05 can mean 5% as a decimal fraction, while 5 can mean 5 percentage points.

- Expected return is reported as a percentage; decimal-fraction results must be multiplied by 100 for display.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "risk_free_rate": 0.04,
    "beta": 1.2,
    "market_return": 0.1,
    "rate_unit": "decimal fraction"
  },
  "expected_outputs": {
    "expected_return_percent": 11.2
  },
  "working": "E(R) = 0.04 + 1.2 × (0.10 − 0.04) = 0.04 + 1.2 × 0.06 = 0.04 + 0.072 = 0.112 = 11.2%."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

An extreme but syntactically numeric input produces a non-finite +Infinity result through floating-point overflow. A robust instrument should reject non-finite inputs or flag the non-finite output rather than display it as an expected return.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/capm-expected-return/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/capm-expected-return/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/capm-expected-return/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`