Calculation contract
exposure = min(target_volatility / estimated_volatility, leverage_cap)| Input | Allowed values | Meaning |
|---|---|---|
| target_volatility | Decimal, 0 to 10 | Desired scale at the estimate frequency |
| estimated_volatility | Decimal, 0.000001 to 10 | Positive risk estimate |
| leverage_cap | Nonnegative multiplier, at most 10 | Maximum allowed model exposure |
Method and interpretation
The default 12% target divided by an 8% estimate requests 1.5 times exposure. The 1.25 cap binds, leaving a model-implied scaled volatility of 10%. The result is below target because the constraint is respected rather than silently relaxed.
The estimate must precede the decision it informs. Replacing it retrospectively with realized volatility can make a historical scaling rule look implausibly precise. This static card has no observation clock, so timing and lag must be supplied by the surrounding study.
Where the reference stops
Estimated scaled volatility is not realized risk. The formula omits financing, margin, transaction costs, gap risk and portfolio changes. Very small estimates can bind the cap; a zero estimate is rejected, not assigned unlimited exposure.
Published synthetic inputs
{
"target_volatility": 0.12,
"estimated_volatility": 0.08,
"leverage_cap": 1.25
}Frozen calculation output
{
"uncapped_exposure": 1.5,
"exposure": 1.25,
"estimated_scaled_volatility": 0.1,
"cap_binding": true
}Same-frequency volatilities. This is a proportional exposure reference, not an order, realized-risk guarantee or borrowing-cost model.
Verification coverage
- Binding/nonbinding caps, zero target and zero cap checked.
- Invalid negative or zero estimate rejected.
Unit and independent-reference checks test arithmetic and rejection rules, not future investment performance.
Method references
Read the assumptions in context
Risk measurementVolatility Targeting Has Lags, Caps and Forecast Error
Scaling exposure by a volatility forecast targets a modeled risk level. Timing, leverage limits and changes in subsequent volatility prevent it from guaranteeing realized risk.
Validation examplesOut-of-sample evidence and multiple testing
Separate chronological evaluation from repeated model selection, and quantify how a hypothetical search across many null tests changes the chance of a false discovery.