Governed daily series
ECB reference observations are transformed into modified cross rates, then simple close-to-close returns are aligned by exact start/end interval.
Historical Hedge Variance Explorer
Compare a primary forex position with a second position you already chose. Model hedge_effectiveness v1.0.0 combines your verified P/L sensitivity for a 1% pair move with exact-aligned daily ECB reference-rate returns and reports the historical sample variance change.
Key Takeaways
- You choose both pairs, both directions and both monetary sensitivities; the page does not recommend a trade.
- Every sensitivity must already be verified in the same account currency. The currency selector formats numbers only.
- The model uses population standard deviation and Pearson correlation from the same exact-aligned historical sample.
- A lower sample variance is backward-looking evidence only. It does not guarantee future protection or quantify maximum loss.
- The page does not calculate an optimal hedge size, derive lots or pips, rank candidates, include trading costs, or project profit.
Two-position historical comparison
Describe two positions with monetary sensitivities you have already checked. The output compares their joint daily-return dispersion with the primary position alone.
Loading governed reference dataNo model output is shown until the source gate passes.
Historical comparison withheldComplete both position profiles, then run the historical comparison.
Primary-only daily dispersion—Historical population estimate
Combined daily dispersion—Two signed sensitivities
Historical sample variance change—Versus primary alone
Residual dispersion ratio—Combined ÷ primary
No model sample
Pearson coefficient—
Primary daily volatility—
Comparison daily volatility—
No interpretation yetThe model must pass its source, sample and input gates first.
Verified monetary sensitivity
Both amounts must describe P/L sensitivity to a 1% pair move using one account currency. The page labels but does not convert them.
No optimization or advice
No candidate ranking, direction choice, lot size, execution cost, future loss, probability, profit projection, or trade recommendation is produced.
What the model calculates
For each selected pair, the page calculates daily simple returns over the chosen calendar window and retains only exact matching return intervals. Pearson model correlation_pearson v1.0.0 supplies the coefficient and the same aligned sample supplies population standard deviation.
a = primary direction × primary sensitivity × primary daily standard deviation (%)
b = comparison direction × comparison sensitivity × comparison daily standard deviation (%)
V_primary = a²
V_combined = a² + b² + 2 × correlation × a × b
historical variance change = (1 − V_combined ÷ V_primary) × 100
b = comparison direction × comparison sensitivity × comparison daily standard deviation (%)
V_primary = a²
V_combined = a² + b² + 2 × correlation × a × b
historical variance change = (1 − V_combined ÷ V_primary) × 100
The monetary dispersion figures are square roots of those historical sample variances. They are not expected profit or loss, value at risk, a stop-loss probability, a maximum-loss estimate, or a forecast.
How to obtain the monetary sensitivity input
Use your broker or platform's instrument-aware profit/loss preview, or independently calculate the change with the correct contract specification and current conversion into your account currency. Record the magnitude corresponding to a one-percentage-point move in each pair.
| Requirement | Why it matters |
|---|---|
| Same account currency | The variance formula combines both amounts directly; mixed currencies would not be comparable. |
| Same 1% move basis | A consistent pair-return unit makes the two sensitivities commensurable. |
| Correct contract and conversion | Pip value and account-currency conversion depend on the instrument and current rates. This route deliberately does not guess them. |
| Positive magnitude plus separate direction | The model applies long/short signs itself, avoiding ambiguous signed user amounts. |
How to interpret the result
- Lower historical sample variance means the two signed sensitivities varied less together than the primary position alone within this sample.
- Higher historical sample variance means the comparison position increased measured dispersion within this sample.
- Residual dispersion ratio below 1 means lower measured dispersion; above 1 means higher measured dispersion. It is not a probability.
- Pearson correlation describes linear co-movement only. It is not causation, stability, or proof that an offset will persist.
Relationships can change abruptly during market stress. Recheck the actual positions, trading costs, margin, swap, execution terms and broker or jurisdiction rules before acting.
Retired pre-governance hedge outputs
The former tool ranked candidate pairs, selected a direction, derived a lot size from static coefficients, assigned an effectiveness score and generated price scenarios. Those outputs were removed because their data, conversion assumptions and model contracts were not sufficiently reproducible. Version 1.0.0 restores only a user-chosen, historical pairwise variance comparison.
Evidence guide
Historical hedge-dispersion methodology
The model aligns simple daily returns by exact interval, calculates Pearson correlation and population standard deviations, then applies the two user-entered signed monetary sensitivities.
combined variance = a² + b² + 2ρab, where a and b are direction-signed sensitivity × sample standard deviation and ρ is the aligned-sample correlation.
Worked example
In the audited perfect-positive fixture, both return series have correlation +1 and both positions have sensitivity 100. When one position is long and the other is short, the equal signed components offset: primary daily dispersion is 33.1662 and combined in-sample dispersion is 0.
The fixture’s dispersion ratio is 0 and its reported historical variance change is 100% lower than the primary series alone.
How to interpret the result
Zero combined dispersion in this constructed sample means exact arithmetic cancellation inside that sample. It does not mean the positions are risk-free: future correlation, price paths, sensitivities, costs and execution can differ.
Assumptions and limits
- Pearson correlation measures linear historical association, not causation or future stability.
- The model depends on aligned daily reference observations and cannot describe intraday gaps or tail dependence.
- Sensitivity inputs must use one account currency and the same one-percentage-point basis.
- Margin, spread, commission, swap, slippage, liquidation and legal restrictions are excluded.
Sources and methodology
- NIST — correlation coefficient formula Primary statistical formula reference.
- NIST/SEMATECH e-Handbook of Statistical Methods Statistical-methodology reference.
- CFTC — retail forex advisory Market and execution risk context.
Frequently Asked Questions
No. You enter both pairs and directions. The output describes historical sample variance for that exact comparison and is not a recommendation.
Lot size alone is not a common monetary unit. Contract specifications, pair prices and account-currency conversion affect the value of a move. A verified account-currency sensitivity keeps those calculations outside this model.
It means the combined signed sensitivities had lower variance than the primary position alone in the displayed historical sample. It does not guarantee future protection, maximum loss, or execution performance.
No. Those costs and requirements vary by broker, account and time. Confirm them directly before considering any additional position.
Version 1 saves only the form inputs in your browser under a separate storage key. It does not connect to a broker account, credentials, orders or balances, and the Clear button removes the saved inputs.
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Disclaimer: The results from this tool are estimates for educational and informational purposes only and may differ from your broker's figures. This is not financial or investment advice. Trading forex and CFDs carries a high level of risk and can result in the loss of all your capital. Always verify calculations with your broker and trade within your risk tolerance.