What the Two-Asset Minimum Variance Calculator is for
Estimate unconstrained minimum-variance weights for two assets.
It makes the prices, cash flows, rates, time periods, weights, and model conventions explicit so you can inspect an entered scenario without hidden live-market assumptions.
Capital and cash flowstime and rate→entered modelScenario resultChanging one assumption changes the model—not the marketAsset 1 weight = (σ₂² − ρσ₁σ₂) ÷ (σ₁² + σ₂² − 2ρσ₁σ₂).
Read the estimate correctly
Use the result within its boundaries
Volatilities 10% and 20% with zero correlation produce weights 80% and 20% and volatility about 8.94%.
This is an unconstrained two-asset mathematical result; weights can be negative or above 100%. Estimates can be unstable and are not an allocation recommendation.
Quick guide
How to use this calculator
Enter the exposure, market, accounting, probability, rate, or risk assumptions named by the fields.
Use consistent currencies, periods, share units, and percentage conventions.
Interpret the output only within the displayed model and limitations.
Fixed decimal scalar arithmetic remains exact until display. Square-root and compound projections are explicitly approximate and reject non-finite results.
Worked example
Worked example
Volatilities 10% and 20% with zero correlation produce weights 80% and 20% and volatility about 8.94%.
Fixed decimals accept 30 digits and 12 decimal places, with absolute values capped at 1e12 per input and general rates capped at 1000%. Formula-specific shares and probability limits are validated separately.
International scope
No currency, exchange, broker, live security data, accounting standard, tax jurisdiction, contract specification, or regulatory disclosure is selected automatically.
Decision boundary
Outputs are arithmetic scenarios, not forecasts, advice, suitability assessments, trading signals, fair-value opinions, risk guarantees, or recommendations.
Calculator-specific assumptions
This is an unconstrained two-asset mathematical result; weights can be negative or above 100%. Estimates can be unstable and are not an allocation recommendation.
