Two-Asset Minimum Variance Calculator
Compare an entered two-asset mix with the minimum-variance long-only mix under entered risks and correlation.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Evaluate portfolio variance across long-only weights and clamp the analytic unconstrained minimum to the 0–100% range.
Variance=w²σA²+(1−w)²σB²+2w(1−w)ρσAσB
Worked example
With volatilities 20% and 10%, correlation zero, minimum risk occurs at 20% A and 80% B, giving about 8.94427% volatility.
Assumptions and input details
No expected-return optimization, leverage, transaction costs or constraints beyond long-only full investment. Inputs are scenarios; the mathematical minimum is not an allocation recommendation. Zero volatilities are allowed. Identical perfectly correlated risks give the same risk at every weight. No live market data or national tax rules are inferred. Enter consistent amounts in one currency unless explicitly stated otherwise.
References: CFA Institute: risk-adjusted performance measures
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Use matched asset return histories to calculate sample covariance, portfolio volatility and variance contributions.
Apply two entered asset-return scenarios to long-only portfolio weights and inspect contributions.
Add balances in different currencies, including debts. Convert the total and compare a table and currency chart.
Reserved advertising space.