Efficient Frontier Calculator

Free ToolNo signup required

Plot the two-asset risk-return curve and find the lowest-risk minimum-variance portfolio.

The Frontier Curve

Every blend of two assets, plotted risk vs return

Minimum Variance

The lowest-risk mix at the tip of the curve

Diversification

See how correlation bends the curve leftwards

Two-Asset Efficient Frontier

Enter the expected return and volatility of two assets and their correlation. We trace every blend of the two and highlight the lowest-risk (minimum-variance) portfolio.

How the Efficient Frontier Works

The Formula

E[Rp] = w·rA + (1−w)·rB
σp² = w²σA² + (1−w)²σB² + 2w(1−w)ρσAσB

Return is a simple weighted average, but risk is not — the correlation term means a blend can be less risky than its parts. Sweeping the weight w from 0 to 1 traces the whole frontier.

Where It Leads

The frontier is the heart of Markowitz portfolio optimisation. Add a risk-free asset and the best portfolio becomes the point where a line from the risk-free rate just touches the curve — the tangency portfolio in the MPT calculator.

Full Portfolio Analytics

A frontier across all your assets

This tool handles two assets; ARIA builds the efficient frontier across your entire multi-asset portfolio, with real correlations and constraints — the optimisation that a two-asset model only hints at.

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