Mean–Variance Lab

Explore Markowitz geometry, the GMVP, asymptotes, tangency portfolio, and the Capital Market Line.

Interactive teaching simulator · all calculations in your browser

Inputs

Expected return μ and volatility σ are annual percentages.

The covariance matrix must be positive definite. Invalid inputs are flagged automatically.

Risk-free rate r_f

Show risk-free asset and CML

Show frontier asymptotes

Show inefficient branch

Show individual assets

Target expected return

Move along the risky frontier. Type any target return directly; the slider and chart will expand automatically when you go beyond the current view.

σ–μ geometry · loading v4

GMVP return

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GMVP risk

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Tangency return

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Tangency Sharpe

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Return

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Risk

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CML risk

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Tangency allocation

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Move the target-return slider.

Watch portfolio weights change along the Markowitz frontier and compare the risky-only solution with the CML.