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Modern Portfolio Theory Calculator

Find the optimal, maximum-Sharpe portfolio — the heart of Markowitz mean-variance optimisation.

Optimal Portfolio

The maximum-Sharpe tangency mix of two assets

Frontier & CML

The efficient frontier and capital market line plotted

Sharpe Ratio

Return earned per unit of risk above the risk-free rate

Two-Asset Mean-Variance Optimisation
Enter two assets and a risk-free rate. We plot the efficient frontier, the minimum-variance portfolio, and the optimal (maximum Sharpe) tangency portfolio along the capital market line.

Typically the short-dated government bond yield.

How Modern Portfolio Theory Works

The Optimal Mix

Sharpe = (E[Rp] − rf) / σp
optimal = max Sharpe on the frontier

MPT picks the blend with the highest Sharpe ratio — the tangency point where the capital market line meets the frontier. It is the best reward-per-risk portfolio of the risky assets.

From Frontier to Choice

The curve itself comes from the efficient frontier; MPT adds the risk-free asset to single out one optimal point. For the full intuition, see Markowitz optimisation in plain English.

Full Portfolio Analytics

Optimise more than two assets

This calculator solves the two-asset case in closed form; ARIA runs mean-variance optimisation across your whole portfolio with real correlations, constraints, and multiple optimisers — the engine behind the theory.

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Related Free Tools

Efficient Frontier Calculator
The risk-return curve without a risk-free rate.
Correlation Calculator
Estimate the correlation input from return data.
Covariance Calculator
The covariance that drives portfolio risk.
Volatility Calculator
Find each asset’s volatility from its returns.
CAPM Calculator
Expected return for a given level of market risk.
Portfolio Beta Calculator
Value-weighted market sensitivity of your holdings.

Frequently Asked Questions