Efficient Frontier Explorer

Direct Answer

The efficient frontier explorer plots the set of portfolios that deliver the maximum expected return for each level of risk, based on the expected returns, volatilities, and correlations you enter for up to six assets. It marks the global minimum-variance portfolio and the tangency portfolio that maximizes the Sharpe ratio given your risk-free rate. All calculations run in your browser for educational exploration, not investment advice.

Tool Inputs

Efficient Frontier Chart

Key Portfolio Results

How to Interpret the Chart

For the underlying math, how the frontier is constructed, the minimum-variance and tangency portfolio formulas, and a worked example, see the companion guide: The Efficient Frontier: Construction and Interpretation.

• Efficient frontier (blue curve): Each point on this curve is a minimum-variance portfolio for a given target expected return. Portfolios below and to the right of the curve are achievable but inefficient. No long-only portfolio can exist above or to the left of the frontier.
• Minimum-variance portfolio (MVP, green dot): The leftmost point on the frontier. This portfolio has the lowest possible variance achievable by any combination of the assets. It sacrifices some expected return in exchange for the minimum attainable risk.
• Tangency portfolio (orange dot): The portfolio on the frontier where the Capital Allocation Line (from the risk-free rate) is tangent to the frontier. This portfolio maximizes the Sharpe ratio (expected excess return per unit of risk) given the risk-free rate you specified.
• Individual assets (gray dots): Each asset appears as a single point. Diversification allows combinations of assets to achieve lower risk than any single asset, moving portfolios to the left of the individual asset scatter.
• All computations use long-only constraints (no short selling). This restricts the feasible set relative to the unconstrained frontier derived in Markowitz's original theory.

References

• Markowitz, H. (1952). "Portfolio Selection." The Journal of Finance, 7(1), 77-91, the original mean-variance framework this tool's frontier, minimum-variance, and tangency-portfolio calculations are built on.
• CFA Institute Research and Policy Center: efficient frontier and tangency portfolio methodology
• SEC Investor.gov: Asset Allocation and Diversification

Educational Disclaimer

This tool is for educational and illustrative purposes only. Inputs represent forward-looking estimates of expected returns, volatilities, and correlations that are unobservable and must be estimated with significant uncertainty. Efficient frontier outputs are highly sensitive to input assumptions, small changes in expected returns can produce large changes in portfolio weights. Past volatilities and correlations do not guarantee future values. This tool does not constitute investment advice.