Efficient Frontier
Explore the risk/return trade-off across every mix of your chosen assets. The frontier curve shows the highest expected return achievable at each level of risk, with the minimum-volatility and maximum-Sharpe portfolios highlighted.
Educational use only — not investment advice
This tool is for educational and informational purposes only and does not provide financial, investment, tax, legal, or accounting advice. Results are hypothetical and based on historical data and assumptions that may be inaccurate. Past performance does not guarantee future results. Consult a licensed professional before making investment decisions.
What is the Efficient Frontier?
Plot the curve of optimal portfolios and locate the minimum-volatility and maximum-Sharpe mixes.
The efficient frontier, from Modern Portfolio Theory, is the set of portfolios offering the highest expected return at each level of risk. This tool estimates expected returns and a covariance matrix from history, then traces the frontier with a constrained mean-variance optimizer, plotting your assets, a cloud of random portfolios, the minimum-volatility portfolio, and the maximum-Sharpe portfolio — with downloadable frontier data.
How to use it
- 1Enter the assets you want to optimize across (e.g. VTI, VEA, VWO, BND, GLD).
- 2Choose a date range, how expected returns are estimated, any per-asset weight limits, and a risk-free rate.
- 3Run it to plot the efficient frontier alongside your assets, with the minimum-volatility and maximum-Sharpe portfolios marked — and the frontier data available to download.
What you'll get
- ✓Efficient frontier curve
- ✓Min-volatility & max-Sharpe portfolios
- ✓Asset and random-portfolio scatter
- ✓Frontier table + CSV
↓ Or build your own below
Assets
How the Efficient Frontier works
The frontier is traced by sweeping a risk-aversion parameter and solving a long-only, box-constrained mean-variance problem with projected-gradient descent — a robust method that respects per-asset weight limits.