What the efficient frontier actually tells you
Harry Markowitz's 1952 insight, the foundation of modern portfolio theory, was simple but not obvious at the time: what matters isn't how risky an asset is on its own, it's how it moves relative to everything else in your portfolio. Two volatile assets that move in opposite directions can combine into a portfolio that's less risky than either one alone.
The efficient frontier is the curve of portfolios that squeeze the most expected return out of every unit of risk. Any portfolio sitting below the curve is leaving return on the table for the risk you're taking; any portfolio to the right of the curve is taking on risk you're not being paid for. Everything on the curve itself is a genuine trade-off — more return only comes with more risk from that point on.
How this tool computes it
We generate thousands of random long-only portfolios (weights are non-negative and sum to 100%), compute each one's expected return and volatility from your inputs, and plot them all. The upper-left boundary of that cloud — the running maximum return at each level of risk — is the simulated efficient frontier. It's an approximation (a true quadratic optimizer would trace the exact curve), but with a few thousand simulated portfolios it converges very closely, and it's the same Monte Carlo approach most practitioners reach for first.
The minimum-variance portfolio is the leftmost point on the frontier — the lowest risk achievable at all, regardless of return. The max-Sharpe portfolio is the point that maximizes return per unit of risk above the risk-free rate — the portfolio a rational investor who can also lend or borrow at the risk-free rate would actually want to hold, sitting where the capital market line is tangent to the frontier.
The honest limitations
This tool takes your expected returns, volatilities, and correlations as given — it can't tell you whether those numbers are right, and in practice, estimating them accurately is the hardest part of using this framework at all. Historical volatility and correlation are reasonably stable; historical returns are a poor predictor of future returns. Treat this as a tool for understanding trade-offs between assets you already have a view on, not a return forecaster.