The Markowitz Efficient Frontier, Explained

Modern portfolio theory, formulated by Harry Markowitz (Nobel Prize in Economics, 1990), starts from a powerful idea: what matters isn't the risk of each asset on its own, but how they combine. Diversifying well can reduce risk without giving up return.

What the efficient frontier is

If you plot every possible portfolio on a chart of risk (X axis) against return (Y axis), you get a cloud of points. The efficient frontier is the upper-left edge of that cloud: the set of portfolios that offer the maximum return for each level of risk (or the minimum risk for each level of return).

Any portfolio below the frontier is suboptimal: there's another one with the same return and less risk, or more return for the same risk.

Notable points on the frontier

• Minimum volatility: the most conservative portfolio on the frontier.
• Maximum Sharpe: the one that best compensates for risk (see what the Sharpe ratio is).
• Maximum Sortino: similar, but penalizing only downside moves.

The role of correlation

The key to diversification is correlation between assets. Combining stocks that don't move together smooths out the portfolio's curve. That's why every ticker page shows its correlation with the S&P 500.

The OjoAlTicker optimizer computes this frontier for whichever assets you choose, combining Monte Carlo simulation with exact optimization.