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Markowitz efficient frontier calculator

Pick as many stocks or ETFs as you like: their historical returns, volatilities and correlations fill in, and you see diversification at work on the efficient frontier.

Pick tickers (two or more, as many as you like) — or play with the example asset classes below.

Returns, volatilities and correlations — editable
AssetAnnual return %Volatility % / yr
Stocks
Bonds
Gold

Correlations of daily returns, from −1 to 1. You edit the upper triangle — the lower one mirrors it.

AssetStocksBondsGold
Stocks1
Bonds0.11
Gold0.050.251

With tickers: annual return and volatility over the last 3 years of their common history (shorter when one of them hasn't traded that long — the window is shown above; the return is the average daily return × 252 — the arithmetic mean the model assumes, higher than the compound annual growth rate for volatile stocks), correlations of daily returns over the same window. Each ticker in its own quote currency. Without tickers: round, illustrative asset-class assumptions (a row you add starts as a neutral placeholder: 5% return, 15% volatility, uncorrelated with the rest). Neither is a forecast.

AssetLowest volatility 🛡️Highest Sharpe ⚖️
Stocks9%42%
Bonds85%44%
Gold6%14%
Return3.43%4.84%
Volatility5.73%8.07%
Sharpe0.250.35

In plain words 💡

Harry Markowitz (Nobel 1990) showed something that sounds like a free lunch 🍽️: if assets don't move perfectly together (correlation below 1), a mix of them can have lower volatility than any one of them alone. Watch the lowest-volatility point land to the left of the single assets on the chart.

The efficient frontier is the set of mixes where no higher return was available for the same risk. The highest-Sharpe point is the one that gave the most return above the risk-free rate per unit of volatility. These are textbook concepts computed on the numbers in the table — not a hint about what anyone should buy.

Where it breaks ⚠️

The output is only as good as the numbers in the table, and past returns say almost nothing about future ones — a stock that rose 70% a year for 3 years will "win" any optimisation, which doesn't mean it will keep doing so. Nudge one asset's return by 1 point and watch the weights jump — which is why Markowitz optimisers are called "error maximisers". Correlations aren't stable either: in a crisis they tend to rise together. And with many tickers, remember the math only sees their common history — one young listing shortens the window for all of them.

Read more 📚

An educational tool: it runs a formula on historical data or on the numbers you type. It is not a forecast or a recommendation, and it knows nothing about your situation.