The Efficient Frontier

You now know how to measure return, risk, and the variance of a combined portfolio. The efficient frontier is what happens when you run those calculations across every possible combination of assets and weights – and plot the results.

Each dot on the chart below represents a portfolio with a specific expected return and standard deviation. The curved line connecting the best portfolios – the ones that offer the highest return for each level of risk – is the efficient frontier.

Any portfolio sitting on the frontier is efficient: you can't get more return without accepting more risk, and you can't reduce risk without sacrificing return. Any portfolio sitting below the frontier is inefficient: a better option exists at the same risk level.

What the Frontier Tells You

The efficient frontier doesn't tell you which portfolio to pick. It tells you which portfolios are worth considering at all – and eliminates every option that is dominated by a better one.

Where you sit on the frontier depends on your risk tolerance:

• Left end of the curve: minimum variance portfolio – lowest possible risk, lower expected return;
• Right end of the curve: maximum return portfolio – highest expected return, highest volatility;
• Your optimal point: the highest Sharpe ratio portfolio – the point where the line from the risk-free rate is tangent to the frontier.

The tangency point is called the market portfolio in Modern Portfolio Theory. It represents the best possible risk-adjusted return available from the given set of assets.

• Below the frontier: inefficient – a better portfolio exists at the same risk level;
• On the frontier: efficient – no improvement is possible without a tradeoff;
• Above the frontier: impossible – no portfolio can exist there given the available assets.