The efficient frontier is the set of portfolios with the highest expected return for each level of risk, measured as volatility. A mix below the curve is inefficient: some portfolio on the frontier earns more for the same risk, or takes less risk for the same return. Harry Markowitz introduced the idea in 1952, and it sits at the centre of modern portfolio theory.
Return: Rp = Σ wi × Ri. Volatility: σp = √(Σi Σj wi × wj × σi × σj × ρij). The frontier is the lowest σp for each target Rp, with every weight wi ≥ 0 and the weights adding up to 1.
Take a stock fund expected to return 8% a year at 18% volatility and a bond fund returning 4% at 6%, with a correlation of 0.2. All in bonds gives 4% at 6% volatility. Moving 4.5% into stocks gives 4.2% at 5.9%: more return and less risk, because the two do not move together. That is the minimum-volatility mix. With a 2% risk-free rate, the maximum-Sharpe mix is 25% stocks and 75% bonds, returning 5.0% at 7.0% volatility for a Sharpe ratio of 0.43, against 0.33 for all bonds. A 60/40 mix also sits on the frontier, at 6.4% and 11.5% volatility, but its Sharpe ratio drops to 0.38.
Try the free efficient frontier calculator with your own tickers, or see the frontier of the holdings you track in the portfolio analyzer, next to your current weights.
The minimum-volatility portfolio is the left tip of the curve, the calmest mix the assets allow. The maximum-Sharpe portfolio is the point where return above the risk-free rate, divided by volatility, is highest. It usually holds more of the riskier assets than the minimum-volatility mix.
No. It is only as good as the returns, volatilities and correlations you feed it. Built from past prices, it shows which mixes worked best in that window, and a different window can move the curve a lot.
Without limits, the optimizer often puts most of the money in the asset with the best recent record. A maximum weight per holding, such as 25%, keeps the frontier to portfolios that stay spread out.