Efficient frontier
The efficient frontier is the set of portfolios offering the highest expected return for each level of risk. Any portfolio below that frontier can be improved: there is another combination of the same assets that returns more without taking on more risk, or takes less risk for the same return. It is the central idea of modern portfolio theory.
How it is calculated
It is not computed with a formula but by solving an optimisation: for each level of risk you find the combination of weights that maximises expected return, and the set of those solutions draws the frontier. Three things are needed: each asset's expected return, its volatility, and the correlation matrix between all of them. Correlation is the piece doing the work: two assets each returning 8 % with 15 % volatility, combined 50/50 with a correlation of 0.3, give a portfolio returning the same 8 % with volatility around 12 %. That point sits above the straight line between the two, and that curvature is the whole of diversification.
The figures in the example are invented and rounded so the arithmetic can be redone by hand. They are not data from any real company.
What it is NOT
It is not a prediction nor a portfolio recommendation: it is the output of the data you fed it. And that is its real problem —expected returns are estimates, and the frontier is extremely sensitive to them: changing one tenth of a point in an asset's expected return can move its optimal weight from 5 % to 40 %. Correlations are not stable either: they rise precisely during drawdowns, which is when diversification ought to be working.
See also
See it on real data
Celsmar computes this from the accounts companies file with their regulator, and shows which line every figure comes from. Free to start, no card.
Definition for informational purposes. It is not financial advice nor a recommendation to buy or sell.