Efficient Frontier, explained.
The mean–variance efficient frontier contains portfolios with the highest expected return for a given variance within a specified feasible set.
Why it happens
Two assumed assets have means 5% and 9% and standard deviations 10% and 20%. Nonnegative weights sum to one. Covariance changes with correlation, bending the portfolio risk–return curve and its minimum-variance point.
The mean–variance efficient frontier contains portfolios with the highest expected return for a given variance within a specified feasible set.
Read the result
The upper branch is efficient only within the two assumed assets and the stated no-shorting constraint.
A worked example
Mix two hypothetical return streams
Set correlation to zero and vary the weight of the higher-return, higher-volatility second asset.
Reveal the minimum-variance point and compare lower-return points that take more risk than it does.
Change correlation to inspect how diversification opportunities depend on an uncertain input, not just on asset count.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Two assumed assets have means 5% and 9% and standard deviations 10% and 20%. Nonnegative weights sum to one. Covariance changes with correlation, bending the portfolio risk–return curve and its minimum-variance point.
Where this idea is useful
A practical use
Separate the mathematical benefit of diversification from the uncertainty involved in estimating returns, risks and correlations.
A common misconception
“An efficient portfolio is guaranteed safe or profitable.”
Efficiency describes a tradeoff between supplied mean and variance within a feasible set; it does not guarantee realised returns or capture every form of risk.
What this explanation leaves out
- Expected returns and covariance are supplied assumptions. Mean–variance efficiency omits tails, costs and estimation error and is not allocation advice.
Why can adding a riskier asset initially reduce portfolio volatility?
The covariance term can offset some individual variance when returns are not perfectly correlated. The exact reduction depends on weights and the supplied correlation.
Which estimated input would move your supposed frontier most if it were wrong?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.