Efficient frontier
Quantitative Finance glossary · Numerical Methods & Optimization
Definition
Set of portfolios with the minimum variance for each level of expected return — the upper boundary of the feasible mean-variance region. With a risk-free asset, the frontier becomes the Capital Market Line E[R_p] = r_f + (E[R_T] - r_f)/(σ_T),σ_p, tangent to the risky-asset frontier at the tangency portfolio T, and the Sharpe ratio is maximised at T. The frontier is notoriously fragile in-sample: estimation error in boldsymbolμ and boldsymbolΣ produces corner-solution weights, motivating Black-Litterman, shrinkage, and resampled-efficiency fixes.
Efficient frontier in plain English
When you build an investment portfolio, you want the highest return for the least bumpiness (risk). The efficient frontier is the set of 'best deals' — for any level of return you'll accept, it's the portfolio that gets there with the smallest ups and downs, so anything below the curve is a wasteful mix you'd never choose. Once you can also park money in a totally safe asset (like a government bond), the math points to one single best mix of risky investments — the tangency portfolio — that everyone should hold, just in bigger or smaller amounts depending on nerve. The catch, and it's a big one: the frontier is calculated from guesses about future returns, and tiny errors in those guesses produce crazy, extreme recommendations, which is why pros use damping tricks (Black-Litterman, shrinkage) to keep it sane.
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