Efficient Frontier Builder

Quadratic optimization with Markowitz's 1952 mean-variance objective. The tool computes the covariance matrix from your input return series, then solves for portfolio weights that minimize variance at a given target return. Sweeping the target gives the frontier.

Covariance estimation is data-hungry. With 10 assets and 60 observations (5 years monthly), the covariance matrix has 55 parameters fit from 60 data points — not enough degrees of freedom for stable estimates. The tool warns at low N. Best practice is 10x observations vs. assets, or use shrinkage.

Yes: long-only (no shorting), max-weight per asset (e.g., no more than 30% in one holding), and minimum-position thresholds. The methodology page documents each constraint. Adding constraints reduces the feasible region and shifts the frontier rightward (lower expected return at given risk).

Two known issues: (1) sensitivity to input estimates — small changes in expected returns produce huge weight swings. (2) underestimation of tail risk — variance ignores skew and kurtosis. The tool lets you toggle a CVaR (Conditional Value at Risk) objective as an alternative. For institutional-grade work, see Black-Litterman or robust optimization.

By default, simple historical mean from the input series. The methodology page warns this is a noisy estimator — for medium-sample series, historical mean is barely better than zero. Users can override with their own forward expected-return vector (e.g., from CAPM or analyst estimates).