mean-variance-optimization

Mean-variance optimization computes tangency portfolio weights by taking expected returns, standard deviations, correlations, and risk-free rate as inputs, then solves for asset allocations that maximize risk-adjusted returns. The Skill constructs and inverts the covariance matrix, normalizes weights to sum to one, and outputs portfolio statistics and Sharpe ratio.

Modern portfolio theory identifies efficient portfolios that maximize expected return for a given risk level by analyzing correlations between assets. This Skill applies mean-variance optimization to find the tangency portfolio—the most efficient risky portfolio offering the highest return per unit of risk taken.

Yes, this Skill supports both long and short positions when computing optimal weights. It allows negative allocations for short positions while maximizing the Sharpe ratio across your multi-asset portfolio.

You need expected returns and standard deviations for each asset, the correlation matrix showing how assets move together, and the risk-free rate. The Skill gathers this data interactively, constructs the covariance matrix, and computes optimal weights.

The Skill constructs the covariance matrix from standard deviations and correlations, validates it for mathematical soundness, computes its inverse for optimization calculations, and rounds final asset weights to four decimals for precision.

The Skill outputs optimal asset weights for each position, portfolio expected return, portfolio standard deviation, Sharpe ratio, and detailed explanations of allocation rationale and diversification benefits.