Mean-Variance Optimisation: Efficient Frontiers and Portfolio Objectives

Summary

The document introduces Modern Portfolio Theory and explains how asset correlation shapes the risk and return of a portfolio. Expected portfolio return is a weighted sum of asset returns, while portfolio variance also depends on covariances. When assets are less positively correlated, combining them can reduce risk without changing the return estimate. The efficient frontier describes the resulting trade-off among feasible portfolios. The framework relies on assumptions such as informed investors and efficient markets, which may not hold in practice.

It outlines common optimisation objectives: inverse-variance weights, minimum volatility, maximum Sharpe ratio, target-return and target-risk portfolios, risk-adjusted return, and maximum diversification. It also describes how a library can support standard and custom objectives and constraints. The article is a conceptual and implementation guide, rather than evidence that any allocation will outperform. Its results depend on estimated returns and covariance, the investor’s constraints and targets, and the validity of the underlying assumptions; the document does not provide a comparative empirical evaluation.

Key ideas

• Portfolio return is a weighted sum of asset returns, while portfolio variance also reflects correlations among assets.
• Lower correlation can reduce portfolio risk without directly changing expected return.
• The efficient frontier represents portfolios offering the best expected return for a given level of risk.
• Mean-variance optimisation supports objectives such as minimum volatility, maximum Sharpe ratio, and target-risk allocation.
• Estimated inputs and theoretical assumptions limit how reliably optimised weights will work in practice.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.