Understanding Portfolio Optimization with Markowitz

Introduction to Modern Portfolio Theory

Portfolio optimization is at the heart of modern wealth management. Developed by Harry Markowitz in 1952, Modern Portfolio Theory (MPT) has revolutionized the way we construct and manage investment portfolios.

The Fundamental Principle

Markowitz's theory is based on a simple but powerful principle: diversification reduces risk without necessarily reducing expected return. By combining assets that are not perfectly correlated, we can create a portfolio that offers a better risk/return ratio than any individual asset.

How Does Markowitz Optimization Work?

Key Components

• Expected Return: The average return you expect to get from each asset
• Volatility (Risk): The variability of returns, measured by standard deviation
• Correlation: The extent to which two assets' prices move together

The Optimization Process

The Markowitz algorithm seeks to:

- Maximize return for a given level of risk, or - Minimize risk for a given level of return

This creates what is called the efficient frontier: a curve representing all possible optimal portfolios.

Benefits for Wealth Management Advisors

Time Savings

Instead of spending hours manually calculating optimal allocations, Markowitz optimization allows you to:

- Generate optimal portfolios in seconds - Quickly test different scenarios - Adapt allocations according to client constraints

Objectivity

The algorithm eliminates emotional biases and provides recommendations based on solid quantitative data.

Personalization

By integrating specific constraints (sectors to avoid, concentration limits, etc.), you can create portfolios that respect each client's preferences and constraints.

Limitations and Improvements

Markowitz Limitations

Markowitz theory assumes that:

- Returns follow a normal distribution - Investors are rational - Correlations remain stable over time

Modern Approaches

To address these limitations, improvements have been developed:

- Black-Litterman: Integrates the portfolio manager's views - Monte Carlo: Simulates thousands of possible scenarios - Robust optimization: Takes into account parameter uncertainty

Conclusion

Portfolio optimization with Markowitz remains a fundamental tool for wealth management advisors. By combining this approach with modern techniques and a deep understanding of client needs, you can create truly optimized portfolios.

ClearFolio integrates these advanced algorithms to allow you to generate optimal portfolios in just a few clicks, while respecting your clients' specific constraints.