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Smart betas, return models and the tangency portfolio weights.

Jan Lennartsson1, Claes Ekman1

  • 1Andra AP-fonden (AP2), Göteborg, Sweden.

Plos One
|June 25, 2024
PubMed
Summary

This study derives exact formulas for tangency portfolio weights, identifying optimal investment strategies across various financial models. Results show these optimal portfolios can differ significantly from market-weighted benchmarks.

Area of Science:

  • Quantitative Finance
  • Investment Management
  • Portfolio Optimization

Background:

  • The tangency portfolio maximizes excess return per unit of risk.
  • Deriving its weights is crucial for optimal investment strategies.
  • Existing methods may not cover diverse return models.

Purpose of the Study:

  • To analytically derive closed-form expressions for tangency portfolio weights.
  • To explore these weights across different underlying return models.
  • To compare tangency portfolios with market-weighted and smart beta portfolios.

Main Methods:

  • Analytical derivation of closed-form solutions for portfolio weights.
  • Application to specific return models, including compound symmetric correlation and CAPM.

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  • Case study analysis comparing estimated weights with market values.

    • Main Results:

    • Closed-form expressions for tangency portfolio weights are derived.
    • Tangency portfolios can align with smart beta products under certain models.
    • Estimated tangency weights may differ substantially from market-weighted portfolios.
    • Portfolio diversification varies significantly based on the underlying return model.

    Conclusions:

    • The derived closed-form expressions provide a robust framework for identifying optimal portfolios.
    • Understanding model-specific tangency weights is essential for practical investment decisions.
    • The findings highlight the potential for significant deviations from traditional market-cap weighting.