Andra AP-fonden (AP2), Göteborg, Sweden.
PLoS One. 2024 Jun 25;19(6):e0305736. doi: 10.1371/journal.pone.0305736. eCollection 2024.
In this paper, we analytically derive closed-form expressions for the tangency portfolio weights: the fully invested portfolio that maximizes the expected return over the risk-free rate, relative to the volatility of the portfolio return. We explicitly derive this portfolio from a range of underlying return models and show examples where it coincides with different well-known smart beta products. Specifically, we find the closed-form expression for the tangency portfolio weights for a return model with compound symmetric correlation matrix. We also deduce the tangency portfolio weights for the CAPM return model and illustrate in a case study that the estimated tangency portfolio weights may distinctly deviate from the market value weighted portfolio. Furthermore, we show that depending on the return model, the tangency portfolio weights may take a diverse set of shapes; from very diversified to highly concentrated portfolios.
在本文中，我们通过分析推导出了相切投资组合权重的闭式表达式：相对于投资组合回报的波动性而言，最大化风险调整后收益的完全投资组合。我们从一系列基础收益模型中明确推导出了这个投资组合，并给出了它与不同知名智能贝塔产品相重合的示例。具体来说，我们找到了具有复合对称相关矩阵的收益模型的相切投资组合权重的闭式表达式。我们还推导出了 CAPM 收益模型的相切投资组合权重，并在案例研究中说明，估计的相切投资组合权重可能与市值加权投资组合明显偏离。此外，我们还表明，根据收益模型的不同，相切投资组合权重可能呈现出多样化的形状；从非常多样化到高度集中的投资组合。
