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Portfolio Optimization for Asymmetric Returns: Maximizing Risk-Adjusted Returns

Updated: Jun 29, 2023

Portfolio optimization is a crucial aspect of investment management, where the goal is to construct a portfolio that maximizes returns while minimizing risk. Traditionally, asset allocation has been based on the mean-variance framework proposed by Markowitz, which assumes that the risk of an investment is solely determined by the variance of its returns. However, this approach fails to account for the intuitive preference of investors towards higher returns and the adverse impact of downside risk.

In recent years, researchers have recognized the presence of asymmetric dependence structures in financial returns. These structures imply that the relationship between asset returns is not symmetrical, with different levels of dependence during positive and negative market conditions. As a result, traditional portfolio optimization techniques may not effectively capture the risk associated with such asymmetries, leading to suboptimal allocation decisions.

Risk Comparison - normal vs skewed asset returns
Risk Comparison - normal vs skewed asset returns

Incorporating Asymmetric Dependence in Portfolio Allocation

To address the shortcomings of traditional portfolio optimization methods, a new approach has emerged that incorporates asymmetric dependence structures in the decision-making process. This approach recognizes that the diversification benefits of portfolio allocation are reduced when assets exhibit asymmetric dependence. By considering the non-symmetrical nature of asset returns, investors can make more informed and efficient allocation decisions.

One method that has gained traction in the field of portfolio optimization is the use of local covariance matrices based on the local Gaussian correlation (LGC). The LGC is a nonparametric measure of local dependence that captures the asymmetric relationship between asset returns. By incorporating the LGC into the portfolio optimization process, investors can construct portfolios that account for the asymmetries in asset returns and effectively manage risk.

The Portfolio Optimization Process

The portfolio optimization process using asymmetric dependence structures is straightforward when utilizing local covariance matrices based on the LGC. These matrices capture the dynamic relationship between assets, allowing for more accurate risk estimation and allocation decisions. The following steps outline the process:

  1. Data Collection: Gather historical returns data for the assets under consideration. This data will serve as the basis for calculating the local covariance matrices and the LGC.

  2. Local Covariance Matrix Calculation: Calculate the local covariance matrix for each asset using a rolling window approach. This involves estimating the covariance between each pair of assets within the specified window.

  3. Local Gaussian Correlation Calculation: Compute the LGC based on the local covariance matrices. The LGC measures the asymmetric dependence between asset returns and provides insights into the risk associated with different market conditions.

  4. Portfolio Optimization: Utilize the local covariance matrices and the LGC to construct an optimized portfolio. This involves solving an optimization problem that maximizes the risk-adjusted returns, taking into account the asymmetries in asset returns.

  5. Evaluation and Monitoring: Regularly evaluate and monitor the performance of the optimized portfolio. Adjust the allocation as necessary to adapt to changing market conditions and ensure the portfolio remains aligned with the investor's objectives.

Outperforming Traditional Approaches

Empirical research has demonstrated the superiority of portfolio optimization methods that incorporate asymmetric dependence structures compared to traditional approaches. When applied to historical data on multiple assets, these methods consistently outperform the equally weighted ("1/N") portfolio and the classical Markowitz portfolio.

By considering the non-symmetrical nature of asset returns and incorporating the LGC, the optimized portfolios are better equipped to manage risk and capture potential opportunities during different market conditions. This approach enhances risk-adjusted returns and provides investors with a more comprehensive and accurate framework for portfolio allocation.

Advantages of Asymmetric Dependence Models

The incorporation of asymmetric dependence models in portfolio optimization offers several advantages over traditional approaches. Some of these advantages include:

  1. Enhanced Risk Management: By considering the asymmetries in asset returns, asymmetric dependence models provide a more accurate assessment of risk. This enables investors to construct portfolios that are better protected during downturns and capitalize on favorable market conditions.

  2. Improved Diversification: Asymmetric dependence models recognize that the benefits of diversification are reduced when assets exhibit asymmetric relationships. By accounting for these asymmetries, investors can construct portfolios that are better diversified and more resilient to market shocks.

  3. Tail Risk Mitigation: Traditional portfolio optimization methods often fail to adequately capture tail risk, which refers to the risk of extreme events. Asymmetric dependence models, on the other hand, explicitly consider tail risk and provide a more comprehensive assessment of portfolio risk.

  4. Customization and Flexibility: Asymmetric dependence models can be tailored to reflect individual investor preferences and risk tolerance. The local covariance matrices and the LGC can be adjusted to express a wide range of preferences, allowing for greater customization and flexibility in portfolio construction.


Portfolio optimization for asymmetric returns is a critical aspect of investment management. By incorporating asymmetric dependence structures using the LGC, investors can construct portfolios that effectively manage risk and maximize risk-adjusted returns. This approach outperforms traditional methods and offers enhanced risk management, improved diversification, tail risk mitigation, and customization. As asymmetric dependence becomes increasingly recognized in financial markets, incorporating it into portfolio optimization strategies will become essential for investors seeking to achieve their investment objectives.

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