Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal...

Area of Science:

• Quantitative Finance
• Financial Econometrics
• Portfolio Management

Background:

• Markowitz portfolio optimization relies on accurate covariance matrix estimation.
• Traditional methods can be sensitive to noise and estimation errors, impacting portfolio performance.
• Exploring nonlinear interactions and advanced filtering techniques may enhance robustness.

Purpose of the Study:

• To evaluate the impact of nonlinear interactions and noise-filtering on Markowitz portfolio allocation.
• To assess the performance of these enhanced covariance matrix techniques using daily financial data.
• To compare the proposed methods against traditional linear and robust estimators.

Main Methods:

• Covariance matrix estimation using Kernel functions.
• Noise-filtering based on Random Matrix Theory eigenvalue distributions.
• Performance evaluation using daily data from seven financial markets (Jan 2000 - Aug 2018).
• Comparison with linear Pearson estimator and robust covariance methods.

Main Results:

• Noise-filtering led to significantly higher risk-adjusted profitability in nearly half of the tested cases.
• Nonlinear approaches demonstrated varied outcomes, with some adding predictive performance and others introducing noise.
• The study identified conditions where nonlinear complexity enhanced or detracted from portfolio predictive power.

Conclusions:

• Noise-filtering techniques offer substantial improvements in portfolio risk-adjusted returns.
• The benefits of nonlinear methods in portfolio optimization are context-dependent and require careful consideration.
• Further research can explore optimal nonlinear feature selection for improved financial forecasting.