291. Adaptive minimum variance portfolio selection by linear shrinkage and expansion
Invited abstract in session MB-12: Portfolio optimization, stream Applications: Finance.
Monday, 10:30-12:30Room: B100/8009
Authors (first author is the speaker)
| 1. | Xiang Zhao
|
| School of Mathematical Sciences, University of Southampton | |
| 2. | Selin Ahipasaoglu
|
| University of Southampton | |
| 3. | Houduo Qi
|
| Data Science and Artificial Intelligence, The Hong Kong Polytechnic University |
Abstract
We study the minimum variance portfolio optimization problem under covariance matrix uncertainty, arising from estimation errors and outliers. Shrinkage methods, which impose structure on the sample covariance matrix by moving it towards a target matrix, are effective when the target matrix is negatively correlated with estimation errors. We extend the linear matrix shrinkage framework to include ``matrix expansion" in which the covariance matrix is allowed to move away from a given target. Using a target matrix constructed with Lagrange multipliers for the long-only portfolio problem, we identify the allowable range for shrinkage and expansion. The optimal modification, which could be shrinkage or expansion under the modified framework, is dynamically selected on the basis of in-sample performance. Our numerical experiments demonstrate that portfolios generated by this method can achieve higher expected returns, superior Sharpe ratios, and improved risk metrics, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). These results suggest that combining shrinkage and expansion in a data-driven framework enhances portfolio performance and robustness.
Keywords
- Optimization in industry, business and finance
- Global optimization
- Data driven optimization
Status: accepted
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