Inference on Optimal Portfolio Weights Using Generalized Pivotal Quantity

• Activity Number: 574
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yuanyuan Zhu*+ and Philip L.H. Yu and Thomas Mathew
• Companies: The University of Hong Kong and The University of Hong Kong and University of Maryland Baltimore County
• Keywords: Optimal portfolio weight ; Generalized pivotal quantity ; Portfolio rebalancing problem ; Generalized confidence interval

Abstract

Asset allocation problem has been widely discussed after Markowitz mean-variance model. We treat the optimal portfolio weights as a random vector and derive its generalized pivotal quantity (GPQ). The GPQ is widely used in hypothesis tests and confidence intervals. We make use of GPQ to make inference of the optimal weights. We obtain the point estimator by averaging all the GPQs. Also we propose different approaches to construct the generalized simultaneous confidence intervals for optimal weights. A simulation study is conducted to compare the GPQ estimators with the classical Markowitz model, bootstrap and shrinkage methods. The results show small mean square error for portfolio weights estimation and satisfactory coverage rate for confidence intervals. Furthermore, an empirical study of a proposed methodology to portfolio rebalancing problem is considered. Results show that the confidence intervals help investors decide whether or not to update the portfolio weights so as to achieve a higher profit.