Optimal Portfolio Choice with Estimation Risk: No Risk-free Asset Case

61 Pages Posted: 10 Feb 2016 Last revised: 23 Mar 2020

See all articles by Raymond Kan

Raymond Kan

University of Toronto - Rotman School of Management

Xiaolu Wang

Iowa State University

Guofu Zhou

Washington University in St. Louis - John M. Olin Business School; China Academy of Financial Research (CAFR)

Date Written: March 21, 20

Abstract

For the popular mean-variance portfolio choice problem in the case without a risk-free asset, we develop a new portfolio strategy to mitigate estimation risk. We show that in both calibrations and real datasets, optimally combining the sample global minimum variance portfolio with a sample zero-investment portfolio is a more effective strategy to deal with estimation risk than alternative strategies proposed in the literature. In addition, the newly derived optimal combining strategy can be readily combined with some existing strategies, such as using the shrinkage covariance matrix estimators of Ledoit and Wolf (2004, 2017) or imposing the factor structure of MacKinlay and Pastor (2000), to further improve portfolio performance. For the combining portfolios, we further obtain the exact distribution of the out-of-sample returns and explicit expressions of the expected out-of-sample utilities, which provide a fast and accurate way of evaluating the portfolios and offer analytical insights into portfolio construction and performance evaluation.

Keywords: portfolio choice, estimation risk, mean-variance optimization, optimal combining

JEL Classification: G11, G12, C11

Suggested Citation

Kan, Raymond and Wang, Xiaolu and Zhou, Guofu, Optimal Portfolio Choice with Estimation Risk: No Risk-free Asset Case (March 21, 20). 29th Australasian Finance and Banking Conference 2016, Rotman School of Management Working Paper No. 2819254, Available at SSRN: https://ssrn.com/abstract=2819254 or http://dx.doi.org/10.2139/ssrn.2819254

Raymond Kan

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S3E6
Canada
416-978-4291 (Phone)
416-971-3048 (Fax)

Xiaolu Wang (Contact Author)

Iowa State University ( email )

613 Wallace Road
Ames, IA 50011-2063
United States

Guofu Zhou

Washington University in St. Louis - John M. Olin Business School ( email )

Washington University
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-6384 (Phone)
314-658-6359 (Fax)

HOME PAGE: http://apps.olin.wustl.edu/faculty/zhou/

China Academy of Financial Research (CAFR)

Shanghai Advanced Institute of Finance
Shanghai P.R.China, 200030
China

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