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PENALIZED PORTFOLIO OPTIMIZATION
by
Yemin Shi
A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(STATISTICS)
May 2011
Copyright 2011 Yemin Shi
Object Description
| Title | Penalized portfolio optimization |
| Author | Shi, Yemin |
| Author email | yeminshi@usc.edu; biostanley@gmail.com |
| Degree | Master of Science |
| Document type | Thesis |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2011-05-01 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-05-02 |
| Advisor (committee chair) | Goldstein, Larry |
| Advisor (committee member) |
James, Gareth Zhang, Jianfeng |
| Abstract | Penalization or regularization is an important integration to the traditional regression method to improve prediction accuracy, speed and adaptability for various problems. Lasso type L1-regularization methods and its variants can reduce the complexity of high dimensional data by feature selection as well as coefficient shrinkage. Fan et al. shows that using an L1-penalty, which he calls “gross-exposure” constraint on the weights in a portfolio, has significant advantages. In particular it can reduce risk and because the L1 penalty sets coefficients to zero, many fewer assets are needed in the portfolio, and are therefore suitable for large-scale portfolio optimization problems. Fan et al. formulated this constrained portfolio risk minimization problem into a convex optimization problem and solved the problem by an efficient least angle regression (LARS) optimizer. However, the implementation of LARS used an approximation to the true optimization criterion. To address this problem, we propose a customized coordinate descent portfolio optimization procedure (CCDPO). The coordinate wise updating scheme can optimize all coefficients of the allocation vector faster than LARS. The warming-up and re-initialization steps in CCDPO prevent the dominant coefficients from growing to extreme values. CCDPO uses the advantage of coefficients scarcity to reduce the optimization load and achieves fast speed. To study the performance of CCDPO, we implement a factor-based covariance estimator for data simulation, and a data integration website for collecting real-life stock price quotes. The optimization results on the simulated data show that CCDPO significantly reduces the portfolio risk. And the penalty factor controls the diversity between empirical risk and actual risk in a similar fashion to the “gross-exposure” constraint.; The ex-post analysis of the real-life Yahoo! Finance data indicates that portfolios optimized by CCDPO have significant less risk than those optimized by the non-constrained optimizer. |
| Keyword | coordinate descent; penalized optimization; L1-penalty; LASSO; regularized regression; portfolio optimization; asset management; feature selection; LARS |
| Coverage date | 2000/2010 |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3839 |
| Rights | Shi, Yemin |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-SHI-4566 |
| Archival file | uscthesesreloadpub_Volume29/etd-SHI-4566.pdf |
Description
| Title | Page 1 |
| Full text | PENALIZED PORTFOLIO OPTIMIZATION by Yemin Shi A Thesis Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (STATISTICS) May 2011 Copyright 2011 Yemin Shi |
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