Quantile regression for index tracking and enhanced indexation

Quantile regression for index tracking and enhanced indexation

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Article ID: iaor20135352
Volume: 64
Issue: 11
Start Page Number: 1676
End Page Number: 1692
Publication Date: Nov 2013
Journal: Journal of the Operational Research Society
Authors: ,
Keywords: statistics: regression, programming: integer
Abstract:

Quantile regression differs from traditional least‐squares regression in that one constructs regression lines for the quantiles of the dependent variable in terms of the independent variable. In this paper we apply quantile regression to two problems in financial portfolio construction, index tracking and enhanced indexation. Index tracking is the problem of reproducing the performance of a stock market index, but without purchasing all of the stocks that make up the index. Enhanced indexation deals with the problem of out‐performing the index. We present a mixed‐integer linear programming formulation of these problems based on quantile regression. Our formulation includes transaction costs, a constraint limiting the number of stocks that can be in the portfolio and a limit on the total transaction cost that can be incurred. Numeric results are presented for eight test problems drawn from major world markets, where the largest of these test problems involves over 2000 stocks.

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