Block Bootstrap Methods and the Choice of Stocks for the Long Run

Forthcoming, Quantitative Finance

24 Pages Posted: 11 Apr 2011 Last revised: 18 Nov 2012

Philippe Cogneau

University of Liege - HEC Management School

Valeriy Zakamulin

University of Agder - School of Business and Law

Date Written: November 24, 2011

Abstract

Financial advisors commonly recommend that the investment horizon should be rather long in order to benefit from the "time diversification". In this case, in order to choose the optimal portfolio, it is necessary to estimate the risk and reward of several alternative portfolios over a long-run given a sample of observations over a short-run. Two interrelated obstacles in these estimations are lack of sufficient data and the uncertainty in the nature of the return generating process. To overcome these obstacles researchers rely heavily on block bootstrap methods. In this paper we demonstrate that the estimates provided by a block bootstrap method are generally biased and we propose two methods of bias reduction. We show that an improper use of a block bootstrap method usually causes underestimation of the risk of a portfolio whose returns are independent over time and overestimation of the risk of a portfolio whose returns are mean-reverting.

Keywords: long-run, time-series data, serial dependence, parameter estimation, bootstrap, block bootstrap

JEL Classification: C13, C14, C15, G11

Suggested Citation

Cogneau, Philippe and Zakamulin, Valeriy, Block Bootstrap Methods and the Choice of Stocks for the Long Run (November 24, 2011). Forthcoming, Quantitative Finance. Available at SSRN: https://ssrn.com/abstract=1806447 or http://dx.doi.org/10.2139/ssrn.1806447

Philippe Cogneau

University of Liege - HEC Management School ( email )

Liège, 4000
Belgium

Valeriy Zakamulin (Contact Author)

University of Agder - School of Business and Law ( email )

Service Box 422
Kristiansand, N-4604
Norway
+47 38141039 (Phone)

HOME PAGE: http://vzakamulin.weebly.com/

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