Block bootstrap methods and the choice of stocks for the long run

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.