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.