| dc.description.abstract | In the portfolio optimization problem, unstable results will occur, which will affect the credibility of the results. In order to understand such problems, this article uses two methods, Performance-Based Regularization (PBR) and Bootstrap methods, for portfolio optimization and examines the effectiveness of the two methods. First, the portfolio optimization problem considers the Mean-Variance of the portfolio risk to be minimized under the certain target rate of return. The first optimization method is PBR, which is modified by Sample Average Approximation (SAA), considers the stability and reliability of the results. The main idea is to constrain the variance of the results from optimization, and use Chebyshev′s inequality to make sure that the results of optimization approach the theoretical value. The second optimization method, Bootstrap, uses a large number of estimators getting from redrawing sample and removing the outliers of results from optimization. The estimated result will be more stable. In a small sample, Bootstrap has more advantages than SAA and PBR that rely on the law of large numbers. I use two criterions to evaluate the performance of the two methods: one is the improvement ratio, which is the numbers of target rate of return have been improved under all different target rate of return, and the other is the degree of improvemen, which is the degree of reducing the variance of the optimization results. This article found that under these different DGPs and measurement methods, Bootstrap′s performance is significantly better than PBR, and Bootstrap still performs well in a small sample. | en_US |