An Approach to Enhanced Indexing

Investment managers often manage a portfolio of stocks with respect to a benchmark. Their primary concern is selecting the best stocks to outperform their benchmark, while constraining their tracking error. The most common way of doing this is to use an optimization framework to maximize the information ratio of their portfolio. In this paper, we develop an unconventional approach to determining how a portfolio should be managed with respect to the benchmark. In particular, given some assumptions, we determine what percentage of the benchmark stocks would be optimal for the portfolio manager to select. The optimal portfolio depends on Fisher's noncentral hypergeometric distribution and the Wallenius noncentral hypergeometric distribution. We find that the optimal selectivity of a benchmark universe varies from 50% to 80%, when managers have selection ability. The information ratio and the selectivity percentage can vary as the selection ability of the portfolio manager changes and as the underlying size of the universe changes. These results are provocative, given that many enhanced index portfolio managers select a low a percentage of the benchmark universe