Manager skill and portfolio size with respect to a benchmark

Abstract

Investment managers often manage a portfolio with respect to a benchmark. Typically, they use a mean‐variance optimization framework to maximize the information ratio of their portfolio. We develop an unconventional approach to this question. Given a set of assumptions, we ask what optimal percentage of the benchmark stocks the portfolio manager should select. This optimal portfolio depends on Fisher's and Wallenius's noncentral hypergeometric distributions. We find that the optimal selectivity of a benchmark universe varies from 50% to 80%. These results are provocative, given that many enhanced index portfolio managers select a low percentage of the benchmark universe.

Enhanced indexing and selectivity theory

“…The work in this paper attempts to further test and examine assumptions about optimal selectivity in an enhanced portfolio (Bolshakov & Chincarini, 2020). The specific purpose of this paper was to relax assumptions about the investment environment using simulations to investigate the impact of the assumptions.…”

“…5 Also, one should note that when ω is unrealistically high, say a value of 10, then the optimal selectivity converges to the percentage of winners in the benchmark. 6 One should also refer to Bolshakov and Chincarini (2020) for the importance of using downside risk in the Fisher calculations due to an exploding IR when ω is very high.…”

“…The paper is organized as follows: Section 2 reviews selectivity theory; Section 3 discusses the data and methodology used in the paper; Section 4 discusses the methods used to relax the theoretical assumptions and the simulation results; Section 5 describes a methodology for a dynamic portfolio process and the simulation results of that process, and Section 6 concludes. Bolshakov and Chincarini (2020) consider the case of a skillful portfolio manager seeking to maximize their IR by choosing a portfolio selectivity ratio when forming their portfolio. The manager's skill is described as a probability weighting advantage to choosing outperforming stocks ('winners') versus under-performing stocks ('losers').…”

“…For a skilful manager, this probability advantage is encompassed in ω (i.e., omega), which is greater than one for a skilled manager and equal to one for an unskilled manager. Bolshakov and Chincarini (2020) brought this entirely new approach to the portfolio management literature that involves the rarely mentioned Fisher and Wallenius Noncentral Hypergeometric distributions. An ω greater than one means the portfolio manager has a higher likelihood of choosing a winner stock rather than a loser stock.…”

Business risks and their impact on business future concerning the entrepreneur’s experience with business bankruptcy: case of Czech Republic

“…In this context, the managerial experience of the owner/manager of the company also comes to the fore. Disadvantages such as inefficient use of time (Ajilchi & Kargar, 2015); lack of organization of employees and processes; lack of owner/manager motivation (Murnieks, Klotz, & Shepherd, 2020;Benzing, Chu, & Kara, 2009;Belas, Dvorsky, Kozubikova, & Cepel, 2019); insufficient attention to detail (Bolshakov & Chincarini, 2020) or insufficient communication experience are also causes of business decline (Lenz, 2019).…”