Abstract

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz portfolio rule and most of its extensions not only underperform the naive 1/N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/N rule with one of the four sophisticated strategies—the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pástor (2000) rule, and the Kan and Zhou (2007) rule—as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice.

Scientific Portfolio AI- Generated Summary

This paper explores the combination of sophisticated and naive approaches to improve portfolio performance. The authors focus on the combination of the 1/N rule with Markowitz-type rules and reaffirm the value of investment theory. They find that their theory-based approach not only enhances the sophisticated strategies but also outperforms the naive 1/N rule in most scenarios.

The paper begins by acknowledging the contributions of various individuals and institutions to the research. It then provides an overview of the mean-variance framework and its practical applications. The authors note that while the framework is widely used in practice, it has limitations, such as the assumption of normality and the need for accurate estimates of expected returns and covariances.

The methodology of the paper is based on the idea of combining portfolio strategies. The authors note that similar ideas have been applied in various portfolio problems, but this paper focuses on the combination of the 1/N rule with Markowitz-type rules. The authors argue that the combination of naive and sophisticated approaches can lead to better portfolio performance than either approach alone.

The paper presents four combination rules, each of which combines the 1/N rule with a different Markowitz-type rule. The authors compare these rules with the 1/N rule and with their uncombined counterparts based on both simulated and real data sets. They find that the combination rules generally outperform the 1/N rule and the uncombined rules.

The authors conclude that their theory-based approach to portfolio diversification can lead to better performance than the naive 1/N rule. They note that their approach is not limited to the specific combination rules presented in the paper and can be extended to other portfolio problems. They also suggest that future research could explore the use of other naive rules, such as equally weighted portfolios, in combination with sophisticated rules.

Overall, this paper provides a valuable contribution to the literature on portfolio diversification strategies. The authors demonstrate that the combination of naive and sophisticated approaches can lead to better portfolio performance than either approach alone. They also provide a framework for combining different portfolio rules and suggest avenues for future research.