Portfolio optimisation: bridging the gap between theory and practice (2407.00887v2)

Abstract: Portfolio optimisation is essential in quantitative investing, but its implementation faces several practical difficulties. One particular challenge is converting optimal portfolio weights into real-life trades in the presence of realistic features, such as transaction costs and integral lots. This is especially important in automated trading, where the entire process happens without human intervention. Several works in literature have extended portfolio optimisation models to account for these features. In this paper, we highlight and illustrate difficulties faced when employing the existing literature in a practical setting, such as computational intractability, numerical imprecision and modelling trade-offs. We then propose a two-stage framework as an alternative approach to address this issue. Its goal is to optimise portfolio weights in the first stage and to generate realistic trades in the second. Through extensive computational experiments, we show that our approach not only mitigates the difficulties discussed above but also can be successfully employed in a realistic scenario. By splitting the problem in two, we are able to incorporate new features without adding too much complexity to any single model. With this in mind we model two novel features that are critical to many investment strategies: first, we integrate two classes of assets, futures contracts and equities, into a single framework, with an example illustrating how this can help portfolio managers in enhancing investment strategies. Second, we account for borrowing costs in short positions, which have so far been neglected in literature but which significantly impact profits in long/short strategies. Even with these new features, our two-stage approach still effectively converts optimal portfolios into actionable trades.

• The paper introduces a novel two-stage framework that efficiently translates optimal asset allocations into actionable trades by integrating equities, futures, and transaction costs.
• The methodology addresses computational intractability and numerical precision issues while incorporating realistic constraints like integral lots and borrowing costs for short positions.
• Extensive computational experiments validate the framework’s effectiveness, showing improved out-of-sample performance and practical utility for automated trading systems.

Bridging Theory and Practice in Portfolio Optimization

The paper "Portfolio optimisation: bridging the gap between theory and practice" by Cristiano Arbex Valle addresses the long-standing practical challenges in implementing portfolio optimization frameworks in real-world environments. The research identifies key limitations of current models used in quantitative finance, particularly the translation of optimal asset weights into executable trades within live trading systems. Such limitations include computational intractability, numerical precision issues, and the inability of existing methods to incorporate realistic features like transaction costs and integral lots effectively.

The paper introduces a novel two-stage framework aimed at addressing these challenges. The first stage of the framework focuses on optimizing portfolio weights using relative formulations, familiar in traditional models, but extends these to integrate futures contracts alongside equities, providing new avenues for diversification and leverage. The paper notes that accounting for the distinct characteristics of futures—such as expiration dates, margins, and leverage—requires careful handling within the optimization process. Adjustments are made to the first-stage constraints to accommodate these features, which, the author argues, offer significant advantages for portfolio managers in enhancing investment strategies.

The second stage of the framework converts the optimal weights from the first stage into actionable trades. This stage uniquely accounts for transaction costs and integral lots, ensuring the practical applicability of the proposed solutions. The author highlights the use of an absolute formulation here, which provides a straightforward way to model transaction costs as financial values, allowing for adjustments that are more reflective of the real trading environment. The paper showcases extensive computational experiments to validate the framework, indicating that the two-stage approach effectively overcomes previously identified limitations.

Moreover, the research introduces borrowing costs for short positions, an often-neglected but critical component for realistic modeling in long/short investment strategies. The empirical examples show how these features can be successfully integrated into the two-stage framework without sacrificing computational tractability. Although the approach is heuristic in nature, the results suggest a promising balance between fidelity to the first-stage optimal weights and the necessary adaptations for real-world execution.

The inclusion of futures contracts, alongside equities, not only allows for improved diversification but also leverages the ease of short and leveraged positions provided by these instruments. The paper offers an empirical demonstration of these benefits using a dataset of S&P 500 stocks and selected futures contracts, illustrating substantial improvements in out-of-sample performance metrics.

This two-stage framework presents clear implications for portfolio theory and practice, suggesting new pathways for automated trading strategies where decisions must be executed without human intervention. While the paper acknowledges the heuristic aspect of the two-stage process, particularly in the second stage's approximation of target portfolios, it argues robustly for the framework's utility when facing the complexities of integrating diverse asset classes and real-world trading conditions.

The research opens several avenues for future exploration, including extending the framework to include other asset classes like options or fixed income, and addressing challenges related to liquidity and trading policies. Additionally, optimizing the second stage for larger asset universes or integrating decentralized portfolio management scenarios could further enhance its applicability in contemporary investment environments.

Overall, the paper represents a significant contribution to the field of quantitative finance and operations research, offering a practical and adaptable solution to bridge the gap between theoretical portfolio optimization and its application within the constraints of real-world trading systems.