Portfolio Optimization

Mitigating Extremal Risks: A Network-Based Portfolio Strategy ArXiv ID: 2409.12208 “View on arXiv” Authors: Unknown Abstract In financial markets marked by inherent volatility, extreme events can result in substantial investor losses. This paper proposes a portfolio strategy designed to mitigate extremal risks. By applying extreme value theory, we evaluate the extremal dependence between stocks and develop a network model reflecting these dependencies. We use a threshold-based approach to construct this complex network and analyze its structural properties. To improve risk diversification, we utilize the concept of the maximum independent set from graph theory to develop suitable portfolio strategies. Since finding the maximum independent set in a given graph is NP-hard, we further partition the network using either sector-based or community-based approaches. Additionally, we use value at risk and expected shortfall as specific risk measures and compare the performance of the proposed portfolios with that of the market portfolio. ...

Kullback-Leibler cluster entropy to quantify volatility correlation and risk diversity ArXiv ID: 2409.10543 “View on arXiv” Authors: Unknown Abstract The Kullback-Leibler cluster entropy $\mathcal{“D_{C”}}[“P | Q”] $ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (SP&500, NASDAQ, DJIA, DAX, FTSEMIB). The Kullback-Leibler functional $\mathcal{“D_{C”}}[“P | Q”] $ provides complementary perspectives about the stochastic volatility process compared to the Shannon functional $\mathcal{“S_{C”}}[“P”]$. While $\mathcal{“D_{C”}}[“P | Q”] $ is maximum at the short time scales, $\mathcal{“S_{C”}}[“P”]$ is maximum at the large time scales leading to complementary optimization criteria tracing back respectively to the maximum and minimum relative entropy evolution principles. The realized volatility is modelled as a time-dependent fractional stochastic process characterized by power-law decaying distributions with positive correlation ($H>1/2$). As a case study, a multiperiod portfolio built on diversity indexes derived from the Kullback-Leibler entropy measure of the realized volatility. The portfolio is robust and exhibits better performances over the horizon periods. A comparison with the portfolio built either according to the uniform distribution or in the framework of the Markowitz theory is also reported. ...

High-Frequency Options Trading | With Portfolio Optimization ArXiv ID: 2408.08866 “View on arXiv” Authors: Unknown Abstract This paper explores the effectiveness of high-frequency options trading strategies enhanced by advanced portfolio optimization techniques, investigating their ability to consistently generate positive returns compared to traditional long or short positions on options. Utilizing SPY options data recorded in five-minute intervals over a one-month period, we calculate key metrics such as Option Greeks and implied volatility, applying the Binomial Tree model for American options pricing and the Newton-Raphson algorithm for implied volatility calculation. Investment universes are constructed based on criteria like implied volatility and Greeks, followed by the application of various portfolio optimization models, including Standard Mean-Variance and Robust Methods. Our research finds that while basic long-short strategies centered on implied volatility and Greeks generally underperform, more sophisticated strategies incorporating advanced Greeks, such as Vega and Rho, along with dynamic portfolio optimization, show potential in effectively navigating the complexities of the options market. The study highlights the importance of adaptability and responsiveness in dynamic portfolio strategies within the high-frequency trading environment, particularly under volatile market conditions. Future research could refine strategy parameters and explore less frequently traded options, offering new insights into high-frequency options trading and portfolio management. ...

A new approach to the theory of optimal income tax ArXiv ID: 2408.14476 “View on arXiv” Authors: Unknown Abstract The Nobel-price winning Mirrlees’ theory of optimal taxation inspired a long sequence of research on its refinement and enhancement. However, an issue of concern has been always the fact that, as was shown in many publications, the optimal schedule in Mirrlees’ paradigm of maximising the total utility (constructed from individually optimised individual ones) usually did not lead to progressive taxation (contradicting the ethically supported practice in developed economies), and often even assigned minimal tax rates to the higher paid strata of society. The first objective of this paper is to support this conclusion by proving a theorem on optimal tax schedule in (practically most exploited) piecewise-linear environment under a simplest natural utility function. The second objective is to suggest a new paradigm for optimal taxation, where instead of just total average utility maximization one introduces a standard deviation of utility as a second parameter (in some analogy with Marcowitz portfolio optimization). We show that this approach leads to transparent and easy interpreted optimality criteria for income tax. ...

Inferring financial stock returns correlation from complex network analysis ArXiv ID: 2407.20380 “View on arXiv” Authors: Unknown Abstract Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the “noise”. Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted as collective modes behavior while the modes under are usually considered as noise. In this analysis we use complex network analysis to simulate the “noise” and the “market” component of the return correlations, by introducing some meaningful correlations in simulated geometric Brownian motion for the stocks. We find that the returns correlation matrix is dominated by stocks with high eigenvector centrality and clustering found in the network. We then use simulated “market” random walks to build an optimal portfolio and find that the overall return performs better than using the historical mean-variance data, up to 50% on short time scale. ...

PO-QA: A Framework for Portfolio Optimization using Quantum Algorithms ArXiv ID: 2407.19857 “View on arXiv” Authors: Unknown Abstract Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve complex problems given the underlying Quantum Computing (QC) infrastructure. Utilizing QC’s applicable strengths to the finance industry’s problems, such as PO, allows us to solve these problems using quantum-based algorithms such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). While the Quantum potential for finance is highly impactful, the architecture and composition of the quantum circuits have not yet been properly defined as robust financial frameworks/algorithms as state of the art in present literature for research and design development purposes. In this work, we propose a novel scalable framework, denoted PO-QA, to systematically investigate the variation of quantum parameters (such as rotation blocks, repetitions, and entanglement types) to observe their subtle effect on the overall performance. In our paper, the performance is measured and dictated by convergence to similar ground-state energy values for resultant optimal solutions by each algorithm variation set for QAOA and VQE to the exact eigensolver (classical solution). Our results provide effective insights into comprehending PO from the lens of Quantum Machine Learning in terms of convergence to the classical solution, which is used as a benchmark. This study paves the way for identifying efficient configurations of quantum circuits for solving PO and unveiling their inherent inter-relationships. ...

Optimal retirement in presence of stochastic labor income: a free boundary approach in an incomplete market ArXiv ID: 2407.19190 “View on arXiv” Authors: Unknown Abstract In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through investments in the risk-free and risky assets that characterize the financial market. ...

Fine-Tuning Large Language Models for Stock Return Prediction Using Newsflow ArXiv ID: 2407.18103 “View on arXiv” Authors: Unknown Abstract Large language models (LLMs) and their fine-tuning techniques have demonstrated superior performance in various language understanding and generation tasks. This paper explores fine-tuning LLMs for stock return forecasting with financial newsflow. In quantitative investing, return forecasting is fundamental for subsequent tasks like stock picking, portfolio optimization, etc. We formulate the model to include text representation and forecasting modules. We propose to compare the encoder-only and decoder-only LLMs, considering they generate text representations in distinct ways. The impact of these different representations on forecasting performance remains an open question. Meanwhile, we compare two simple methods of integrating LLMs’ token-level representations into the forecasting module. The experiments on real news and investment universes reveal that: (1) aggregated representations from LLMs’ token-level embeddings generally produce return predictions that enhance the performance of long-only and long-short portfolios; (2) in the relatively large investment universe, the decoder LLMs-based prediction model leads to stronger portfolios, whereas in the small universes, there are no consistent winners. Among the three LLMs studied (DeBERTa, Mistral, Llama), Mistral performs more robustly across different universes; (3) return predictions derived from LLMs’ text representations are a strong signal for portfolio construction, outperforming conventional sentiment scores. ...

Hopfield Networks for Asset Allocation ArXiv ID: 2407.17645 “View on arXiv” Authors: Unknown Abstract We present the first application of modern Hopfield networks to the problem of portfolio optimization. We performed an extensive study based on combinatorial purged cross-validation over several datasets and compared our results to both traditional and deep-learning-based methods for portfolio selection. Compared to state-of-the-art deep-learning methods such as Long-Short Term Memory networks and Transformers, we find that the proposed approach performs on par or better, while providing faster training times and better stability. Our results show that Modern Hopfield Networks represent a promising approach to portfolio optimization, allowing for an efficient, scalable, and robust solution for asset allocation, risk management, and dynamic rebalancing. ...

Large-scale Time-Varying Portfolio Optimisation using Graph Attention Networks ArXiv ID: 2407.15532 “View on arXiv” Authors: Unknown Abstract Apart from assessing individual asset performance, investors in financial markets also need to consider how a set of firms performs collectively as a portfolio. Whereas traditional Markowitz-based mean-variance portfolios are widespread, network-based optimisation techniques offer a more flexible tool to capture complex interdependencies between asset values. However, most of the existing studies do not contain firms at risk of default and remove any firms that drop off indices over a certain time. This is the first study to also incorporate such firms in portfolio optimisation on a large scale. We propose and empirically test a novel method that leverages Graph Attention networks (GATs), a subclass of Graph Neural Networks (GNNs). GNNs, as deep learning-based models, can exploit network data to uncover nonlinear relationships. Their ability to handle high-dimensional data and accommodate customised layers for specific purposes makes them appealing for large-scale problems such as mid- and small-cap portfolio optimisation. This study utilises 30 years of data on mid-cap firms, creating graphs of firms using distance correlation and the Triangulated Maximally Filtered Graph approach. These graphs are the inputs to a GAT model incorporating weight and allocation constraints and a loss function derived from the Sharpe ratio, thus focusing on maximising portfolio risk-adjusted returns. This new model is benchmarked against a network characteristic-based portfolio, a mean variance-based portfolio, and an equal-weighted portfolio. The results show that the portfolio produced by the GAT-based model outperforms all benchmarks and is consistently superior to other strategies over a long period, while also being informative of market dynamics. ...