Portfolio Optimization

Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals ArXiv ID: 2308.15135 “View on arXiv” Authors: Unknown Abstract In this article we introduce a portfolio optimisation framework, in which the use of rough path signatures (Lyons, 1998) provides a novel method of incorporating path-dependencies in the joint signal-asset dynamics, naturally extending traditional factor models, while keeping the resulting formulas lightweight and easily interpretable. We achieve this by representing a trading strategy as a linear functional applied to the signature of a path (which we refer to as “Signature Trading” or “Sig-Trading”). This allows the modeller to efficiently encode the evolution of past time-series observations into the optimisation problem. In particular, we derive a concise formulation of the dynamic mean-variance criterion alongside an explicit solution in our setting, which naturally incorporates a drawdown control in the optimal strategy over a finite time horizon. Secondly, we draw parallels between classical portfolio stategies and Sig-Trading strategies and explain how the latter leads to a pathwise extension of the classical setting via the “Signature Efficient Frontier”. Finally, we give examples when trading under an exogenous signal as well as examples for momentum and pair-trading strategies, demonstrated both on synthetic and market data. Our framework combines the best of both worlds between classical theory (whose appeal lies in clear and concise formulae) and between modern, flexible data-driven methods that can handle more realistic datasets. The advantage of the added flexibility of the latter is that one can bypass common issues such as the accumulation of heteroskedastic and asymmetric residuals during the optimisation phase. Overall, Sig-Trading combines the flexibility of data-driven methods without compromising on the clarity of the classical theory and our presented results provide a compelling toolbox that yields superior results for a large class of trading strategies. ...

Learning to Learn Financial Networks for Optimising Momentum Strategies ArXiv ID: 2308.12212 “View on arXiv” Authors: Unknown Abstract Network momentum provides a novel type of risk premium, which exploits the interconnections among assets in a financial network to predict future returns. However, the current process of constructing financial networks relies heavily on expensive databases and financial expertise, limiting accessibility for small-sized and academic institutions. Furthermore, the traditional approach treats network construction and portfolio optimisation as separate tasks, potentially hindering optimal portfolio performance. To address these challenges, we propose L2GMOM, an end-to-end machine learning framework that simultaneously learns financial networks and optimises trading signals for network momentum strategies. The model of L2GMOM is a neural network with a highly interpretable forward propagation architecture, which is derived from algorithm unrolling. The L2GMOM is flexible and can be trained with diverse loss functions for portfolio performance, e.g. the negative Sharpe ratio. Backtesting on 64 continuous future contracts demonstrates a significant improvement in portfolio profitability and risk control, with a Sharpe ratio of 1.74 across a 20-year period. ...

Analysis of Optimal Portfolio Management Using Hierarchical Clustering ArXiv ID: 2308.11202 “View on arXiv” Authors: Unknown Abstract Portfolio optimization is a task that investors use to determine the best allocations for their investments, and fund managers implement computational models to help guide their decisions. While one of the most common portfolio optimization models in the industry is the Markowitz Model, practitioners recognize limitations in its framework that lead to suboptimal out-of-sample performance and unrealistic allocations. In this study, I refine the Markowitz Model by incorporating machine learning to improve portfolio performance. By using a hierarchical clustering-based approach, I am able to enhance portfolio performance on a risk-adjusted basis compared to the Markowitz Model, across various market factors. ...

D-TIPO: Deep time-inconsistent portfolio optimization with stocks and options ArXiv ID: 2308.10556 “View on arXiv” Authors: Unknown Abstract In this paper, we propose a machine learning algorithm for time-inconsistent portfolio optimization. The proposed algorithm builds upon neural network based trading schemes, in which the asset allocation at each time point is determined by a a neural network. The loss function is given by an empirical version of the objective function of the portfolio optimization problem. Moreover, various trading constraints are naturally fulfilled by choosing appropriate activation functions in the output layers of the neural networks. Besides this, our main contribution is to add options to the portfolio of risky assets and a risk-free bond and using additional neural networks to determine the amount allocated into the options as well as their strike prices. We consider objective functions more in line with the rational preference of an investor than the classical mean-variance, apply realistic trading constraints and model the assets with a correlated jump-diffusion SDE. With an incomplete market and a more involved objective function, we show that it is beneficial to add options to the portfolio. Moreover, it is shown that adding options leads to a more constant stock allocation with less demand for drastic re-allocations. ...

ChatGPT-based Investment Portfolio Selection ArXiv ID: 2308.06260 “View on arXiv” Authors: Unknown Abstract In this paper, we explore potential uses of generative AI models, such as ChatGPT, for investment portfolio selection. Trusting investment advice from Generative Pre-Trained Transformer (GPT) models is a challenge due to model “hallucinations”, necessitating careful verification and validation of the output. Therefore, we take an alternative approach. We use ChatGPT to obtain a universe of stocks from S&P500 market index that are potentially attractive for investing. Subsequently, we compared various portfolio optimization strategies that utilized this AI-generated trading universe, evaluating those against quantitative portfolio optimization models as well as comparing to some of the popular investment funds. Our findings indicate that ChatGPT is effective in stock selection but may not perform as well in assigning optimal weights to stocks within the portfolio. But when stocks selection by ChatGPT is combined with established portfolio optimization models, we achieve even better results. By blending strengths of AI-generated stock selection with advanced quantitative optimization techniques, we observed the potential for more robust and favorable investment outcomes, suggesting a hybrid approach for more effective and reliable investment decision-making in the future. ...

Correlation-diversified portfolio construction by finding maximum independent set in large-scale market graph ArXiv ID: 2308.04769 “View on arXiv” Authors: Unknown Abstract Correlation-diversified portfolios can be constructed by finding the maximum independent sets (MISs) in market graphs with edges corresponding to correlations between two stocks. The computational complexity to find the MIS increases exponentially as the size of the market graph increases, making the MIS selection in a large-scale market graph difficult. Here we construct a diversified portfolio by solving the MIS problem for a large-scale market graph with a combinatorial optimization solver (an Ising machine) based on a quantum-inspired algorithm called simulated bifurcation (SB) and investigate the investment performance of the constructed portfolio using long-term historical market data. Comparisons using stock universes of various sizes [“TOPIX 100, Nikkei 225, TOPIX 1000, and TOPIX (including approximately 2,000 constituents)”] show that the SB-based solver outperforms conventional MIS solvers in terms of computation-time and solution-accuracy. By using the SB-based solver, we optimized the parameters of a MIS portfolio strategy through iteration of the backcast simulation that calculates the performance of the MIS portfolio strategy based on a large-scale universe covering more than 1,700 Japanese stocks for a long period of 10 years. It has been found that the best MIS portfolio strategy (Sharpe ratio = 1.16, annualized return/risk = 16.3%/14.0%) outperforms the major indices such as TOPIX (0.66, 10.0%/15.2%) and MSCI Japan Minimum Volatility Index (0.64, 7.7%/12.1%) for the period from 2013 to 2023. ...

A quantum double-or-nothing game: The Kelly Criterion for Spins ArXiv ID: 2308.01305 “View on arXiv” Authors: Unknown Abstract A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is accrued through astute betting. As information is gained from the stream of particles, the measurement directions are progressively adjusted, and the portfolio growth rate is raised. The optimal quantum strategy is determined numerically and shown to differ from the classical strategy, which is associated with the Kelly criterion. The paper contributes to the development of quantum finance, as aspects of portfolio optimisation are extended to the quantum realm. ...

An exploration of the mathematical structure and behavioural biases of 21st century financial crises ArXiv ID: 2307.15402 “View on arXiv” Authors: Unknown Abstract In this paper we contrast the dynamics of the 2022 Ukraine invasion financial crisis with notable financial crises of the 21st century - the dot-com bubble, global financial crisis and COVID-19. We study the similarity in market dynamics and associated implications for equity investors between various financial market crises and we introduce new mathematical techniques to do so. First, we study the strength of collective dynamics during different market crises, and compare suitable portfolio diversification strategies with respect to the unique number of sectors and stocks for optimal systematic risk reduction. Next, we introduce a new linear operator method to quantify distributional distance between equity returns during various crises. Our method allows us to fairly compare underlying stock and sector performance during different time periods, normalising for those collective dynamics driven by the overall market. Finally, we introduce a new combinatorial portfolio optimisation framework driven by random sampling to investigate whether particular equities and equity sectors are more effective in maximising investor risk-adjusted returns during market crises. ...

Transfer Learning for Portfolio Optimization ArXiv ID: 2307.13546 “View on arXiv” Authors: Unknown Abstract In this work, we explore the possibility of utilizing transfer learning techniques to address the financial portfolio optimization problem. We introduce a novel concept called “transfer risk”, within the optimization framework of transfer learning. A series of numerical experiments are conducted from three categories: cross-continent transfer, cross-sector transfer, and cross-frequency transfer. In particular, 1. a strong correlation between the transfer risk and the overall performance of transfer learning methods is established, underscoring the significance of transfer risk as a viable indicator of “transferability”; 2. transfer risk is shown to provide a computationally efficient way to identify appropriate source tasks in transfer learning, enhancing the efficiency and effectiveness of the transfer learning approach; 3. additionally, the numerical experiments offer valuable new insights for portfolio management across these different settings. ...

Diversifying an Index ArXiv ID: 2311.10713 “View on arXiv” Authors: Unknown Abstract In July 2023, Nasdaq announced a `Special Rebalance’ of the Nasdaq-100 index to reduce the index weights of its large constituents. A rebalance as suggested currently by Nasdaq index methodology may have several undesirable effects. These effects can be avoided by a different, but simple rebalancing strategy. Such rebalancing is easily computable and guarantees (a) that the maximum overall index weight does not increase through the rebalancing and (b) that the order of index weights is preserved. ...