Equities

Class of topological portfolios: Are they better than classical portfolios? ArXiv ID: 2601.03974 “View on arXiv” Authors: Anubha Goel, Amita Sharma, Juho Kanniainen Abstract Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize persistence landscapes, a type of summary statistics for persistent homology, to capture the topological variation of returns, blossoming a novel concept of ``Topological Risk". Our proposed topological risk then quantifies portfolio risk by tracking time-varying topological properties of assets through the $L_p$ norm of the persistence landscape. Through optimization, we derive an optimal portfolio that minimizes this topological risk. Numerical experiments conducted using nearly a decade long S&P 500 data demonstrate the superior performance of our TDA-based portfolios in comparison to the seven popular portfolio optimization models and two benchmark portfolio strategies, the naive $1/N$ portfolio and the S&P 500 market index, in terms of excess mean return, and several financial ratios. The outcome remains consistent through out the computational analysis conducted for the varying size of holding and investment time horizon. These results underscore the potential of our TDA-based topological risk metric in providing a more comprehensive understanding of portfolio dynamics than traditional statistical measures. As such, it holds significant relevance for modern portfolio management practices. ...

Smart Predict–then–Optimize Paradigm for Portfolio Optimization in Real Markets ArXiv ID: 2601.04062 “View on arXiv” Authors: Wang Yi, Takashi Hasuike Abstract Improvements in return forecast accuracy do not always lead to proportional improvements in portfolio decision quality, especially under realistic trading frictions and constraints. This paper adopts the Smart Predict–then–Optimize (SPO) paradigm for portfolio optimization in real markets, which explicitly aligns the learning objective with downstream portfolio decision quality rather than pointwise prediction accuracy. Within this paradigm, predictive models are trained using an SPO-based surrogate loss that directly reflects the performance of the resulting investment decisions. To preserve interpretability and robustness, we employ linear predictors built on return-based and technical-indicator features and integrate them with portfolio optimization models that incorporate transaction costs, turnover control, and regularization. We evaluate the proposed approach on U.S. ETF data (2015–2025) using a rolling-window backtest with monthly rebalancing. Empirical results show that decision-focused training consistently improves risk-adjusted performance over predict–then–optimize baselines and classical optimization benchmarks, and yields strong robustness during adverse market regimes (e.g., the 2020 COVID-19). These findings highlight the practical value of the Smart Predict–then–Optimize paradigm for portfolio optimization in realistic and non-stationary financial environments. ...

Trading with market resistance and concave price impact ArXiv ID: 2601.03215 “View on arXiv” Authors: Youssef Ouazzani Chahdi, Nathan De Carvalho, Grégoire Szymanski Abstract We consider an optimal trading problem under a market impact model with endogenous market resistance generated by a sophisticated trader who (partially) detects metaorders and trades against them to exploit price overreactions induced by the order flow. The model features a concave transient impact driven by a power-law propagator with a resistance term responding to the trader’s rate via a fixed-point equation involving a general resistance function. We derive a (non)linear stochastic Fredholm equation as the first-order optimality condition satisfied by optimal trading strategies. Existence and uniqueness of the optimal control are established when the resistance function is linear, and an existence result is obtained when it is strictly convex using coercivity and weak lower semicontinuity of the associated profit-and-loss functional. We also propose an iterative scheme to solve the nonlinear stochastic Fredholm equation and prove an exponential convergence rate. Numerical experiments confirm this behavior and illustrate optimal round-trip strategies under “buy” signals with various decay profiles and different market resistance specifications. ...

On lead-lag estimation of non-synchronously observed point processes ArXiv ID: 2601.01871 “View on arXiv” Authors: Takaaki Shiotani, Takaki Hayashi, Yuta Koike Abstract This paper introduces a new theoretical framework for analyzing lead-lag relationships between point processes, with a special focus on applications to high-frequency financial data. In particular, we are interested in lead-lag relationships between two sequences of order arrival timestamps. The seminal work of Dobrev and Schaumburg proposed model-free measures of cross-market trading activity based on cross-counts of timestamps. While their method is known to yield reliable results, it faces limitations because its original formulation inherently relies on discrete-time observations, an issue we address in this study. Specifically, we formulate the problem of estimating lead-lag relationships in two point processes as that of estimating the shape of the cross-pair correlation function (CPCF) of a bivariate stationary point process, a quantity well-studied in the neuroscience and spatial statistics literature. Within this framework, the prevailing lead-lag time is defined as the location of the CPCF’s sharpest peak. Under this interpretation, the peak location in Dobrev and Schaumburg’s cross-market activity measure can be viewed as an estimator of the lead-lag time in the aforementioned sense. We further propose an alternative lead-lag time estimator based on kernel density estimation and show that it possesses desirable theoretical properties and delivers superior numerical performance. Empirical evidence from high-frequency financial data demonstrates the effectiveness of our proposed method. ...

Temporal Kolmogorov-Arnold Networks (T-KAN) for High-Frequency Limit Order Book Forecasting: Efficiency, Interpretability, and Alpha Decay ArXiv ID: 2601.02310 “View on arXiv” Authors: Ahmad Makinde Abstract High-Frequency trading (HFT) environments are characterised by large volumes of limit order book (LOB) data, which is notoriously noisy and non-linear. Alpha decay represents a significant challenge, with traditional models such as DeepLOB losing predictive power as the time horizon (k) increases. In this paper, using data from the FI-2010 dataset, we introduce Temporal Kolmogorov-Arnold Networks (T-KAN) to replace the fixed, linear weights of standard LSTMs with learnable B-spline activation functions. This allows the model to learn the ‘shape’ of market signals as opposed to just their magnitude. This resulted in a 19.1% relative improvement in the F1-score at the k = 100 horizon. The efficacy of T-KAN networks cannot be understated, producing a 132.48% return compared to the -82.76% DeepLOB drawdown under 1.0 bps transaction costs. In addition to this, the T-KAN model proves quite interpretable, with the ‘dead-zones’ being clearly visible in the splines. The T-KAN architecture is also uniquely optimized for low-latency FPGA implementation via High level Synthesis (HLS). The code for the experiments in this project can be found at https://github.com/AhmadMak/Temporal-Kolmogorov-Arnold-Networks-T-KAN-for-High-Frequency-Limit-Order-Book-Forecasting. ...

Capital allocation and tail central moments for the multivariate normal mean-variance mixture distribution ArXiv ID: 2601.00568 “View on arXiv” Authors: Enrique Calderín-Ojeda, Yuyu Chen, Soon Wei Tan Abstract Capital allocation is a procedure used to assess the risk contributions of individual risk components to the total risk of a portfolio. While the conditional tail expectation (CTE)-based capital allocation is arguably the most popular capital allocation method, its inability to reflect important tail behaviour of losses necessitates a more accurate approach. In this paper, we introduce a new capital allocation method based on the tail central moments (TCM), generalising the tail covariance allocation informed by the tail variance. We develop analytical expressions of the TCM as well as the TCM-based capital allocation for the class of normal mean-variance mixture distributions, which is widely used to model asymmetric and heavy-tailed data in finance and insurance. As demonstrated by a numerical analysis, the TCM-based capital allocation captures several significant patterns in the tail region of equity losses that remain undetected by the CTE, enhancing the understanding of the tail risk contributions of risk components. ...

Uncertainty-Adjusted Sorting for Asset Pricing with Machine Learning ArXiv ID: 2601.00593 “View on arXiv” Authors: Yan Liu, Ye Luo, Zigan Wang, Xiaowei Zhang Abstract Machine learning is central to empirical asset pricing, but portfolio construction still relies on point predictions and largely ignores asset-specific estimation uncertainty. We propose a simple change: sort assets using uncertainty-adjusted prediction bounds instead of point predictions alone. Across a broad set of ML models and a U.S. equity panel, this approach improves portfolio performance relative to point-prediction sorting. These gains persist even when bounds are built from partial or misspecified uncertainty information. They arise mainly from reduced volatility and are strongest for flexible machine learning models. Identification and robustness exercises show that these improvements are driven by asset-level rather than time or aggregate predictive uncertainty. ...

A Global Optimal Theory of Portfolio beyond R-$σ$ Model ArXiv ID: 2601.00281 “View on arXiv” Authors: Yifan Liu, Shi-Dong Liang Abstract The deviation of the efficient market hypothesis (EMH) for the practical economic system allows us gain the arbitrary or risk premium in finance markets. We propose the triplet $(R,H,σ)$ theory to give the local and global optimal portfolio, which eneralize from the $(R,σ)$ model. We present the formulation of the triplet $(R,H,σ)$ model and give the Pareto optimal solution as well as comparing it with the numerical investigations for the Chinese stock market. We define the local optimal weights of the triplet $(\mathbf{“w”}{“R”},\mathbf{“w”}{“H”},\mathbf{“w”}_σ)$, which constructs the triangle of the quasi-optimal investing subspace such that we further define the centroid of the triangle or the incenter of the triangle as the optimal investing weights, which optimizes the mean return, the arbitrary or risk premium and the volatility risk. By investigating numerically the Chinese stock market as an example we demonstrate the validity of the formulation and obtain the global optimal strategy and quasi-optimal investing subspace. The theory provides an efficient way to design the portfolio for different style investors, conservative or aggressive investors, in finance market to maximize the mean return and arbitrary or risk premium with a small volatility risk. ...

Core-Periphery Dynamics in Market-Conditioned Financial Networks: A Conditional P-Threshold Mutual Information Approach ArXiv ID: 2601.00395 “View on arXiv” Authors: Kundan Mukhia, Imran Ansari, S R Luwang, Md Nurujjaman Abstract This study investigates how financial market structure reorganizes during the COVID-19 crash using a conditional p-threshold mutual information (MI) based Minimum Spanning Tree (MST) framework. We analyze nonlinear dependencies among the largest stocks from four diverse QUAD countries: the US, Japan, Australia, and India. Crashes are identified using the Hellinger distance and Hilbert spectrum; a crash occurs when HD = mu_H + 2*sigma_H, segmenting data into pre-crash, crash, and post-crash periods. Conditional p-threshold MI filters out common market effects and applies permutation-based significance testing. Resulting validated dependencies are used to construct MST networks for comparison across periods. Networks become more integrated during the crash, with shorter path lengths, higher centrality, and lower algebraic connectivity, indicating fragility. Core-periphery structure declines, with increased periphery vulnerability, and disassortative mixing facilitates shock transmission. Post-crash networks show only partial recovery. Aftershock analysis using the Gutenberg-Richter law indicates higher relative frequency of large volatility events following the crash. Results are consistent across all markets, highlighting the conditional p-threshold MI framework for capturing nonlinear interdependencies and systemic vulnerability. ...

Generative AI-enhanced Sector-based Investment Portfolio Construction ArXiv ID: 2512.24526 “View on arXiv” Authors: Alina Voronina, Oleksandr Romanko, Ruiwen Cao, Roy H. Kwon, Rafael Mendoza-Arriaga Abstract This paper investigates how Large Language Models (LLMs) from leading providers (OpenAI, Google, Anthropic, DeepSeek, and xAI) can be applied to quantitative sector-based portfolio construction. We use LLMs to identify investable universes of stocks within S&P 500 sector indices and evaluate how their selections perform when combined with classical portfolio optimization methods. Each model was prompted to select and weight 20 stocks per sector, and the resulting portfolios were compared with their respective sector indices across two distinct out-of-sample periods: a stable market phase (January-March 2025) and a volatile phase (April-June 2025). Our results reveal a strong temporal dependence in LLM portfolio performance. During stable market conditions, LLM-weighted portfolios frequently outperformed sector indices on both cumulative return and risk-adjusted (Sharpe ratio) measures. However, during the volatile period, many LLM portfolios underperformed, suggesting that current models may struggle to adapt to regime shifts or high-volatility environments underrepresented in their training data. Importantly, when LLM-based stock selection is combined with traditional optimization techniques, portfolio outcomes improve in both performance and consistency. This study contributes one of the first multi-model, cross-provider evaluations of generative AI algorithms in investment management. It highlights that while LLMs can effectively complement quantitative finance by enhancing stock selection and interpretability, their reliability remains market-dependent. The findings underscore the potential of hybrid AI-quantitative frameworks, integrating LLM reasoning with established optimization techniques, to produce more robust and adaptive investment strategies. ...