Portfolio Allocation

Integration of Wavelet Transform Convolution and Channel Attention with LSTM for Stock Price Prediction based Portfolio Allocation ArXiv ID: 2507.01973 “View on arXiv” Authors: Junjie Guo Abstract Portfolio allocation via stock price prediction is inherently difficult due to the notoriously low signal-to-noise ratio of stock time series. This paper proposes a method by integrating wavelet transform convolution and channel attention with LSTM to implement stock price prediction based portfolio allocation. Stock time series data first are processed by wavelet transform convolution to reduce the noise. Processed features are then reconstructed by channel attention. LSTM is utilized to predict the stock price using the final processed features. We construct a portfolio consists of four stocks with trading signals predicted by model. Experiments are conducted by evaluating the return, Sharpe ratio and max drawdown performance. The results indicate that our method achieves robust performance even during period of post-pandemic downward market. ...

Uncertainty-Aware Strategies: A Model-Agnostic Framework for Robust Financial Optimization through Subsampling ArXiv ID: 2506.07299 “View on arXiv” Authors: Hans Buehler, Blanka Horvath, Yannick Limmer, Thorsten Schmidt Abstract This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the unavailability of the true probability measure forces reliance on an empirical approximation, and even small misestimations can lead to significant deviations in decision quality. Building on the framework of Klibanoff et al. (2005), we enhance the conventional objective - whether this is expected utility in an investing context or a hedging metric - by superimposing an outer “uncertainty measure”, motivated by traditional monetary risk measures, on the space of models. In scenarios where a natural model distribution is lacking or Bayesian methods are impractical, we propose an ad hoc subsampling strategy, analogous to bootstrapping in statistical finance and related to mini-batch sampling in deep learning, to approximate model uncertainty. To address the quadratic memory demands of naive implementations, we also present an adapted stochastic gradient descent algorithm that enables efficient parallelization. Through analytical, simulated, and empirical studies - including multi-period, real data and high-dimensional examples - we demonstrate that uncertainty measures outperform traditional mixture of measures strategies and our model-agnostic subsampling-based approach not only enhances robustness against model risk but also achieves performance comparable to more elaborate Bayesian methods. ...

Bayesian Optimization for CVaR-based portfolio optimization ArXiv ID: 2503.17737 “View on arXiv” Authors: Unknown Abstract Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained minimization problems, seeking to minimize the conditional value-at-risk (a computationally intensive risk measure) under a minimum expected return constraint. The proposed algorithms utilize a new acquisition function, which drives sampling towards the optimal region. Additionally, a new two-stage procedure is developed, which significantly reduces the number of evaluations of the expensive-to-evaluate objective function. The proposed algorithm’s competitive performance is demonstrated through practical examples. ...

Reinforcement-Learning Portfolio Allocation with Dynamic Embedding of Market Information ArXiv ID: 2501.17992 “View on arXiv” Authors: Unknown Abstract We develop a portfolio allocation framework that leverages deep learning techniques to address challenges arising from high-dimensional, non-stationary, and low-signal-to-noise market information. Our approach includes a dynamic embedding method that reduces the non-stationary, high-dimensional state space into a lower-dimensional representation. We design a reinforcement learning (RL) framework that integrates generative autoencoders and online meta-learning to dynamically embed market information, enabling the RL agent to focus on the most impactful parts of the state space for portfolio allocation decisions. Empirical analysis based on the top 500 U.S. stocks demonstrates that our framework outperforms common portfolio benchmarks and the predict-then-optimize (PTO) approach using machine learning, particularly during periods of market stress. Traditional factor models do not fully explain this superior performance. The framework’s ability to time volatility reduces its market exposure during turbulent times. Ablation studies confirm the robustness of this performance across various reinforcement learning algorithms. Additionally, the embedding and meta-learning techniques effectively manage the complexities of high-dimensional, noisy, and non-stationary financial data, enhancing both portfolio performance and risk management. ...

High-dimensional covariance matrix estimators on simulated portfolios with complex structures ArXiv ID: 2412.08756 “View on arXiv” Authors: Unknown Abstract We study the allocation of synthetic portfolios under hierarchical nested, one-factor, and diagonal structures of the population covariance matrix in a high-dimensional scenario. The noise reduction approaches for the sample realizations are based on random matrices, free probability, deterministic equivalents, and their combination with a data science hierarchical method known as two-step covariance estimators. The financial performance metrics from the simulations are compared with empirical data from companies comprising the S&P 500 index using a moving window and walk-forward analysis. The portfolio allocation strategies analyzed include the minimum variance portfolio (both with and without short-selling constraints) and the hierarchical risk parity approach. Our proposed hierarchical nested covariance model shows signatures of complex system interactions. The empirical financial data reproduces stylized portfolio facts observed in the complex and one-factor covariance models. The two-step estimators proposed here improve several financial metrics under the analyzed investment strategies. The results pave the way for new risk management and diversification approaches when the number of assets is of the same order as the number of transaction days in the investment portfolio. ...

Robust Reinforcement Learning with Dynamic Distortion Risk Measures ArXiv ID: 2409.10096 “View on arXiv” Authors: Unknown Abstract In a reinforcement learning (RL) setting, the agent’s optimal strategy heavily depends on her risk preferences and the underlying model dynamics of the training environment. These two aspects influence the agent’s ability to make well-informed and time-consistent decisions when facing testing environments. In this work, we devise a framework to solve robust risk-aware RL problems where we simultaneously account for environmental uncertainty and risk with a class of dynamic robust distortion risk measures. Robustness is introduced by considering all models within a Wasserstein ball around a reference model. We estimate such dynamic robust risk measures using neural networks by making use of strictly consistent scoring functions, derive policy gradient formulae using the quantile representation of distortion risk measures, and construct an actor-critic algorithm to solve this class of robust risk-aware RL problems. We demonstrate the performance of our algorithm on a portfolio allocation example. ...

Optimal portfolio allocation with uncertain covariance matrix ArXiv ID: 2311.07478 “View on arXiv” Authors: Unknown Abstract In this paper, we explore the portfolio allocation problem involving an uncertain covariance matrix. We calculate the expected value of the Constant Absolute Risk Aversion (CARA) utility function, marginalized over a distribution of covariance matrices. We show that marginalization introduces a logarithmic dependence on risk, as opposed to the linear dependence assumed in the mean-variance approach. Additionally, it leads to a decrease in the allocation level for higher uncertainties. Our proposed method extends the mean-variance approach by considering the uncertainty associated with future covariance matrices and expected returns, which is important for practical applications. ...

Portfolio Optimization Rules beyond the Mean-Variance Approach ArXiv ID: 2305.08530 “View on arXiv” Authors: Unknown Abstract In this paper, we revisit the relationship between investors’ utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(μ,σ,κ)$ returns and compare them with the mean-variance approach, which is based on Gaussian returns. We reveal that in the limit of small $\fracμσ$, the Markowitz contribution is accompanied by a skewness term. We also obtain the allocation rules when the expected return is a random normal variable in an average and worst-case scenarios, which allows us to take into account uncertainty of the predicted returns. An optimal worst-case scenario solution smoothly approximates between equal weights and minimum variance portfolio, presenting an attractive convex alternative to the risk parity portfolio. We address the issue of handling singular covariance matrices by imposing conditional independence structure on the precision matrix directly. Finally, utilizing a microscopic portfolio model with random drift and analytical expression for the expected utility function with log-normal distributed cross-sectional returns, we demonstrate the influence of model parameters on portfolio construction. This comprehensive approach enhances allocation weight stability, mitigates instabilities associated with the mean-variance approach, and can prove valuable for both short-term traders and long-term investors. ...

Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach ArXiv ID: 2305.16152 “View on arXiv” Authors: Unknown Abstract This paper studies the multi-period mean-variance portfolio allocation problem with transaction costs. Many methods have been proposed these last years to challenge the famous uni-period Markowitz strategy.But these methods cannot integrate transaction costs or become computationally heavy and hardly applicable. In this paper, we try to tackle this allocation problem by proposing an innovative approach which relies on representing the set of admissible portfolios by a finite dimensional Wiener chaos expansion. This numerical method is able to find an optimal strategy for the allocation problem subject to transaction costs. To complete the study, the link between optimal portfolios submitted to transaction costs and the underlying risk aversion is investigated. Then a competitive and compliant benchmark based on the sequential uni-period Markowitz strategy is built to highlight the efficiency of our approach. ...