Portfolio Optimization

Causal Portfolio Optimization: Principles and Sensitivity-Based Solutions ArXiv ID: 2504.05743 “View on arXiv” Authors: Unknown Abstract Fundamental and necessary principles for achieving efficient portfolio optimization based on asset and diversification dynamics are presented. The Commonality Principle is a necessary and sufficient condition for identifying optimal drivers of a portfolio in terms of its diversification dynamics. The proof relies on the Reichenbach Common Cause Principle, along with the fact that the sensitivities of portfolio constituents with respect to the common causal drivers are themselves causal. A conformal map preserves idiosyncratic diversification from the unconditional setting while optimizing systematic diversification on an embedded space of these sensitivities. Causal methodologies for combinatorial driver selection are presented, such as the use of Bayesian networks and correlation-based algorithms from Reichenbach’s principle. Limitations of linear models in capturing causality are discussed, and included for completeness alongside more advanced models such as neural networks. Portfolio optimization methods are presented that map risk from the sensitivity space to other risk measures of interest. Finally, the work introduces a novel risk management framework based on Common Causal Manifolds, including both theoretical development and experimental validation. The sensitivity space is predicted along the common causal manifold, which is modeled as a causal time system. Sensitivities are forecasted using SDEs calibrated to data previously extracted from neural networks to move along the manifold via its tangent bundles. An optimization method is then proposed that accumulates information across future predicted tangent bundles on the common causal time system manifold. It aggregates sensitivity-based distance metrics along the trajectory to build a comprehensive sensitivity distance matrix. This matrix enables trajectory-wide optimal diversification, taking into account future dynamics. ...

Relative portfolio optimization via a value at risk based constraint ArXiv ID: 2503.20340 “View on arXiv” Authors: Unknown Abstract In this paper, we consider $n$ agents who invest in a general financial market that is free of arbitrage and complete. The aim of each investor is to maximize her expected utility while ensuring, with a specified probability, that her terminal wealth exceeds a benchmark defined by her competitors’ performance. This setup introduces an interdependence between agents, leading to a search for Nash equilibria. In the case of two agents and CRRA utility, we are able to derive all Nash equilibria in terms of terminal wealth. For $n>2$ agents and logarithmic utility we distinguish two cases. In the first case, the probabilities in the constraint are small and we can characterize all Nash equilibria. In the second case, the probabilities are larger and we look for Nash equilibria in a certain set. We also discuss the impact of the competition using some numerical examples. As a by-product, we solve some portfolio optimization problems with probability constraints. ...

Practical Portfolio Optimization with Metaheuristics:Pre-assignment Constraint and Margin Trading ArXiv ID: 2503.15965 “View on arXiv” Authors: Unknown Abstract Portfolio optimization is a critical area in finance, aiming to maximize returns while minimizing risk. Metaheuristic algorithms were shown to solve complex optimization problems efficiently, with Genetic Algorithms and Particle Swarm Optimization being among the most popular methods. This paper introduces an innovative approach to portfolio optimization that incorporates pre-assignment to limit the search space for investor preferences and better results. Additionally, taking margin trading strategies in account and using a rare performance ratio to evaluate portfolio efficiency. Through an illustrative example, this paper demonstrates that the metaheuristic-based methodology yields superior risk-adjusted returns compared to traditional benchmarks. The results highlight the potential of metaheuristics with help of assets filtering in enhancing portfolio performance in terms of risk adjusted return. ...

Statistical applications of the 20/60/20 rule in risk management and portfolio optimization ArXiv ID: 2504.02840 “View on arXiv” Authors: Unknown Abstract This paper explores the applications of the 20/60/20 rule-a heuristic method that segments data into top-performing, average-performing, and underperforming groups-in mathematical finance. We review the statistical foundations of this rule and demonstrate its usefulness in risk management and portfolio optimization. Our study highlights three key applications. First, we apply the rule to stock market data, showing that it enables effective population clustering. Second, we introduce a novel, easy-to-implement method for extracting heavy-tail characteristics in risk management. Third, we integrate spatial reasoning based on the 20/60/20 rule into portfolio optimization, enhancing robustness and improving performance. To support our findings, we develop a new measure for quantifying tail heaviness and employ conditional statistics to reconstruct the unconditional distribution from the core data segment. This reconstructed distribution is tested on real financial data to evaluate whether the 20/60/20 segmentation effectively balances capturing extreme risks with maintaining the stability of central returns. Our results offer insights into financial data behavior under heavy-tailed conditions and demonstrate the potential of the 20/60/20 rule as a complementary tool for decision-making in finance. ...

Decision by Supervised Learning with Deep Ensembles: A Practical Framework for Robust Portfolio Optimization ArXiv ID: 2503.13544 “View on arXiv” Authors: Unknown Abstract We propose Decision by Supervised Learning (DSL), a practical framework for robust portfolio optimization. DSL reframes portfolio construction as a supervised learning problem: models are trained to predict optimal portfolio weights, using cross-entropy loss and portfolios constructed by maximizing the Sharpe or Sortino ratio. To further enhance stability and reliability, DSL employs Deep Ensemble methods, substantially reducing variance in portfolio allocations. Through comprehensive backtesting across diverse market universes and neural architectures, shows superior performance compared to both traditional strategies and leading machine learning-based methods, including Prediction-Focused Learning and End-to-End Learning. We show that increasing the ensemble size leads to higher median returns and more stable risk-adjusted performance. The code is available at https://github.com/DSLwDE/DSLwDE. ...

Risk-aware Trading Portfolio Optimization ArXiv ID: 2503.04662 “View on arXiv” Authors: Unknown Abstract We investigate portfolio optimization in financial markets from a trading and risk management perspective. We term this task Risk-Aware Trading Portfolio Optimization (RATPO), formulate the corresponding optimization problem, and propose an efficient Risk-Aware Trading Swarm (RATS) algorithm to solve it. The key elements of RATPO are a generic initial portfolio P, a specific set of Unique Eligible Instruments (UEIs), their combination into an Eligible Optimization Strategy (EOS), an objective function, and a set of constraints. RATS searches for an optimal EOS that, added to P, improves the objective function repecting the constraints. RATS is a specialized Particle Swarm Optimization method that leverages the parameterization of P in terms of UEIs, enables parallel computation with a large number of particles, and is fully general with respect to specific choices of the key elements, which can be customized to encode financial knowledge and needs of traders and risk managers. We showcase two RATPO applications involving a real trading portfolio made of hundreds of different financial instruments, an objective function combining both market risk (VaR) and profit&loss measures, constrains on market sensitivities and UEIs trading costs. In the case of small-sized EOS, RATS successfully identifies the optimal solution and demonstrates robustness with respect to hyper-parameters tuning. In the case of large-sized EOS, RATS markedly improves the portfolio objective value, optimizing risk and capital charge while respecting risk limits and preserving expected profits. Our work bridges the gap between the implementation of effective trading strategies and compliance with stringent regulatory and economic capital requirements, allowing a better alignment of business and risk management objectives. ...

Systemic Risk Management via Maximum Independent Set in Extremal Dependence Networks ArXiv ID: 2503.15534 “View on arXiv” Authors: Unknown Abstract The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of their performance, apply extreme value theory to assess the extremal dependence among stocks of financial institutions, and construct a network model based on a threshold approach that captures extremal dependence. Our analysis reveals different dependence structures in the Chinese and U.S. financial systems. By applying the maximum independent set (MIS) from graph theory, we identify a subset of institutions with minimal extremal dependence, facilitating the construction of diversified portfolios resilient to risk contagion. We also compare the performance of our proposed portfolios with that of the market portfolios in the two economies. ...

Liquidity-adjusted Return and Volatility, and Autoregressive Models ArXiv ID: 2503.08693 “View on arXiv” Authors: Unknown Abstract We construct liquidity-adjusted return and volatility using purposely designed liquidity metrics (liquidity jump and liquidity diffusion) that incorporate additional liquidity information. Based on these measures, we introduce a liquidity-adjusted ARMA-GARCH framework to address the limitations of traditional ARMA-GARCH models, which are not effectively in modeling illiquid assets with high liquidity variability, such as cryptocurrencies. We demonstrate that the liquidity-adjusted model improves model fit for cryptocurrencies, with greater volatility sensitivity to past shocks and reduced volatility persistence of erratic past volatility. Our model is validated by the empirical evidence that the liquidity-adjusted mean-variance (LAMV) portfolios outperform the traditional mean-variance (TMV) portfolios. ...

Framework for asset-liability management with fixed-term securities ArXiv ID: 2502.19213 “View on arXiv” Authors: Unknown Abstract We consider an optimal investment-consumption problem for a utility-maximizing investor who has access to assets with different liquidity and whose consumption rate as well as terminal wealth are subject to lower-bound constraints. Assuming utility functions that satisfy standard conditions, we develop a methodology for deriving the optimal strategies in semi-closed form. Our methodology is based on the generalized martingale approach and the decomposition of the problem into subproblems. We illustrate our approach by deriving explicit formulas for agents with power-utility functions and discuss potential extensions of the proposed framework. In numerical studies, we substantiate how the parameters of our framework impact the optimal proportion of initial capital allocated to the illiquid asset, the monetary value that the investor subjectively assigns to the fixed-term asset, and the potential of the illiquid asset to increase terminal the terminal value of liabilities without loss in the investor’s expected utility. ...

Regret-Optimized Portfolio Enhancement through Deep Reinforcement Learning and Future Looking Rewards ArXiv ID: 2502.02619 “View on arXiv” Authors: Unknown Abstract This paper introduces a novel agent-based approach for enhancing existing portfolio strategies using Proximal Policy Optimization (PPO). Rather than focusing solely on traditional portfolio construction, our approach aims to improve an already high-performing strategy through dynamic rebalancing driven by PPO and Oracle agents. Our target is to enhance the traditional 60/40 benchmark (60% stocks, 40% bonds) by employing the Regret-based Sharpe reward function. To address the impact of transaction fee frictions and prevent signal loss, we develop a transaction cost scheduler. We introduce a future-looking reward function and employ synthetic data training through a circular block bootstrap method to facilitate the learning of generalizable allocation strategies. We focus on two key evaluation measures: return and maximum drawdown. Given the high stochasticity of financial markets, we train 20 independent agents each period and evaluate their average performance against the benchmark. Our method not only enhances the performance of the existing portfolio strategy through strategic rebalancing but also demonstrates strong results compared to other baselines. ...