Portfolio Management

Worst-case values of target semi-variances with applications to robust portfolio selection ArXiv ID: 2410.01732 “View on arXiv” Authors: Unknown Abstract The expected regret and target semi-variance are two of the most important risk measures for downside risk. When the distribution of a loss is uncertain, and only partial information of the loss is known, their worst-case values play important roles in robust risk management for finance, insurance, and many other fields. Jagannathan (1977) derived the worst-case expected regrets when only the mean and variance of a loss are known and the loss is arbitrary, symmetric, or non-negative. While Chen et al. (2011) obtained the worst-case target semi-variances under similar conditions but focusing on arbitrary losses. In this paper, we first complement the study of Chen et al. (2011) on the worst-case target semi-variances and derive the closed-form expressions for the worst-case target semi-variance when only the mean and variance of a loss are known and the loss is symmetric or non-negative. Then, we investigate worst-case target semi-variances over uncertainty sets that represent undesirable scenarios faced by an investors. Our methods for deriving these worst-case values are different from those used in Jagannathan (1977) and Chen et al. (2011). As applications of the results derived in this paper, we propose robust portfolio selection methods that minimize the worst-case target semi-variance of a portfolio loss over different uncertainty sets. To explore the insights of our robust portfolio selection methods, we conduct numerical experiments with real financial data and compare our portfolio selection methods with several existing portfolio selection models related to the models proposed in this paper. ...

A Deep Reinforcement Learning Framework For Financial Portfolio Management ArXiv ID: 2409.08426 “View on arXiv” Authors: Unknown Abstract In this research paper, we investigate into a paper named “A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem” [“arXiv:1706.10059”]. It is a portfolio management problem which is solved by deep learning techniques. The original paper proposes a financial-model-free reinforcement learning framework, which consists of the Ensemble of Identical Independent Evaluators (EIIE) topology, a Portfolio-Vector Memory (PVM), an Online Stochastic Batch Learning (OSBL) scheme, and a fully exploiting and explicit reward function. Three different instants are used to realize this framework, namely a Convolutional Neural Network (CNN), a basic Recurrent Neural Network (RNN), and a Long Short-Term Memory (LSTM). The performance is then examined by comparing to a number of recently reviewed or published portfolio-selection strategies. We have successfully replicated their implementations and evaluations. Besides, we further apply this framework in the stock market, instead of the cryptocurrency market that the original paper uses. The experiment in the cryptocurrency market is consistent with the original paper, which achieve superior returns. But it doesn’t perform as well when applied in the stock market. ...

Optimizing Portfolio with Two-Sided Transactions and Lending: A Reinforcement Learning Framework ArXiv ID: 2408.05382 “View on arXiv” Authors: Unknown Abstract This study presents a Reinforcement Learning (RL)-based portfolio management model tailored for high-risk environments, addressing the limitations of traditional RL models and exploiting market opportunities through two-sided transactions and lending. Our approach integrates a new environmental formulation with a Profit and Loss (PnL)-based reward function, enhancing the RL agent’s ability in downside risk management and capital optimization. We implemented the model using the Soft Actor-Critic (SAC) agent with a Convolutional Neural Network with Multi-Head Attention (CNN-MHA). This setup effectively manages a diversified 12-crypto asset portfolio in the Binance perpetual futures market, leveraging USDT for both granting and receiving loans and rebalancing every 4 hours, utilizing market data from the preceding 48 hours. Tested over two 16-month periods of varying market volatility, the model significantly outperformed benchmarks, particularly in high-volatility scenarios, achieving higher return-to-risk ratios and demonstrating robust profitability. These results confirm the model’s effectiveness in leveraging market dynamics and managing risks in volatile environments like the cryptocurrency market. ...

On the optimal design of a new class of proportional portfolio insurance strategies in a jump-diffusion framework ArXiv ID: 2407.21148 “View on arXiv” Authors: Unknown Abstract In this paper, we investigate an optimal investment problem associated with proportional portfolio insurance (PPI) strategies in the presence of jumps in the underlying dynamics. PPI strategies enable investors to mitigate downside risk while still retaining the potential for upside gains. This is achieved by maintaining an exposure to risky assets proportional to the difference between the portfolio value and the present value of the guaranteed amount. While PPI strategies are known to be free of downside risk in diffusion modeling frameworks with continuous trading, see e.g., Cont and Tankov (2009), real market applications exhibit a significant non-negligible risk, known as gap risk, which increases with the multiplier value. The goal of this paper is to determine the optimal PPI strategy in a setting where gap risk may occur, due to downward jumps in the asset price dynamics. We consider a loss-averse agent who aims at maximizing the expected utility of the terminal wealth exceeding a minimum guarantee. Technically, we model agent’s preferences with an S-shaped utility functions to accommodate the possibility that gap risk occurs, and address the optimization problem via a generalization of the martingale approach that turns to be valid under market incompleteness in a jump-diffusion framework. ...

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. ...

Risk management in multi-objective portfolio optimization under uncertainty ArXiv ID: 2407.19936 “View on arXiv” Authors: Unknown Abstract In portfolio optimization, decision makers face difficulties from uncertainties inherent in real-world scenarios. These uncertainties significantly influence portfolio outcomes in both classical and multi-objective Markowitz models. To address these challenges, our research explores the power of robust multi-objective optimization. Since portfolio managers frequently measure their solutions against benchmarks, we enhance the multi-objective min-regret robustness concept by incorporating these benchmark comparisons. This approach bridges the gap between theoretical models and real-world investment scenarios, offering portfolio managers more reliable and adaptable strategies for navigating market uncertainties. Our framework provides a more nuanced and practical approach to portfolio optimization under real-world conditions. ...

Explainable Post hoc Portfolio Management Financial Policy of a Deep Reinforcement Learning agent ArXiv ID: 2407.14486 “View on arXiv” Authors: Unknown Abstract Financial portfolio management investment policies computed quantitatively by modern portfolio theory techniques like the Markowitz model rely on a set on assumptions that are not supported by data in high volatility markets. Hence, quantitative researchers are looking for alternative models to tackle this problem. Concretely, portfolio management is a problem that has been successfully addressed recently by Deep Reinforcement Learning (DRL) approaches. In particular, DRL algorithms train an agent by estimating the distribution of the expected reward of every action performed by an agent given any financial state in a simulator. However, these methods rely on Deep Neural Networks model to represent such a distribution, that although they are universal approximator models, they cannot explain its behaviour, given by a set of parameters that are not interpretable. Critically, financial investors policies require predictions to be interpretable, so DRL agents are not suited to follow a particular policy or explain their actions. In this work, we developed a novel Explainable Deep Reinforcement Learning (XDRL) approach for portfolio management, integrating the Proximal Policy Optimization (PPO) with the model agnostic explainable techniques of feature importance, SHAP and LIME to enhance transparency in prediction time. By executing our methodology, we can interpret in prediction time the actions of the agent to assess whether they follow the requisites of an investment policy or to assess the risk of following the agent suggestions. To the best of our knowledge, our proposed approach is the first explainable post hoc portfolio management financial policy of a DRL agent. We empirically illustrate our methodology by successfully identifying key features influencing investment decisions, which demonstrate the ability to explain the agent actions in prediction time. ...

Benchmarking M6 Competitors: An Analysis of Financial Metrics and Discussion of Incentives ArXiv ID: 2406.19105 “View on arXiv” Authors: Unknown Abstract The M6 Competition assessed the performance of competitors using a ranked probability score and an information ratio (IR). While these metrics do well at picking the winners in the competition, crucial questions remain for investors with longer-term incentives. To address these questions, we compare the competitors’ performance to a number of conventional (long-only) and alternative indices using standard industry metrics. We apply factor models to measure the competitors’ value-adds above industry-standard benchmarks and find that competitors with more extreme performance are less dependent on the benchmarks. We also uncover that most competitors could not generate significant out-performance compared to randomly selected long-only and long-short portfolios but did generate out-performance compared to short-only portfolios. We further introduce two new strategies by picking the competitors with the best (Superstars) and worst (Superlosers) recent performance and show that it is challenging to identify skill amongst investment managers. We also discuss the incentives of winning the competition compared to professional investors, where investors wish to maximize fees over an extended period of time. ...

The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments ArXiv ID: 2407.09536 “View on arXiv” Authors: Unknown Abstract We engineer blockchain based risk managed portfolios by creating three funds with distinct risk and return profiles: 1) Alpha - high risk portfolio; 2) Beta - mimics the wider market; and 3) Gamma - represents the risk free rate adjusted to beat inflation. Each of the sub-funds (Alpha, Beta and Gamma) provides risk parity because the weight of each asset in the corresponding portfolio is set to be inversely proportional to the risk derived from investing in that asset. This can be equivalently stated as equal risk contributions from each asset towards the overall portfolio risk. We provide detailed mechanics of combining assets - including mathematical formulations - to obtain better risk managed portfolios. The descriptions are intended to show how a risk parity based efficient frontier portfolio management engine - that caters to different risk appetites of investors by letting each individual investor select their preferred risk-return combination - can be created seamlessly on blockchain. Any Investor - using decentralized ledger technology - can select their desired level of risk, or return, and allocate their wealth accordingly among the sub funds, which balance one another under different market conditions. This evolution of the risk parity principle - resulting in a mechanism that is geared to do well under all market cycles - brings more robust performance and can be termed as conceptual parity. We have given several numerical examples that illustrate the various scenarios that arise when combining Alpha, Beta and Gamma to obtain Parity. The final investment frontier is now possible - a modification to the efficient frontier, thus becoming more than a mere theoretical construct - on blockchain since anyone from anywhere can participate at anytime to obtain wealth appreciation based on their financial goals. ...

Mean-Variance Portfolio Selection in Long-Term Investments with Unknown Distribution: Online Estimation, Risk Aversion under Ambiguity, and Universality of Algorithms ArXiv ID: 2406.13486 “View on arXiv” Authors: Unknown Abstract The standard approach for constructing a Mean-Variance portfolio involves estimating parameters for the model using collected samples. However, since the distribution of future data may not resemble that of the training set, the out-of-sample performance of the estimated portfolio is worse than one derived with true parameters, which has prompted several innovations for better estimation. Instead of treating the data without a timing aspect as in the common training-backtest approach, this paper adopts a perspective where data gradually and continuously reveal over time. The original model is recast into an online learning framework, which is free from any statistical assumptions, to propose a dynamic strategy of sequential portfolios such that its empirical utility, Sharpe ratio, and growth rate asymptotically achieve those of the true portfolio, derived with perfect knowledge of the future data. When the distribution of future data follows a normal shape, the growth rate of wealth is shown to increase by lifting the portfolio along the efficient frontier through the calibration of risk aversion. Since risk aversion cannot be appropriately predetermined, another proposed algorithm updates this coefficient over time, forming a dynamic strategy that approaches the optimal empirical Sharpe ratio or growth rate associated with the true coefficient. The performance of these proposed strategies can be universally guaranteed under stationary stochastic markets. Furthermore, in certain time-reversible stochastic markets, the so-called Bayesian strategy utilizing true conditional distributions, based on past market information during investment, does not perform better than the proposed strategies in terms of empirical utility, Sharpe ratio, or growth rate, which, in contrast, do not rely on conditional distributions. ...