Portfolio Management

Dynamic portfolio selection for nonlinear law-dependent preferences ArXiv ID: 2311.06745 “View on arXiv” Authors: Unknown Abstract This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of stochastic maximum principle, we establish verification theorems for equilibrium strategies, accommodating both random market coefficients and incomplete markets. We derive the first-order condition (FOC) for the equilibrium strategies, using a notion of functional derivatives with respect to probability distributions. Then, with the help of the FOC we obtain the equilibrium strategies in closed form for two classes of implicitly defined preferences: CRRA and CARA betweenness preferences, with deterministic market coefficients. Finally, to show applications of our theoretical results to problems with random market coefficients, we examine the weighted utility. We reveal that the equilibrium strategy can be described by a coupled system of Quadratic Backward Stochastic Differential Equations (QBSDEs). The well-posedness of this system is generally open but is established under the special structures of our problem. ...

A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models ArXiv ID: 2309.05977 “View on arXiv” Authors: Unknown Abstract We develop a efficient, easy-to-implement, and strictly monotone numerical integration method for Mean-Variance (MV) portfolio optimization in realistic contexts, which involve jump-diffusion dynamics of the underlying controlled processes, discrete rebalancing, and the application of investment constraints, namely no-bankruptcy and leverage. A crucial element of the MV portfolio optimization formulation over each rebalancing interval is a convolution integral, which involves a conditional density of the logarithm of the amount invested in the risky asset. Using a known closed-form expression for the Fourier transform of this density, we derive an infinite series representation for the conditional density where each term is strictly positive and explicitly computable. As a result, the convolution integral can be readily approximated through a monotone integration scheme, such as a composite quadrature rule typically available in most programming languages. The computational complexity of our method is an order of magnitude lower than that of existing monotone finite difference methods. To further enhance efficiency, we propose an implementation of the scheme via Fast Fourier Transforms, exploiting the Toeplitz matrix structure. The proposed monotone scheme is proven to be both $\ell_{"\infty"}$-stable and pointwise consistent, and we rigorously establish its pointwise convergence to the unique solution of the MV portfolio optimization problem. We also intuitively demonstrate that, as the rebalancing time interval approaches zero, the proposed scheme converges to a continuously observed impulse control formulation for MV optimization expressed as a Hamilton-Jacobi-Bellman Quasi-Variational Inequality. Numerical results show remarkable agreement with benchmark solutions obtained through finite differences and Monte Carlo simulation, underscoring the effectiveness of our approach. ...

Generating drawdown-realistic financial price paths using path signatures ArXiv ID: 2309.04507 “View on arXiv” Authors: Unknown Abstract A novel generative machine learning approach for the simulation of sequences of financial price data with drawdowns quantifiably close to empirical data is introduced. Applications such as pricing drawdown insurance options or developing portfolio drawdown control strategies call for a host of drawdown-realistic paths. Historical scenarios may be insufficient to effectively train and backtest the strategy, while standard parametric Monte Carlo does not adequately preserve drawdowns. We advocate a non-parametric Monte Carlo approach combining a variational autoencoder generative model with a drawdown reconstruction loss function. To overcome issues of numerical complexity and non-differentiability, we approximate drawdown as a linear function of the moments of the path, known in the literature as path signatures. We prove the required regularity of drawdown function and consistency of the approximation. Furthermore, we obtain close numerical approximations using linear regression for fractional Brownian and empirical data. We argue that linear combinations of the moments of a path yield a mathematically non-trivial smoothing of the drawdown function, which gives one leeway to simulate drawdown-realistic price paths by including drawdown evaluation metrics in the learning objective. We conclude with numerical experiments on mixed equity, bond, real estate and commodity portfolios and obtain a host of drawdown-realistic paths. ...

Black-Litterman, Bayesian Shrinkage, and Factor Models in Portfolio Selection: You Can Have It All ArXiv ID: 2308.09264 “View on arXiv” Authors: Unknown Abstract Mean-variance analysis is widely used in portfolio management to identify the best portfolio that makes an optimal trade-off between expected return and volatility. Yet, this method has its limitations, notably its vulnerability to estimation errors and its reliance on historical data. While shrinkage estimators and factor models have been introduced to improve estimation accuracy through bias-variance trade-offs, and the Black-Litterman model has been developed to integrate investor opinions, a unified framework combining three approaches has been lacking. Our study debuts a Bayesian blueprint that fuses shrinkage estimation with view inclusion, conceptualizing both as Bayesian updates. This model is then applied within the context of the Fama-French approach factor models, thereby integrating the advantages of each methodology. Finally, through a comprehensive empirical study in the US equity market spanning a decade, we show that the model outperforms both the simple $1/N$ portfolio and the optimal portfolios based on sample estimators. ...

Portfolio Selection via Topological Data Analysis ArXiv ID: 2308.07944 “View on arXiv” Authors: Unknown Abstract Portfolio management is an essential part of investment decision-making. However, traditional methods often fail to deliver reasonable performance. This problem stems from the inability of these methods to account for the unique characteristics of multivariate time series data from stock markets. We present a two-stage method for constructing an investment portfolio of common stocks. The method involves the generation of time series representations followed by their subsequent clustering. Our approach utilizes features based on Topological Data Analysis (TDA) for the generation of representations, allowing us to elucidate the topological structure within the data. Experimental results show that our proposed system outperforms other methods. This superior performance is consistent over different time frames, suggesting the viability of TDA as a powerful tool for portfolio selection. ...

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via $\ell_0$-Constrained Portfolio ArXiv ID: 2309.10152 “View on arXiv” Authors: Unknown Abstract Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and avoiding illiquid assets. To achieve portfolio sparsity, conventional studies have utilized $\ell_p$-norm regularizations as a continuous surrogate of the $\ell_0$-norm regularization. Although these formulations can construct sparse portfolios, their practical application is challenging due to the intricate and time-consuming process of tuning parameters to define the precise upper limit of assets in the portfolio. In this paper, we propose a new problem formulation of sparse index tracking using an $\ell_0$-norm constraint that enables easy control of the upper bound on the number of assets in the portfolio. Moreover, our approach offers a choice between constraints on portfolio and turnover sparsity, further reducing transaction costs by limiting asset updates at each rebalancing interval. Furthermore, we develop an efficient algorithm for solving this problem based on a primal-dual splitting method. Finally, we illustrate the effectiveness of the proposed method through experiments on the S&P500 and Russell3000 index datasets. ...

Combining Reinforcement Learning and Barrier Functions for Adaptive Risk Management in Portfolio Optimization ArXiv ID: 2306.07013 “View on arXiv” Authors: Unknown Abstract Reinforcement learning (RL) based investment strategies have been widely adopted in portfolio management (PM) in recent years. Nevertheless, most RL-based approaches may often emphasize on pursuing returns while ignoring the risks of the underlying trading strategies that may potentially lead to great losses especially under high market volatility. Therefore, a risk-manageable PM investment framework integrating both RL and barrier functions (BF) is proposed to carefully balance the needs for high returns and acceptable risk exposure in PM applications. Up to our understanding, this work represents the first attempt to combine BF and RL for financial applications. While the involved RL approach may aggressively search for more profitable trading strategies, the BF-based risk controller will continuously monitor the market states to dynamically adjust the investment portfolio as a controllable measure for avoiding potential losses particularly in downtrend markets. Additionally, two adaptive mechanisms are provided to dynamically adjust the impact of risk controllers such that the proposed framework can be flexibly adapted to uptrend and downtrend markets. The empirical results of our proposed framework clearly reveal such advantages against most well-known RL-based approaches on real-world data sets. More importantly, our proposed framework shed lights on many possible directions for future investigation. ...

Predictably Bad Investments: Evidence from Venture Capitalists ArXiv ID: ssrn-4135861 “View on arXiv” Authors: Unknown Abstract Do institutional investors invest efficiently? To study this question I combine a novel dataset of over 16,000 startups (representing over $9 billion in investm Keywords: Venture Capital, Institutional Investors, Startup Investment, Portfolio Management, Efficiency, Private Equity / Venture Capital Complexity vs Empirical Score Math Complexity: 3.0/10 Empirical Rigor: 7.0/10 Quadrant: Street Traders Why: The paper uses standard machine learning methods rather than advancing novel mathematics, but it employs a large, novel dataset and rigorous empirical analysis (counterfactual portfolio construction, robustness checks, and measurement of economic magnitude) to backtest investment strategies. flowchart TD RQ["Research Question: Do institutional investors invest efficiently?"] --> I["Inputs: 16,000+ startups & $9B+ investments"] I --> M["Methodology: Performance vs. Investment Timing analysis"] M --> CP["Computation: Out-of-sample return predictions"] CP --> F1["Predictably Bad Investments: Poor timing leads to predictable low returns"] F1 --> F2["Outcomes: Evidence of inefficiency & suboptimal portfolio management"]

Does Sustainability Generate Better Financial Performance? Review, Meta-analysis, and Propositions ArXiv ID: ssrn-3708495 “View on arXiv” Authors: Unknown Abstract Sustainability in business and ESG (environmental, social, and governance) in finance have exploded in popularity among researchers and practitioners. We survey Keywords: ESG (Environmental, Social, and Governance), Sustainable Finance, Asset Pricing, Portfolio Management, Literature Review, Multi-Asset Complexity vs Empirical Score Math Complexity: 3.5/10 Empirical Rigor: 8.0/10 Quadrant: Street Traders Why: The paper relies on large-scale meta-analysis of existing studies rather than novel mathematical modeling, yet demonstrates high empirical rigor through systematic review of 1,141 papers and providing public replication data and methodology. flowchart TD A["Research Goal:<br>Does Sustainability Improve Financial Performance?"] B["Methodology:<br>Systematic Review & Meta-Analysis"] C["Data Inputs:<br>Existing Studies on ESG & Returns"] D["Computational Process:<br>Aggregation & Bias Correction"] E["Outcome 1: Positive<br>ESG-Return Relationship"] F["Outcome 2: Risk-Based<br>Explanations Dominate"] G["Proposition:<br>ESG as Risk Factor in Asset Pricing"] A --> B B --> C C --> D D --> E D --> F E & F --> G

AlphaPortfolio: Direct Construction Through Deep Reinforcement Learning and Interpretable AI ArXiv ID: ssrn-3554486 “View on arXiv” Authors: Unknown Abstract We directly optimize the objectives of portfolio management via deep reinforcement learning—an alternative to conventional supervised-learning paradigms that Keywords: Deep Reinforcement Learning, Portfolio Optimization, Artificial Intelligence, Asset Allocation, Portfolio Management Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 9.0/10 Quadrant: Holy Grail Why: The paper employs advanced deep reinforcement learning (RL) with attention-based neural networks (Transformers/LSTMs) and polynomial sensitivity analysis, which involves high mathematical complexity; it also provides out-of-sample performance metrics (Sharpe ratios, alphas) and robustness checks across market conditions, indicating strong empirical backing for implementation. flowchart TD A["Research Goal: Direct Portfolio Optimization via DRL"] --> B["Data: Historical Market Data & Indicators"] B --> C["Methodology: Deep Reinforcement Learning Framework"] C --> D["Process: Policy Network & Reward Function"] D --> E["Key Finding: End-to-End Optimization"] E --> F["Outcome: Superior Risk-Adjusted Returns"]