Portfolio Optimization

Double Descent in Portfolio Optimization: Dance between Theoretical Sharpe Ratio and Estimation Accuracy ArXiv ID: 2411.18830 “View on arXiv” Authors: Unknown Abstract We study the relationship between model complexity and out-of-sample performance in the context of mean-variance portfolio optimization. Representing model complexity by the number of assets, we find that the performance of low-dimensional models initially improves with complexity but then declines due to overfitting. As model complexity becomes sufficiently high, the performance improves with complexity again, resulting in a double ascent Sharpe ratio curve similar to the double descent phenomenon observed in artificial intelligence. The underlying mechanisms involve an intricate interaction between the theoretical Sharpe ratio and estimation accuracy. In high-dimensional models, the theoretical Sharpe ratio approaches its upper limit, and the overfitting problem is reduced because there are more parameters than data restrictions, which allows us to choose well-behaved parameters based on inductive bias. ...

Predictive Power of LLMs in Financial Markets ArXiv ID: 2411.16569 “View on arXiv” Authors: Unknown Abstract Predicting the movement of the stock market and other assets has been valuable over the past few decades. Knowing how the value of a certain sector market may move in the future provides much information for investors, as they use that information to develop strategies to maximize profit or minimize risk. However, market data are quite noisy, and it is challenging to choose the right data or the right model to create such predictions. With the rise of large language models, there are ways to analyze certain data much more efficiently than before. Our goal is to determine whether the GPT model provides more useful information compared to other traditional transformer models, such as the BERT model. We shall use data from the Federal Reserve Beige Book, which provides summaries of economic conditions in different districts in the US. Using such data, we then employ the LLM’s to make predictions on the correlations. Using these correlations, we then compare the results with well-known strategies and determine whether knowing the economic conditions improves investment decisions. We conclude that the Beige Book does contain information regarding correlations amongst different assets, yet the GPT model has too much look-ahead bias and that traditional models still triumph. ...

Research on Optimal Portfolio Based on Multifractal Features ArXiv ID: 2411.15712 “View on arXiv” Authors: Unknown Abstract Providing optimal portfolio selection for investors has always been one of the hot topics in academia. In view of the traditional portfolio model could not adapt to the actual capital market and can provide erroneous results. This paper innovatively constructs a mean-detrended cross-correlation portfolio model (M-DCCP model), This model is designed to embed detrended cross-correlation between different simultaneously recorded time series in the presence of nonstationary into the reward-risk criterion. We illustrate the model’s effectiveness by selected five composite indexes (SSE 50, CSI 300, SSE 500, CSI 1000 and CSI 2000) in China A-share market. The empirical results show that compared with traditional mean-variance portfolio model (M-VP model), the M-DCCP model is more conducive for investors to construct optimal portfolios under the different fluctuation exponent preference and time scales preference, so as to improve portfolio’s performance. ...

M6 Investment Challenge: The Role of Luck and Strategic Considerations ArXiv ID: 2412.04490 “View on arXiv” Authors: Unknown Abstract This article investigates the influence of luck and strategic considerations on performance of teams participating in the M6 investment challenge. We find that there is insufficient evidence to suggest that the extreme Sharpe ratios observed are beyond what one would expect by chance, given the number of teams, and thus not necessarily indicative of the possibility of consistently attaining abnormal returns. Furthermore, we introduce a stylized model of the competition to derive and analyze a portfolio strategy optimized for attaining the top rank. The results demonstrate that the task of achieving the top rank is not necessarily identical to that of attaining the best investment returns in expectation. It is possible to improve one’s chances of winning, even without the ability to attain abnormal returns, by choosing portfolio weights adversarially based on the current competition ranking. Empirical analysis of submitted portfolio weights aligns with this finding. ...

Mirror Descent Algorithms for Risk Budgeting Portfolios ArXiv ID: 2411.12323 “View on arXiv” Authors: Unknown Abstract This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and sub-additive risk measures. We employ Mirror Descent algorithms to determine the optimal risk budgeting weights in both deterministic and stochastic settings, establishing convergence along with an explicit non-asymptotic quantitative rate for the averaged algorithm. A comprehensive numerical analysis follows, illustrating our theoretical findings across various risk measures – including standard deviation, Expected Shortfall, deviation measures, and Variantiles – and comparing the performance with that of the standard stochastic gradient descent method recently proposed in the literature. ...

Financial News-Driven LLM Reinforcement Learning for Portfolio Management ArXiv ID: 2411.11059 “View on arXiv” Authors: Unknown Abstract Reinforcement learning (RL) has emerged as a transformative approach for financial trading, enabling dynamic strategy optimization in complex markets. This study explores the integration of sentiment analysis, derived from large language models (LLMs), into RL frameworks to enhance trading performance. Experiments were conducted on single-stock trading with Apple Inc. (AAPL) and portfolio trading with the ING Corporate Leaders Trust Series B (LEXCX). The sentiment-enhanced RL models demonstrated superior net worth and cumulative profit compared to RL models without sentiment and, in the portfolio experiment, outperformed the actual LEXCX portfolio’s buy-and-hold strategy. These results highlight the potential of incorporating qualitative market signals to improve decision-making, bridging the gap between quantitative and qualitative approaches in financial trading. ...

Optimal portfolio under ratio-type periodic evaluation in stochastic factor models under convex trading constraints ArXiv ID: 2411.13579 “View on arXiv” Authors: Unknown Abstract This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon, featuring the dynamic adjustments in portfolio decision according to past achievements. Under power utility, we transform the original infinite horizon optimal control problem into an auxiliary terminal wealth optimization problem under a modified utility function. To cope with the convex trading constraints, we further introduce an auxiliary unconstrained optimization problem in a modified market model and develop the martingale duality approach to establish the existence of the dual minimizer such that the optimal unconstrained wealth process can be obtained using the dual representation. With the help of the duality results in the auxiliary problems, the relationship between the constrained and unconstrained models as well as some fixed point arguments, we finally derive and verify the optimal constrained portfolio process in a periodic manner for the original problem over an infinite horizon. ...

Portfolio Optimization with Feedback Strategies Based on Artificial Neural Networks ArXiv ID: 2411.09899 “View on arXiv” Authors: Unknown Abstract With the recent advancements in machine learning (ML), artificial neural networks (ANN) are starting to play an increasingly important role in quantitative finance. Dynamic portfolio optimization is among many problems that have significantly benefited from a wider adoption of deep learning (DL). While most existing research has primarily focused on how DL can alleviate the curse of dimensionality when solving the Hamilton-Jacobi-Bellman (HJB) equation, some very recent developments propose to forego derivation and solution of HJB in favor of empirical utility maximization over dynamic allocation strategies expressed through ANN. In addition to being simple and transparent, this approach is universally applicable, as it is essentially agnostic about market dynamics. To showcase the method, we apply it to optimal portfolio allocation between a cash account and the S&P 500 index modeled using geometric Brownian motion or the Heston model. In both cases, the results are demonstrated to be on par with those under the theoretical optimal weights assuming isoelastic utility and real-time rebalancing. A set of R codes for a broad class of stochastic volatility models are provided as a supplement. ...

Isotropic Correlation Models for the Cross-Section of Equity Returns ArXiv ID: 2411.08864 “View on arXiv” Authors: Unknown Abstract This note discusses some of the aspects of a model for the covariance of equity returns based on a simple “isotropic” structure in which all pairwise correlations are taken to be the same value. The effect of the structure on feasible values for the common correlation of returns and on the “effective degrees of freedom” within the equity cross-section are discussed, as well as the impact of this constraint on the asymptotic Normality of portfolio returns. An eigendecomposition of the covariance matrix is presented and used to partition variance into that from a common “market” factor and “non-diversifiable” idiosyncratic risk. A empirical analysis of the recent history of the returns of S&P 500 Index members is presented and compared to the expectations from both this model and linear factor models. This analysis supports the isotropic covariance model and does not seem to provide evidence in support of linear factor models. Analysis of portfolio selection under isotropic correlation is presented using mean-variance optimization for both heteroskedastic and homoskedastic cases. Portfolio selection for negative exponential utility maximizers is also discussed for the general case of distributions of returns with elliptical symmetry. The fact that idiosyncratic risk may not be removed by diversification in a model that the data supports undermines the basic premises of structures such as the C.A.P.M. and A.P.T. If the cross-section of equity returns is more accurately described by this structure then an inevitable consequence is that picking stocks is not a “pointless” activity, as the returns to residual risk would be non-zero. ...

Optimal two-parameter portfolio management strategy with transaction costs ArXiv ID: 2411.07949 “View on arXiv” Authors: Unknown Abstract We consider a simplified model for optimizing a single-asset portfolio in the presence of transaction costs given a signal with a certain autocorrelation and cross-correlation structure. In our setup, the portfolio manager is given two one-parameter controls to influence the construction of the portfolio. The first is a linear filtering parameter that may increase or decrease the level of autocorrelation in the signal. The second is a numerical threshold that determines a symmetric “no-trade” zone. Portfolio positions are constrained to a single unit long or a single unit short. These constraints allow us to focus on the interplay between the signal filtering mechanism and the hysteresis introduced by the “no-trade” zone. We then formulate an optimization problem where we aim to minimize the frequency of trades subject to a fixed return level of the portfolio. We show that maintaining a no-trade zone while removing autocorrelation entirely from the signal yields a locally optimal solution. For any given “no-trade” zone threshold, this locally optimal solution also achieves the maximum attainable return level, and we derive a quantitative lower bound for the amount of improvement in terms of the given threshold and the amount of autocorrelation removed. ...