Sharpe Ratio

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. ...

Supervised Autoencoders with Fractionally Differentiated Features and Triple Barrier Labelling Enhance Predictions on Noisy Data ArXiv ID: 2411.12753 “View on arXiv” Authors: Unknown Abstract This paper investigates the enhancement of financial time series forecasting with the use of neural networks through supervised autoencoders (SAE), to improve investment strategy performance. Using the Sharpe and Information Ratios, it specifically examines the impact of noise augmentation and triple barrier labeling on risk-adjusted returns. The study focuses on Bitcoin, Litecoin, and Ethereum as the traded assets from January 1, 2016, to April 30, 2022. Findings indicate that supervised autoencoders, with balanced noise augmentation and bottleneck size, significantly boost strategy effectiveness. However, excessive noise and large bottleneck sizes can impair performance. ...

Large-scale Time-Varying Portfolio Optimisation using Graph Attention Networks ArXiv ID: 2407.15532 “View on arXiv” Authors: Unknown Abstract Apart from assessing individual asset performance, investors in financial markets also need to consider how a set of firms performs collectively as a portfolio. Whereas traditional Markowitz-based mean-variance portfolios are widespread, network-based optimisation techniques offer a more flexible tool to capture complex interdependencies between asset values. However, most of the existing studies do not contain firms at risk of default and remove any firms that drop off indices over a certain time. This is the first study to also incorporate such firms in portfolio optimisation on a large scale. We propose and empirically test a novel method that leverages Graph Attention networks (GATs), a subclass of Graph Neural Networks (GNNs). GNNs, as deep learning-based models, can exploit network data to uncover nonlinear relationships. Their ability to handle high-dimensional data and accommodate customised layers for specific purposes makes them appealing for large-scale problems such as mid- and small-cap portfolio optimisation. This study utilises 30 years of data on mid-cap firms, creating graphs of firms using distance correlation and the Triangulated Maximally Filtered Graph approach. These graphs are the inputs to a GAT model incorporating weight and allocation constraints and a loss function derived from the Sharpe ratio, thus focusing on maximising portfolio risk-adjusted returns. This new model is benchmarked against a network characteristic-based portfolio, a mean variance-based portfolio, and an equal-weighted portfolio. The results show that the portfolio produced by the GAT-based model outperforms all benchmarks and is consistently superior to other strategies over a long period, while also being informative of market dynamics. ...

Data-generating process and time-series asset pricing ArXiv ID: 2405.10920 “View on arXiv” Authors: Unknown Abstract We study the data-generating processes for factors expressed in return differences, which the literature on time-series asset pricing seems to have overlooked. For the factors’ data-generating processes or long-short zero-cost portfolios, a meaningful definition of returns is impossible; further, the compounded market factor (MF) significantly underestimates the return difference between the market and the risk-free rate compounded separately. Surprisingly, if MF were treated coercively as periodic-rebalancing long-short (i.e., the same as size and value), Fama-French three-factor (FF3) would be economically unattractive for lacking compounding and irrelevant for suffering from the small “size of an effect.” Otherwise, FF3 might be misspecified if MF were buy-and-hold long-short. Finally, we show that OLS with net returns for single-index models leads to inflated alphas, exaggerated t-values, and overestimated Sharpe ratios (SR); worse, net returns may lead to pathological alphas and SRs. We propose defining factors (and SRs) with non-difference compound returns. ...

Supervised Autoencoder MLP for Financial Time Series Forecasting ArXiv ID: 2404.01866 “View on arXiv” Authors: Unknown Abstract This paper investigates the enhancement of financial time series forecasting with the use of neural networks through supervised autoencoders, aiming to improve investment strategy performance. It specifically examines the impact of noise augmentation and triple barrier labeling on risk-adjusted returns, using the Sharpe and Information Ratios. The study focuses on the S&P 500 index, EUR/USD, and BTC/USD as the traded assets from January 1, 2010, to April 30, 2022. Findings indicate that supervised autoencoders, with balanced noise augmentation and bottleneck size, significantly boost strategy effectiveness. However, excessive noise and large bottleneck sizes can impair performance, highlighting the importance of precise parameter tuning. This paper also presents a derivation of a novel optimization metric that can be used with triple barrier labeling. The results of this study have substantial policy implications, suggesting that financial institutions and regulators could leverage techniques presented to enhance market stability and investor protection, while also encouraging more informed and strategic investment approaches in various financial sectors. ...

Nonlinear shifts and dislocations in financial market structure and composition ArXiv ID: 2403.15163 “View on arXiv” Authors: Unknown Abstract This paper develops new mathematical techniques to identify temporal shifts among a collection of US equities partitioned into a new and more detailed set of market sectors. Although conceptually related, our three analyses reveal distinct insights about financial markets, with meaningful implications for investment managers. First, we explore a variety of methods to identify nonlinear shifts in market sector structure and describe the mathematical connection between the measure used and the captured phenomena. Second, we study network structure with respect to our new market sectors and identify meaningfully connected sector-to-sector mappings. Finally, we conduct a series of sampling experiments over different sample spaces and contrast the distribution of Sharpe ratios produced by long-only, long-short and short-only investment portfolios. In addition, we examine the sector composition of the top-performing portfolios for each of these portfolio styles. In practice, the methods proposed in this paper could be used to identify regime shifts, optimally structured portfolios, and better communities of equities. ...

Comparison of Markowitz Model and Single-Index Model on Portfolio Selection of Malaysian Stocks ArXiv ID: 2401.05264 “View on arXiv” Authors: Unknown Abstract Our article is focused on the application of Markowitz Portfolio Theory and the Single Index Model on 10-year historical monthly return data for 10 stocks included in FTSE Bursa Malaysia KLCI, which is also our market index, as well as a risk-free asset which is the monthly fixed deposit rate. We will calculate the minimum variance portfolio and maximum Sharpe portfolio for both the Markowitz model and Single Index model subject to five different constraints, with the results presented in the form of tables and graphs such that comparisons between the different models and constraints can be made. We hope this article will help provide useful information for future investors who are interested in the Malaysian stock market and would like to construct an efficient investment portfolio. Keywords: Markowitz Portfolio Theory, Single Index Model, FTSE Bursa Malaysia KLCI, Efficient Portfolio ...

Optimization of portfolios with cryptocurrencies: Markowitz and GARCH-Copula model approach ArXiv ID: 2401.00507 “View on arXiv” Authors: Unknown Abstract The growing interest in cryptocurrencies has drawn the attention of the financial world to this innovative medium of exchange. This study aims to explore the impact of cryptocurrencies on portfolio performance. We conduct our analysis retrospectively, assessing the performance achieved within a specific time frame by three distinct portfolios: one consisting solely of equities, bonds, and commodities; another composed exclusively of cryptocurrencies; and a third, which combines both ’traditional’ assets and the best-performing cryptocurrency from the second portfolio.To achieve this, we employ the classic variance-covariance approach, utilizing the GARCH-Copula and GARCH-Vine Copula methods to calculate the risk structure. The optimal asset weights within the optimized portfolios are determined through the Markowitz optimization problem. Our analysis predominantly reveals that the portfolio comprising both cryptocurrency and traditional assets exhibits a higher Sharpe ratio from a retrospective viewpoint and demonstrates more stable performances from a prospective perspective. We also provide an explanation for our choice of portfolio optimization based on the Markowitz approach rather than CVaR and ES. ...

Optimal Linear Signal: An Unsupervised Machine Learning Framework to Optimize PnL with Linear Signals ArXiv ID: 2401.05337 “View on arXiv” Authors: Unknown Abstract This study presents an unsupervised machine learning approach for optimizing Profit and Loss (PnL) in quantitative finance. Our algorithm, akin to an unsupervised variant of linear regression, maximizes the Sharpe Ratio of PnL generated from signals constructed linearly from exogenous variables. The methodology employs a linear relationship between exogenous variables and the trading signal, with the objective of maximizing the Sharpe Ratio through parameter optimization. Empirical application on an ETF representing U.S. Treasury bonds demonstrates the model’s effectiveness, supported by regularization techniques to mitigate overfitting. The study concludes with potential avenues for further development, including generalized time steps and enhanced corrective terms. ...

A Comparative Study of Portfolio Optimization Methods for the Indian Stock Market ArXiv ID: 2310.14748 “View on arXiv” Authors: Unknown Abstract This chapter presents a comparative study of the three portfolio optimization methods, MVP, HRP, and HERC, on the Indian stock market, particularly focusing on the stocks chosen from 15 sectors listed on the National Stock Exchange of India. The top stocks of each cluster are identified based on their free-float market capitalization from the report of the NSE published on July 1, 2022 (NSE Website). For each sector, three portfolios are designed on stock prices from July 1, 2019, to June 30, 2022, following three portfolio optimization approaches. The portfolios are tested over the period from July 1, 2022, to June 30, 2023. For the evaluation of the performances of the portfolios, three metrics are used. These three metrics are cumulative returns, annual volatilities, and Sharpe ratios. For each sector, the portfolios that yield the highest cumulative return, the lowest volatility, and the maximum Sharpe Ratio over the training and the test periods are identified. ...