Maximum Drawdown Research Articles

A Deep Learning Approach with Extensive Sentiment Analysis for Quantitative Investment

Recently, deep-learning-based quantitative investment is playing an increasingly important role in the field of finance. However, due to the complexity of the stock market, establishing effective quantitative investment methods is facing challenges from various aspects because of the complexity of the stock market. Existing research has inadequately utilized stock news information, overlooking significant details within news content. By constructing a deep hybrid model for comprehensive analysis of historical trading data and news information, complemented by momentum trading strategies, this paper introduces a novel quantitative investment approach. For the first time, we fully consider two dimensions of news, including headlines and contents, and further explore their combined impact on modeling stock price. Our approach initially employs fundamental analysis to screen valuable stocks. Subsequently, we built technical factors based on historical trading data. We then integrated news headlines and content summarized through language models to extract semantic information and representations. Lastly, we constructed a deep neural model to capture global features by combining technical factors with semantic representations, enabling stock prediction and trading decisions. Empirical results conducted on over 4000 stocks from the Chinese stock market demonstrated that incorporating news content enriched semantic information and enhanced objectivity in sentiment analysis. Our proposed method achieved an annualized return rate of 32.06% with a maximum drawdown rate of 5.14%. It significantly outperformed the CSI 300 index, indicating its applicability to guiding investors in making more effective investment strategies and realizing considerable returns.

Performance Evaluation of Chinese Stock Mutual Funds

Based on a data from January 2003 to July 2020, I compare market index with mutual funds in Chinese stock market. First, I compare the cumulative return of market with that of mutual funds. Mutual funds have obvious advantages. Next, I compare their volatilities, Sharpe ratios, Sortino ratios, and maximum drawdowns. Based on these performance proxies, Chinese stock mutual funds still outperform the market index. Finally, I research the persistence of fund performance. Mutual funds with better performance in the past year tend to have higher returns in the next month.

Enhancing Portfolio Performances through LSTM and Covariance Shrinkage

Portfolio optimization is a crucial aspect of finance, requiring advanced analytical tools and modeling techniques. This paper proposes a new method for portfolio optimization that combines Long Short-Term Memory (LSTM) forecasting with Covariance Shrinkage and Mean-Variance Optimization (MVO) to construct diversified portfolios that maximize risk-adjusted returns. The study utilizes an LSTM-based model to predict stock prices, evaluating its performance using the RMSE metric. The calculated RMSE of 0.0849 indicates accurate and robust predictions. The portfolio constructed shows different weights each day for different assets based on the minimum variance and maximum Sharpe ratio portfolios. As of January 3rd, 2023, the assets with the largest proportion in the Maximum Sharpe Ratio portfolio and in the Minimum Volatility portfolio, are respectively BA, accounting for 27.64% of the portfolio and PG, accounting for 32.66% of the portfolio. This paper compares the performance of the proposed method and benchmark methods by applying 30 daily portfolio weights to real returns. The portfolio constructed by the proposed method has higher cumulative return with a higher Sharpe ratio and lower maximum drawdown, indicating a better ability to diversify risks and create returns. The proposed method offers a new perspective on portfolio optimization, which can potentially benefit investors and asset managers.

Tail risk in the Chinese stock market: An AEV model on the maximal drawdowns

This paper proposes a novel autoregressive extreme value (AEV) framework with covariates to capture the time-dependent dynamics of financial tail risk. Using the intra-day maxima of 5-minute potential drawdowns for CSI300 in the Chinese stock market, the study estimates an AEV(1,1) model with the effects of the foreign exchange market, interest rate market, and commodity futures market. The empirical results suggest that the commodity futures market plays a role in driving the maximal drawdown. Moreover, the tail index of AEV sensitively captures the clustering of tail behaviors in the Chinese stock market. Finally, the backtesting evidence further demonstrates that AEV exhibits satisfactory forecasting performance for Value-at-Risk in the Chinese stock market.

Model-based reinforcement learning with non-Gaussian environment dynamics and its application to portfolio optimization.

The rapid development of quantitative portfolio optimization in financial engineering has produced promising results in AI-based algorithmic trading strategies. However, the complexity of financial markets poses challenges for comprehensive simulation due to various factors, such as abrupt transitions, unpredictable hidden causal factors, and heavy tail properties. This paper aims to address these challenges by employing heavy-tailed preserving normalizing flows to simulate the high-dimensional joint probability of the complex trading environment under a model-based reinforcement learning framework. Through experiments with various stocks from three financial markets (Dow, NASDAQ, and S&P), we demonstrate that Dow outperforms the other two based on multiple evaluation metrics in our testing system. Notably, our proposed method mitigates the impact of unpredictable financial market crises during the COVID-19 pandemic, resulting in a lower maximum drawdown. Additionally, we explore the explanation of our reinforcement learning algorithm, employing the pattern causality method to study interactive relationships among stocks, analyzing dynamics of training for loss functions to ensure convergence, visualizing high-dimensional state transition data with t-SNE to uncover effective patterns for portfolio optimization, and utilizing eigenvalue analysis to study convergence properties of the environment's model.

Portfolio optimization using predictive auxiliary classifier generative adversarial networks

In financial engineering, portfolio optimization has been of consistent interest. Portfolio optimization is a process of modulating asset distributions to maximize expected returns and minimize risks. Despite numerous studies on shallow learning models, they have shown limited success in analyzing the complex nature of massive stock data, a task where recent deep learning models excel. However, the deterministic nature of conventional deep learning models impedes their consideration of portfolio risk due to an inherent lack of uncertainty quantification in their predictions. This paper proposes a novel portfolio weighting strategy, incorporating both risk and return considerations within a deep learning framework. We propose the Predictive Auxiliary Classifier Generative Adversarial Networks (PredACGAN), a probabilistic deep learning model, to measure prediction uncertainty. The PredACGAN generator leverages latent vectors and historical stock prices to predict future returns. The model synthesizes predictive distributions from various latent vectors and past prices. The associated risk is produced via the entropy of these distributions, facilitating portfolio optimization through both return and risk considerations. The proposed algorithm removes high-risk assets from the investment universe at rebalancing moments, enabling PredACGAN to optimize portfolios considering both return and risk. We evaluated PredACGAN and the accompanying algorithm with S&P 500 stocks from 1990 to 2020, with portfolios rebalanced monthly based on PredACGAN predictions and risk measures. The PredACGAN portfolios yielded 9.123% annual returns and a 1.054 Sharpe ratio, outperforming a risk-agnostic portfolio yielding 1.024% annual returns and a 0.236 Sharpe ratio. The PredACGAN portfolio also exhibited lower maximum drawdowns, highlighting its effectiveness.

Numerical simulation of a managed aquifer recharge system designed to supply drinking water to the city of Amsterdam, The Netherlands

Managed aquifer recharge (MAR) is increasingly used to secure drinking water supply worldwide. The city of Amsterdam (The Netherlands) depends largely on the MAR in coastal dunes for water supply. A new MAR scheme is proposed for the production of 10 × 106 m3/year, as required in the next decade. The designed MAR system consists of 10 infiltration ponds in an artificially created sandbank, and 25 recovery wells placed beneath the ponds in a productive aquifer. Several criteria were met for the design, such as a minimum residence time of 60 days and maximum drawdown of 5 cm. Steady-state and transient flow models were calibrated. The flow model computed the infiltration capacity of the ponds and drawdowns caused by the MAR. A hypothetical tracer transport model was used to compute the travel times from the ponds to the wells and recovery efficiency of the wells. The results demonstrated that 98% of the infiltrated water was captured by the recovery wells which accounted for 65.3% of the total abstraction. Other sources include recharge from precipitation (6.7%), leakages from surface water (13.1%), and natural groundwater reserve (14.9%). Sensitivity analysis indicated that the pond conductance and hydraulic conductivity of the sand aquifer in between the ponds and wells are important for the infiltration capacity. The temperature simulation showed that the recovered water in the wells has a stable temperature of 9.8–12.5 °C which is beneficial for post-treatment processes. The numerical modelling approach is useful and helps to gain insights for implementation of the MAR.

Multi-step reward ensemble methods for adaptive stock trading

Stock trading can be considered a Markov decision process that comes naturally to applying reinforcement learning (RL) to this field. Numerous studies have proposed various methods to combine stock trading with RL, where only one single reward function is used to fit the market. However, the market in the real world shows distinct patterns in different periods, such as bullish or bearish. A reward function in bullish periods may perform poorly in bearish periods. In our work, we construct several kinds of multi-step future-price-based reward functions (profit-based reward and regularized-based reward), considering that the market changes consistently. Moreover, we propose two ensemble rewards based on the greedy method (MSR-GME, the abbreviation for Multi-Step Rewards Greedy Method Ensemble) and Thompson sampling (MSR-TSE, the abbreviation for Multi-Step Rewards Thompson Sampling Ensemble) to help agents to make adaptive trading decisions under distinct market patterns. We conduct extensive experiments to verify the mechanisms and the superiority of our constructed reward functions from multiple aspects. The results show the two constructed single-reward functions outperform both the buy-and-hold strategy (B&H) and the historical-price-based rewards consistently to a large extent (for example, the profit-based reward achieves at most 7.3 times the Sortino ratio and 78.6% lower maximum drawdown than B&H). Moreover, the ensemble rewards can substantially improve strategy performance in achieving higher profits and lower risks (for example, MSR-TSE achieves at most 49.7 times profits and 8.85 times Sortino ratio than B&H). We also find that MSR-TSE is risk-averse, but MSR-GME is risk-aggressive, indicating that Thompson sampling is an intensely competitive ensemble method, especially in bearish markets.

Improving Stock Market Predictions: An Equity Forecasting Scanner Using Long Short-Term Memory Method with Dynamic Indicators for Malaysia Stock Market

Stock market predictions are a challenging problem due to the dynamic and complex nature of financial data. This study proposes an approach that integrates the domain knowledge of investors with a long-short-term memory (LSTM) algorithm for predicting stock prices. The proposed approach involves collecting data from investors in the form of technical indicators and using them as input for the LSTM model. The model is then trained and tested using a dataset of 100 stocks. The accuracy of the model is evaluated using various metrics, including the average prediction accuracy, average cumulative return, Sharpe ratio, and maximum drawdown. The results are compared to the performance of other strategies, including the random selection of technical indicators. The simulation results demonstrate that the proposed model outperforms the other strategies in terms of accuracy and performance in a 100-stock investment simulation, highlighting the potential of integrating investor domain knowledge with machine learning algorithms for stock price prediction.

A general method for analysis and valuation of drawdown risk

Drawdown risk is a major concern in financial markets. We develop a novel method to solve the first passage problem of the drawdown process for general one-dimensional Markov processes (including time-inhomogeneous ones) as well as regime-switching and stochastic volatility models. We compute its Laplace transform based on continuous-time Markov chain (CTMC) approximation and invert the Laplace transform numerically to obtain the first passage probabilities and the distribution of the maximum drawdown. We prove convergence of our method for general Markov models and provide sharp estimate of the convergence rate for a general class of jump-diffusion models. We apply our method to price and hedge maximum drawdown options and demonstrate its accuracy and efficiency through various numerical experiments. In addition, we can apply our method to calculate the Calmar ratio for investment analysis, and quantify the contributions of assets to the drawdown risk of a portfolio when the assets follow multivariate exponential Lévy models.

Surviving Black Swans III: Timing US Sector Funds

The typical small investor makes on average about 5% a year in investment gains, just half of what the market does. Moreover, most investment funds also underperform compared to the broader market. In two previous papers, we explored how a specific and simple approach to algorithmic trading can help both types of investors achieve strong results. For concreteness, we focused attention on investing in a single variable, in our case, a major US-based index such as SPX and IXIC, individually. For illustrative purposes, we also considered some highly traded tech stock examples. In this paper, we extend our work to study the US sector funds, and for the first time in our series, we also consider trading multiple variables at a time to see how that may differ from our single-variable investment strategy. To simplify matters, we consider an initial equal weighted portfolio of several sector funds, selected randomly without any analysis, and assume that each is traded independently. To simplify further, we do no rebalancing in our study, though that is an essential part of money management according to modern portfolio theory. We nevertheless obtain interesting and informative results. We can typically improve on the performance of most sector funds compared to buy-and-hold (hereafter referred to as BnH). Moreover, as an example of portfolio growth, a portfolio of five equal weighted sector funds in BnH achieves 6.5× growth over 20 years (ending in March 2023), whereas our approach achieves 12.4× growth—nearly 2× better, at roughly half the maximum drawdown. That is a strong win for both professional and home investors.

Effect of Different Screen Types on Head Loss in Deep Wells Used for Irrigation

This research was carried out with the help of a deep well simulator, which is commonly utilized for irrigation studies. In this study, flow types based on Reynolds number, well drawdown, head losses, and cost changes of these head losses were analyzed for four different sieve types used in wells. In addition, the flow types and head losses for the types of screen used were examined as per the theoretical calculations.
 Theoretically, the turbulent head loss among types of screens was calculated at the highest (0.37 m) in the bridge slot screen (ST4) and at least (0.028 m) in the round slot (ST3). The drawdown is the sum of the head losses for deep wells. Among the well-types, the maximum drawdown (113.46 cm) was measured within the bridge slot well type (WT4), and the minimum drawdown (50.37 cm) was measured in the horizontal slot oblong well type (WT2). The least head loss per unit flow rate in the wells was measured in the well, which was formed with a horizontal oblong slot (WT2) screen. Here, gravel and screen hole position affected the percentage of clogging in the screens. Overclogging of the screens caused the narrowing of the opening area, increased flow velocity and turbulent head loss, and increased drawdown.
 It has been revealed that the use of a horizontal oblong slot screen minimizes the head loss in the wells, depending on the physical properties of the gravel used in this study. One of the most important factors to be considered in well designs is the compatibility of the screen type depending on the physical properties of the gravel. Even the change of the geometric shape among the screen types having similar apertures changed the blockage of the gravel, causing the head loss to change. The well-designers should pay attention to the selection of gravel depending on the screen type or the selection of the screen depending on the type of gravel used.

Heterogeneous tail generalized common factor modeling

A multivariate normal mean–variance heterogeneous tails mixture distribution is proposed for the joint distribution of financial factors and asset returns (referred to as Factor-HGH). The proposed latent variable model incorporates a Cholesky decomposition of the dispersion matrix to ensure a rich dependency structure for capturing the stylized facts of the data. It generalizes several existing model structures, with or without financial factors. It is further applicable in large dimensions due to a fast ECME estimation algorithm. The advantages of modelling financial factors and asset returns jointly under non-Gaussian errors are illustrated in an empirical comparison study between the proposed Factor-HGH model and classical financial factor models. While the results for the Fama–French 49 industry portfolios are in line with Gaussian-based models, in the case of highly tail heterogeneous cryptocurrencies, the portfolio based on the Factor-HGH model almost doubles the average return while keeping the volatility, the maximum drawdown, the turnover, and the expected shortfall at a low level.

Performance measurement of crypto funds

Crypto funds (CFs) are a growing intermediary in cryptocurrency markets. We evaluate CF performance using metrics based on alphas, value at risk, lower partial moments, and maximum drawdown. The performance of actively managed CFs is heterogeneous: While the average fund in our sample does not outperform the overall cryptocurrency market, there seem to be some few funds with superior skills. Given the non-normal nature of fund returns, the choice of the performance measure affects the rank orders of funds. Compared to the Sharpe ratio, the most commonly applied metric in the asset management practice, performance measures based on alphas and maximum drawdown lead to diverging fund rankings. Depending on their ranking order of preferences, CF investors should consider a bundle of metrics for fund selection and performance measurement.

A Deep Trend-Following Trading Strategy for Equity Markets

In this article, the authors present a new deep trend-following strategy that selectively buys constituents of the S&P 500 Index that are estimated to be upward trending. Therefore, they construct a binary momentum indicator based on a recursive algorithm and then train a convolutional neural network combined with a long short-term memory model to classify periods that are defined as upward trends. The strategy, which can be used as an alternative to traditional quantitative momentum ranking models, generates returns up to 27.3% per annum over the out-of-sample period from January 2010 to December 2019 and achieves a Sharpe ratio of 1.3 after accounting for transaction costs on daily data. The authors show that volatility scaling can further increase the risk–return profile and lower the maximum drawdown of the strategy.

Meta-Labeling: Calibration and Position Sizing

Meta-labeling is a recently developed tool for determining the position size of a trade. It involves applying a secondary model to produce an output that can be interpreted as the estimated probability of a profitable trade, which can then be used to size positions. Before sizing the position, probability calibration can be applied to bring the model’s estimates closer to true posterior probabilities. This article investigates the use of these estimated probabilities, both uncalibrated and calibrated, in six position sizing algorithms. The algorithms used in this article include established methods used in practice and variations thereon, as well as a novel method called sigmoid optimal position sizing. The position sizing methods are evaluated and compared using strategy metrics such as the Sharpe ratio and maximum drawdown. The results indicate that the performance of fixed position sizing methods is significantly improved by calibration, whereas methods that estimate their functions from the training data do not gain any significant advantage from probability calibration.

Generalized Deep Reinforcement Learning for Trading

This paper proposes generalized deep reinforcement learning with multivariate state space, discrete rewards, and adaptive synchronization for trading any stock held in the S&P 500. Specifically, the proposed trading model observes the daily historical data of a stock held in the S&P 500 and multiple market-indicating securities (SPY, IEF, EUR=X, GSG), selects a trading action, and observes a discrete reward that is based on the correctness of the selected action and independent of the volatility of stocks. The proposed trading model’s reward-maximizing behavior is optimized by using a standard deep q-network (DQN) with adaptive synchronization that stabilizes and enables to track learning performance on generalizing new experiences from each stock. The proposed trading model was trained on the top 50 holdings of the S&P 500 and tested on the top 100 holdings of the S&P 500 starting from 2006 to 2022. Experimental results suggest that the proposed trading model significantly outperforms the 100% long-strategy benchmark in terms of annualized return, Sharpe ratio, and maximum drawdown.

Stock Market Analysis Using Time Series Relational Models for Stock Price Prediction

The ability to predict stock prices is essential for informing investment decisions in the stock market. However, the complexity of various factors influencing stock prices has been widely studied. Traditional methods, which rely on time-series information for a single stock, are incomplete as they lack a holistic perspective. The linkage effect in the stock market, where stock prices are influenced by those of associated stocks, necessitates the use of more comprehensive data. Currently, stock relationship information is mainly obtained through industry classification data from third-party platforms, but these data are often approximate and subject to time lag. To address this, this paper proposes a time series relational model (TSRM) that integrates time and relationship information. The TSRM utilizes transaction data of stocks to automatically obtain stock classification through a K-means model and derives stock relationships. The time series information, extracted using long short-term memory (LSTM), and relationship information, extracted with a graph convolutional network (GCN), are integrated to predict stock prices. The TSRM was tested in the Chinese Shanghai and Shenzhen stock markets, with results showing an improvement in cumulative returns by 44% and 41%, respectively, compared to the baseline, and a reduction in maximum drawdown by 4.9% and 6.6%, respectively.

Contextual combinatorial bandit on portfolio management

Portfolio optimization is a classic problem in finance, and assumptions are generally accepted about the stochastic dynamics of prices and market information. The Linear Upper Confidence Bound (LinUCB) algorithm based on bandit learning is a typical reinforcement learning approach that can be a data-driven approach to the portfolio problem. Most investors may have inconsistent preferences for different assets; therefore, the reward function needs to be designed to balance exploration (allocating part of the investment to searching among other alternative portfolios) and exploitation (concentrating the investment on the historically best portfolio). The study consists of developing a two-stage investing strategy that uses the supervised adaptive decision tree approach to build a pool of candidate portfolios and the reinforcement LinUCB algorithm to derive a portfolio update rule with respect to a specific utility function. The two-stage strategy has been tested on CSI300 constitute stocks listed on the Shanghai Stock Exchange. The accumulated returns, as well as other performance measures (e.g., maximum drawdown, Sharpe ratio, and information ratio) at different testing periods achieved by the model, can well outperform the benchmark index.

Effect of Pre-Existing Underground Structures on Groundwater Flow and Strata Movement Induced by Dewatering and Excavation

Based on an actual excavation of a metro station in Tianjin, China, a fluid–solid coupling numerical model was developed to study the characteristics of groundwater flow and strata movement induced by dewatering and excavation considering the barrier effect of pre-existing adjacent underground structures. Two parameters were selected for the model: the distance between the excavation and the existing underground structure (D), and the buried depth of the adjacent structure (H). By comparing the distribution of groundwater drawdown and deformation modes of the retaining structure and the strata under different working conditions, the influence mechanism of adjacent structures on the movement of groundwater and strata was revealed. The results show that the pile foundations have different effects on the groundwater flow and excavation deformation. Generally, the maximum groundwater drawdown could be enlarged by considering the adjacent underground structure, while the retaining structure deflection would be reduced and the ground settlement could be either enlarged or reduced. Additionally, as D decreases and H increases, a much greater groundwater drawdown and a much smaller retaining structure deflection would appear, which together affect the ground behavior. On the one hand, greater groundwater drawdown would lead to greater ground settlement by soil consolidation, while on the other hand, a smaller retaining structure deflection would lead to smaller ground settlement. Thus, a complex development of ground settlement would appear, and a specific analysis should be performed to assess this in practice, based on a specific H and D.