Sports Betting: an application of neural networks and modern portfolio theory to the English Premier League ArXiv ID: 2307.13807 “View on arXiv” Authors: Unknown Abstract This paper presents a novel approach for optimizing betting strategies in sports gambling by integrating Von Neumann-Morgenstern Expected Utility Theory, deep learning techniques, and advanced formulations of the Kelly Criterion. By combining neural network models with portfolio optimization, our method achieved remarkable profits of 135.8% relative to the initial wealth during the latter half of the 20/21 season of the English Premier League. We explore complete and restricted strategies, evaluating their performance, risk management, and diversification. A deep neural network model is developed to forecast match outcomes, addressing challenges such as limited variables. Our research provides valuable insights and practical applications in the field of sports betting and predictive modeling. ...

Interpretable ML for High-Frequency Execution ArXiv ID: 2307.04863 “View on arXiv” Authors: Unknown Abstract Order placement tactics play a crucial role in high-frequency trading algorithms and their design is based on understanding the dynamics of the order book. Using high quality high-frequency data and a set of microstructural features, we exhibit strong state dependence properties of the fill probability function. We train a neural network to infer the fill probability function for a fixed horizon. Since we aim at providing a high-frequency execution framework, we use a simple architecture. A weighting method is applied to the loss function such that the model learns from censored data. By comparing numerical results obtained on both digital asset centralized exchanges (CEXs) and stock markets, we are able to analyze dissimilarities between feature importances of the fill probability of small tick crypto pairs and Euronext equities. The practical use of this model is illustrated with a fixed time horizon execution problem in which both the decision to post a limit order or to immediately execute and the optimal distance of placement are characterized. We discuss the importance of accurately estimating the clean-up cost that occurs in the case of a non-execution and we show it can be well approximated by a smooth function of market features. We finally assess the performance of our model with a backtesting approach that avoids the insertion of hypothetical orders and makes possible to test the order placement algorithm with orders that realistically impact the price formation process. ...

dYdX: Liquidity Providers’ Incentive Programme Review ArXiv ID: 2307.03935 “View on arXiv” Authors: Unknown Abstract Liquidity providers are currently incentivised to provide liquidity through the LP Incentives Programme on dYdX. Based on the various parameters - makerVolume, depths and spreads, they are rewarded accordingly based on their activities. Given the maturity of the BTC and ETH markets, alongside other altcoins which enjoy a consistent amount of liquidity, this paper aims to update the formula to encourage more active and efficient liquidity, improving the overall trading experience. In this research, I begin by providing a basic understanding of spread management, before introducing the methodology with the various metrics and conditions. This includes gathering orderbooks on a minute interval and reconstructing the depths based on historical trades to establish an upper bound. I end off by providing recommendations to update the maxSpread parameter and alternative mechanisms/solutions to improve the existing market structures. ...

Time-limited Metaheuristics for Cardinality-constrained Portfolio Optimisation ArXiv ID: 2307.04045 “View on arXiv” Authors: Unknown Abstract A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the problem realistic, constraints can be imposed on the number of assets held in the portfolio and the maximum proportion of the portfolio that can be allocated to an asset. This problem is unsolvable using quadratic programming, which means that the optimal solution cannot be calculated. A group of algorithms, called metaheuristics, can find near-optimal solutions in a practical computing time. These algorithms have been successfully used in constrained portfolio optimisation. However, in past studies the computation time of metaheuristics is not limited, which means that the results differ in both quality and computation time, and cannot be easily compared. This study proposes a different way of testing metaheuristics, limiting their computation time to a certain duration, yielding results that differ only in quality. Given that in some use cases the priority is the quality of the solution and in others the speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics - simulated annealing, tabu search, and genetic algorithm - were evaluated on five sets of historical market data with different numbers of assets. Although the metaheuristics could not find a competitive solution in 1 second, simulated annealing found a near-optimal solution in 5 seconds in all but one dataset. The lowest quality solutions were obtained by genetic algorithm. ...

Action-State Dependent Dynamic Model Selection ArXiv ID: 2307.04754 “View on arXiv” Authors: Unknown Abstract A model among many may only be best under certain states of the world. Switching from a model to another can also be costly. Finding a procedure to dynamically choose a model in these circumstances requires to solve a complex estimation procedure and a dynamic programming problem. A Reinforcement learning algorithm is used to approximate and estimate from the data the optimal solution to this dynamic programming problem. The algorithm is shown to consistently estimate the optimal policy that may choose different models based on a set of covariates. A typical example is the one of switching between different portfolio models under rebalancing costs, using macroeconomic information. Using a set of macroeconomic variables and price data, an empirical application to the aforementioned portfolio problem shows superior performance to choosing the best portfolio model with hindsight. ...

Are there Dragon Kings in the Stock Market? ArXiv ID: 2307.03693 “View on arXiv” Authors: Unknown Abstract We undertake a systematic study of historic market volatility spanning roughly five preceding decades. We focus specifically on the time series of realized volatility (RV) of the S&P500 index and its distribution function. As expected, the largest values of RV coincide with the largest economic upheavals of the period: Savings and Loan Crisis, Tech Bubble, Financial Crisis and Covid Pandemic. We address the question of whether these values belong to one of the three categories: Black Swans (BS), that is they lie on scale-free, power-law tails of the distribution; Dragon Kings (DK), defined as statistically significant upward deviations from BS; or Negative Dragons Kings (nDK), defined as statistically significant downward deviations from BS. In analyzing the tails of the distribution with RV > 40, we observe the appearance of “potential” DK which eventually terminate in an abrupt plunge to nDK. This phenomenon becomes more pronounced with the increase of the number of days over which the average RV is calculated – here from daily, n=1, to “monthly,” n=21. We fit the entire distribution with a modified Generalized Beta (mGB) distribution function, which terminates at a finite value of the variable but exhibits a long power-law stretch prior to that, as well as Generalized Beta Prime (GB2) distribution function, which has a power-law tail. We also fit the tails directly with a straight line on a log-log scale. In order to ascertain BS, DK or nDK behavior, all fits include their confidence intervals and p-values are evaluated for the data points to check if they can come from the respective distributions. ...

Bayesian Forecasting of Stock Returns on the JSE using Simultaneous Graphical Dynamic Linear Models ArXiv ID: 2307.08665 “View on arXiv” Authors: Unknown Abstract Cross-series dependencies are crucial in obtaining accurate forecasts when forecasting a multivariate time series. Simultaneous Graphical Dynamic Linear Models (SGDLMs) are Bayesian models that elegantly capture cross-series dependencies. This study forecasts returns of a 40-dimensional time series of stock data from the Johannesburg Stock Exchange (JSE) using SGDLMs. The SGDLM approach involves constructing a customised dynamic linear model (DLM) for each univariate time series. At each time point, the DLMs are recoupled using importance sampling and decoupled using mean-field variational Bayes. Our results suggest that SGDLMs forecast stock data on the JSE accurately and respond to market gyrations effectively. ...

Decentralised Finance and Automated Market Making: Execution and Speculation ArXiv ID: 2307.03499 “View on arXiv” Authors: Unknown Abstract Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This work studies optimal trading and statistical arbitrage in CPMs where balancing exchange rate risk and execution costs is key. Empirical evidence shows that execution costs are accurately estimated by the convexity of the trading function. These convexity costs are linear in the trade size and are nonlinear in the depth of liquidity and in the exchange rate. We develop models for when exchange rates form in a competing centralised exchange, in a CPM, or in both venues. Finally, we derive computationally efficient strategies that account for stochastic convexity costs and we showcase their out-of-sample performance. ...

Deep Inception Networks: A General End-to-End Framework for Multi-asset Quantitative Strategies ArXiv ID: 2307.05522 “View on arXiv” Authors: Unknown Abstract We introduce Deep Inception Networks (DINs), a family of Deep Learning models that provide a general framework for end-to-end systematic trading strategies. DINs extract time series (TS) and cross sectional (CS) features directly from daily price returns. This removes the need for handcrafted features, and allows the model to learn from TS and CS information simultaneously. DINs benefit from a fully data-driven approach to feature extraction, whilst avoiding overfitting. Extending prior work on Deep Momentum Networks, DIN models directly output position sizes that optimise Sharpe ratio, but for the entire portfolio instead of individual assets. We propose a novel loss term to balance turnover regularisation against increased systemic risk from high correlation to the overall market. Using futures data, we show that DIN models outperform traditional TS and CS benchmarks, are robust to a range of transaction costs and perform consistently across random seeds. To balance the general nature of DIN models, we provide examples of how attention and Variable Selection Networks can aid the interpretability of investment decisions. These model-specific methods are particularly useful when the dimensionality of the input is high and variable importance fluctuates dynamically over time. Finally, we compare the performance of DIN models on other asset classes, and show how the space of potential features can be customised. ...

On Unified Adaptive Portfolio Management ArXiv ID: 2307.03391 “View on arXiv” Authors: Unknown Abstract This paper introduces a unified framework for adaptive portfolio management, integrating dynamic Black-Litterman (BL) optimization with the general factor model, Elastic Net regression, and mean-variance portfolio optimization, which allows us to generate investors views and mitigate potential estimation errors systematically. Specifically, we propose an innovative dynamic sliding window algorithm to respond to the constantly changing market conditions. This algorithm allows for the flexible window size adjustment based on market volatility, generating robust estimates for factor modeling, time-varying BL estimations, and optimal portfolio weights. Through extensive ten-year empirical studies using the top 100 capitalized assets in the S&P 500 index, accounting for turnover transaction costs, we demonstrate that this combined approach leads to computational advantages and promising trading performances. ...