Kelly Criterion

Forecast-to-Fill: Benchmark-Neutral Alpha and Billion-Dollar Capacity in Gold Futures (2015-2025) ArXiv ID: 2511.08571 “View on arXiv” Authors: Mainak Singha, Jose Aguilera-Toste, Vinayak Lahiri Abstract We test whether simple, interpretable state variables-trend and momentum-can generate durable out-of-sample alpha in one of the world’s most liquid assets, gold. Using a rolling 10-year training and 6-month testing walk-forward from 2015 to 2025 (2,793 trading days), we convert a smoothed trend-momentum regime signal into volatility-targeted, friction-aware positions through fractional, impact-adjusted Kelly sizing and ATR-based exits. Out of sample, the strategy delivers a Sharpe ratio of 2.88 and a maximum drawdown of 0.52 percent, net of 0.7 basis-point linear cost and a square-root impact term (gamma = 0.02). A regression on spot-gold returns yields a 43 percent annualized return (CAGR approximately 43 percent) and a 37 percent alpha (Sharpe = 2.88, IR = 2.09) at a 15 percent volatility target with beta approximately 0.03, confirming benchmark-neutral performance. Bootstrap confidence intervals ([“2.49, 3.27”]) and SPA tests (p = 0.000) confirm statistical significance and robustness to latency, reversal, and cost stress. We conclude that forecast-to-fill engineering-linking transparent signals to executable trades with explicit risk, cost, and impact control-can transform modest predictability into allocator-grade, billion-dollar-scalable alpha. ...

Deep Reinforcement Learning for Optimal Asset Allocation Using DDPG with TiDE ArXiv ID: 2508.20103 “View on arXiv” Authors: Rongwei Liu, Jin Zheng, John Cartlidge Abstract The optimal asset allocation between risky and risk-free assets is a persistent challenge due to the inherent volatility in financial markets. Conventional methods rely on strict distributional assumptions or non-additive reward ratios, which limit their robustness and applicability to investment goals. To overcome these constraints, this study formulates the optimal two-asset allocation problem as a sequential decision-making task within a Markov Decision Process (MDP). This framework enables the application of reinforcement learning (RL) mechanisms to develop dynamic policies based on simulated financial scenarios, regardless of prerequisites. We use the Kelly criterion to balance immediate reward signals against long-term investment objectives, and we take the novel step of integrating the Time-series Dense Encoder (TiDE) into the Deep Deterministic Policy Gradient (DDPG) RL framework for continuous decision-making. We compare DDPG-TiDE with a simple discrete-action Q-learning RL framework and a passive buy-and-hold investment strategy. Empirical results show that DDPG-TiDE outperforms Q-learning and generates higher risk adjusted returns than buy-and-hold. These findings suggest that tackling the optimal asset allocation problem by integrating TiDE within a DDPG reinforcement learning framework is a fruitful avenue for further exploration. ...

Sizing the Risk: Kelly, VIX, and Hybrid Approaches in Put-Writing on Index Options ArXiv ID: 2508.16598 “View on arXiv” Authors: Maciej Wysocki Abstract This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility exceeds realized volatility, the practical implementation of short-dated volatility-selling strategies remains underdeveloped in the literature. This study evaluates three position sizing approaches: the Kelly criterion, VIX-based volatility regime scaling, and a novel hybrid method combining both. Using SPXW options with expirations from 0 to 5 days, the analysis explores a broad design space, including moneyness levels, volatility estimators, and memory horizons. Results show that ultra-short-dated, far out-of-the-money options deliver superior risk-adjusted returns. The hybrid sizing method consistently balances return generation with robust drawdown control, particularly under low-volatility conditions such as those seen in 2024. The study offers new insights into volatility harvesting, introducing a dynamic sizing framework that adapts to shifting market regimes. It also contributes practical guidance for constructing short-dated option strategies that are robust across market environments. These findings have direct applications for institutional investors seeking to enhance portfolio efficiency through systematic exposure to volatility premia. ...

Through the Looking Glass: Bitcoin Treasury Companies ArXiv ID: 2507.14910 “View on arXiv” Authors: B K Meister Abstract Bitcoin treasury companies have taken stock markets by storm amassing billions of dollars worth of tokens in hundreds of entities. The paper discusses, how leverage - whether created through corporate debt or investors using stock as loan collateral - fuels this trend. The extension of the binary-choice Kelly criterion to incorporate uncertainty in the form of the Kullback-Leibler divergence or more generally Bregman divergence is also briefly discussed. ...

Statistical arbitrage in multi-pair trading strategy based on graph clustering algorithms in US equities market ArXiv ID: 2406.10695 “View on arXiv” Authors: Unknown Abstract The study seeks to develop an effective strategy based on the novel framework of statistical arbitrage based on graph clustering algorithms. Amalgamation of quantitative and machine learning methods, including the Kelly criterion, and an ensemble of machine learning classifiers have been used to improve risk-adjusted returns and increase immunity to transaction costs over existing approaches. The study seeks to provide an integrated approach to optimal signal detection and risk management. As a part of this approach, innovative ways of optimizing take profit and stop loss functions for daily frequency trading strategies have been proposed and tested. All of the tested approaches outperformed appropriate benchmarks. The best combinations of the techniques and parameters demonstrated significantly better performance metrics than the relevant benchmarks. The results have been obtained under the assumption of realistic transaction costs, but are sensitive to changes in some key parameters. ...

Sizing the bets in a focused portfolio ArXiv ID: 2402.15588 “View on arXiv” Authors: Unknown Abstract The paper provides a mathematical model and a tool for the focused investing strategy as advocated by Buffett, Munger, and others from this investment community. The approach presented here assumes that the investor’s role is to think about probabilities of different outcomes for a set of businesses. Based on these assumptions, the tool calculates the optimal allocation of capital for each of the investment candidates. The model is based on a generalized Kelly Criterion with options to provide constraints that ensure: no shorting, limited use of leverage, providing a maximum limit to the risk of permanent loss of capital, and maximum individual allocation. The software is applied to an example portfolio from which certain observations about excessive diversification are obtained. In addition, the software is made available for public use. ...

Robust Long-Term Growth Rate of Expected Utility for Leveraged ETFs ArXiv ID: 2310.02084 “View on arXiv” Authors: Unknown Abstract This paper analyzes the robust long-term growth rate of expected utility and expected return from holding a leveraged exchange-traded fund (LETF). When the Markovian model parameters in the reference asset are uncertain, the robust long-term growth rate is derived by analyzing the worst-case parameters among an uncertainty set. We compute the growth rate and describe the optimal leverage ratio maximizing the robust long-term growth rate. To achieve this, the worst-case parameters are analyzed by the comparison principle, and the growth rate of the worst-case is computed using the martingale extraction method. The robust long-term growth rates are obtained explicitly under a number of models for the reference asset, including the geometric Brownian motion (GBM), Cox–Ingersoll–Ross (CIR), 3/2, and Heston and 3/2 stochastic volatility models. Additionally, we demonstrate the impact of stochastic interest rates, such as the Vasicek and inverse GARCH short rate models. This paper is an extended work of \citet{“Leung2017”}. ...

A quantum double-or-nothing game: The Kelly Criterion for Spins ArXiv ID: 2308.01305 “View on arXiv” Authors: Unknown Abstract A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is accrued through astute betting. As information is gained from the stream of particles, the measurement directions are progressively adjusted, and the portfolio growth rate is raised. The optimal quantum strategy is determined numerically and shown to differ from the classical strategy, which is associated with the Kelly criterion. The paper contributes to the development of quantum finance, as aspects of portfolio optimisation are extended to the quantum realm. ...

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. ...