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A recent study, Determining Optimal Trading Rules Without Backtesting, challenges the conventional reliance on backtesting for optimizing trading strategies. The paper argues that overfitting in backtesting can lead to misleadingly strong performance during testing but poor real-world results. To address this issue, the study proposes a new methodology for determining Optimal Trading Rules (OTR) without backtesting.

Instead of using a backtesting engine, the methodology builds on alternative modeling techniques and presents empirical evidence that an optimal solution exists when prices follow a discrete Ornstein-Uhlenbeck (O-U) process. The study then demonstrates how to numerically compute this optimal trading rule.

Methodology

The proposed OTR framework follows these steps:

1. Price Process Modeling: Assumes that asset prices follow a discrete Ornstein-Uhlenbeck (O-U) process, which exhibits mean-reverting properties, meaning prices tend to revert to a long-term average.

2. Model Parameter Estimation: Estimates key parameters of the O-U process (e.g., mean reversion speed, volatility) using historical price data.

3. Profit and Loss Targets: Defines stop-loss and profit-taking levels with various combinations.

4. Monte Carlo Simulation: Simulates price trajectories using the estimated parameters and applies different stop-loss and profit-taking rules to calculate returns.

5. Sharpe Ratio Optimization: Computes the Sharpe ratio for each combination and selects the trading rule that maximizes risk-adjusted returns as the optimal strategy.

Key Findings & Case Studies

The study’s primary contribution is demonstrating that optimal trading rules can be derived without backtesting under certain market conditions. Specifically, when prices follow an O-U process, selecting specific stop-loss and profit-taking levels leads to an optimal strategy.

1. Case: Long-Term Equilibrium at Zero (Market Makers)

• This scenario represents liquidity providers such as market makers.

• When the half-life of mean reversion is short (i.e., prices revert quickly), the optimal strategy is to use tight profit-taking levels and wider stop-loss levels.

• This approach secures small but frequent gains while tolerating temporary losses.

• The model shows that in this case, the Sharpe ratio can reach up to 3.2, indicating strong risk-adjusted returns.

2. Case: Long-Term Equilibrium Above Zero (Hedge Funds & Asset Managers)

• This scenario applies to investors holding long-term positions.

• Since positions have a higher probability of being profitable, the profit-taking threshold is set higher compared to market makers.

3. Case: Long-Term Equilibrium Below Zero (Risk-Averse Traders)

• This scenario applies to traders aiming to minimize losses and exit positions quickly.

• The strategy prioritizes early exits on losing trades to protect capital.

For each scenario, the study visualizes the Sharpe ratio across different stop-loss and profit-taking levels using heat maps, enabling traders to intuitively identify the optimal trading rule based on market conditions.

This research presents a novel approach to avoiding backtesting overfitting and developing more robust trading strategies. While it was previously assumed that backtesting was necessary for optimizing trading rules, this study demonstrates that under certain conditions, an optimal strategy can be determined theoretically.

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