This paper introduces the Mean Absolute Directional Loss (MADL) function, a novel loss metric designed for optimizing machine learning models in algorithmic investment strategies (AIS). Unlike classical loss functions such as MAE or RMSE, which penalize forecast errors regardless of direction, MADL directly measures the profit or loss from a trading signal by comparing the sign and magnitude of predicted returns against realized returns. The function is defined as the average of the negative product of the sign of the product of realized and predicted returns and the absolute realized return, making it directly aligned with the goal of maximizing trading profits. The authors argue that this alignment leads to better hyperparameter selection and model estimation for AIS.

The empirical validation uses an LSTM model with a walk-forward testing procedure on daily simple returns of Bitcoin and Crude Oil (USO ETF) from 2013 to 2021. Four combinations of loss functions for hyperparameter tuning and model estimation are compared: MADL/MADL, MADL/MAE, MAE/MAE, and MAE/MADL. Results consistently show that the MADL/MADL approach outperforms all other combinations across multiple risk-adjusted performance metrics (IR*, IR**, IR***) for both assets. For Bitcoin, MADL/MADL achieves an annualized return of 109.94% with a maximum drawdown of 75.04%, while for Crude Oil it yields a positive return of 5.25% compared to a -10.59% loss for Buy & Hold. Regression tests confirm a significant positive alpha for the MADL/MADL strategy on Bitcoin. The paper concludes that MADL is a more appropriate loss function for AIS and suggests future extensions such as squared penalization to address large losses.