Accurate day-ahead demand forecasting is crucial for optimizing the performance of home energy management systems. Traditional forecasting methods often decouple the forecasting task and the subsequent decision marking, resulting in imbalanced economic penalties from load deviations. Furthermore, the rise of digitization has led to a massive increase in fine-grained smart meter data stored daily, posing significant challenges to customers' data privacy and security. To address these technical challenges, this study proposes a personalized federated learning methodology that incorporates a cost-oriented loss function. This methodology is designed to learn end-user-specific patterns, reduce penalization costs, and preserve customer privacy. Comparative analyses reveal that the proposed method, which utilizes a cost-oriented loss function and L2 regularization, outperforms traditional symmetric loss functions in terms of efficiency and economic benefits. The results confirm that this personalized federated learning approach consistently achieves the lowest error rates and penalization costs compared to other methods. Additionally, sensitivity analyses indicate that even households with limited historical consumption data can achieve accurate load predictions using the personalized federated learning approach.