Title: Semi-Variance Reduction for Fair Federated Learning. Abstract: Ensuring fairness in Federated Learning (FL) systems, i.e. ensuring a satisfactory performance for all of the diverse clients in the systems, is an important and challenging problem. There are multiple fair FL algorithms in the literature, which have been relatively successful in providing fairness. However, these algorithms mostly emphasize on the loss functions of worst-off clients to improve their performance, which often results in the suppression of well-performing ones. As a consequence, the system's overall average performance is usually sacrificed for achieving fairness. Motivated by this and inspired by two well-known risk modeling methods in Finance, Mean-Variance and Mean-Semi-Variance, we propose and study two new fair FL algorithms, Variance Reduction (VRed) and Semi-Variance Reduction (Semi-VRed). VRed encourages equality between clients loss functions by penalizing their variance. In contrast, Semi-VRed penalizes the discrepancy of only the worst-off clients loss functions from the average loss. Through extensive experiments on multiple vision and language datasets, we show that, Semi-VRed achieves SoTA performance in scenarios with highly heterogeneous data distributions by improving both fairness and the system overall average performance at the same time.