Despite the importance role played by Interest Rate Swaps, as in debt structuring, regulatory requirements and risk management, sounding analyzes related to the hedging of portfolios made by swaps are not clear in the financial literature. To partially fill this lack, we provide here the study corresponding to a parallel shift of the interest rate. The suitable swap sensitivities to make use in hedging and risk management are obtained here as a byproduct of our analyses. They may be seen as the analogue of the well known bond duration and convexity in the swap framework. Our present results might provide a support for practitioners, using portfolio of swaps and/or bonds, in their hedge decision-making.