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In order to guard forward contracts from the locational marginal price (LMP) volatility, financial transmission rights (FTRs) are issued in the centralized power markets. However, the current FTR system can provide hedge only against the congestion components of LMP differentials. Consequently, the loss components remain unhedged. To bridge the gap, a framework is developed in this paper to implement an FTR system that will provide hedge against the loss prices. The availability of loss-hedging FTRs in addition to the congestion hedging FTRs further reduces the exposure of the forward market participants to the LMP volatility. The loss-hedging framework developed is carefully designed to fit the practical environment. All the primary issues for the implementation of loss-hedging FTRs, such as the revenue adequacy test, auction, and auction revenue rights, are carefully addressed. Revenue adequacy of loss-hedging FTRs can be ensured by means of a test called as the offset capacity test. Some efficient policies are also designed for the successful functioning of loss-hedging FTRs. At the end of the paper, a case study is carried out to assess the effectiveness of the methodology developed.