The paper proposes a forward market for the hedging of loss-related risk within a Locational Marginal Pricing (LMP) framework. The necessity for hedging losses arises from the volatility in the cost of marginal losses for electricity transactions, and from the surplus of loss-related revenues collected by the ISO under LMP. The hedging instruments proposed here, like FTRs for hedging congestion risk, simultaneously serve as a market-based mechanism for distributing the revenue surplus. The total loss hedging value for the entire market is shown to by the ISO. Formulas are derived for combined exactly equal the marginal loss related surplus collected by the ISO. Formulas are derived for combined congestion and loss hedging.