The accounting term Hedge relationship relates to the treatment of an insurance contract for risk mitigation on an underlying asset, and the set of tests for the valuation of this insurer/insuree contract.
[1] More specifically, "Hedge relationship" describes the criteria for including the fair value of derivatives on balance sheet as part of an effort to regulate and normalize the use of hedging in corporate accounting.
The context: These contracts are valuable to a company and standardized means of including their fair value on corporate balance sheets is of interest to lenders and investors.
For companies operating outside of the financial services sector an effective hedge should protect against undue loss without being a major component of company income statements.
Testing must be performed on both elements of the hedge relationship to ensure that the risk mitigation value of the hedge would be effectively reflected in the insurees profit and loss ledger.