Basis risk includes the risk of an unfavourable change in the relationship between the price of a derivative and the market value of an underlying asset or liability being hedged.
For example resulting in a smaller profit being enjoyed on a hedging derivative, than the loss suffered on the underlying exposure.
Good hedge design therefore seeks to eliminate or minimise basis risk in the hedged position, so far as practicable.
Basis risk also arises in bank funding.
It arises when the reference rates used for the pricing of assets and their funding are different.
For example, a UK bank's mortgage assets might be priced by reference to BBR (the Bank of England's Official Bank Rate) plus a margin, while the bank's funding is priced at LIBOR (plus a margin).
The bank's net interest income depends on the differential between BBR and LIBOR.
Basis risk - in this context - means the risk of adverse changes in the differential between BBR and LIBOR. An adverse change might compress the bank's net interest income, or even result in losses.