Final answer:
The risk in the statement indicating a bank's potential inability to meet its payment obligations is known as 'Liquidity Risk.' It can occur during scenarios like bank runs or when a mismatch between the repayment timelines of assets and liabilities exists.
Step-by-step explanation:
The type of risk described by the statement "the potential inability of a bank to meet its payment obligations in a timely and cost-effective manner" is Option 3: Liquidity Risk. Liquidity risk occurs when a financial institution like a bank cannot meet its short-term financial demands without incurring substantial losses. This can happen, for example, when many depositors withdraw their funds simultaneously, a scenario often referred to as a bank run. In such cases, if the bank's assets, such as loans and bonds, are tied up for long periods and cannot be quickly converted to cash without significant loss, the bank faces severe liquidity problems. The situation is exacerbated if the bank faces higher interest rates and must decide between raising the rates it pays to depositors, causing possible negative cash flows, or losing its depositor base to competitors offering higher rates.