Bank capital performs several important roles except:

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The question asks about the roles of bank capital and which option does not describe one of those roles.
Option a: 'helping to maintain public confidence and avoid bank runs in case of loan borrowers default.' This reflects a fundamental function of bank capital: higher capital levels act as a cushion that enhances confidence among depositors and markets, reducing the likelihood of runs when borrowers default. So this statement is aligned with how capital supports stability.
Option b: 'providing some protections to the depositors in case of liquidation.' Bank capital contributes to a bank’s solvency; in liquidation, capital absorbs losses before depositors, thereby offering a layer of protection. This is a recognized role of capital in protecting creditors and the integrity of the system.
Option c: 'increasing the bank's interest rate margin.' Capital does not directly determine or increase the interest rate margin. Margins are more closely related to the loan pricing, funding costs, and overall interest rate environment, while capital serves to absorb losses and support stability rather than to expand pricing power. As such, this statement mischaracterizes the function of bank capital.
Option d: 'serving as a source of funds for expansion.' Banks use their own capital alongside deposits and wholesale funding to support growth and expansion projects. While not the sole source, capital clearly plays a role in funding expansion efforts, so this is a valid function.
In summary, option a describes stability-related benefits of capital, option b describes depositor protection in liquidation, option d describes funding for growth, and option c wrongly attributes to capital an effect on interest rate margins rather than on solvency and stability. The incorrect assertion among the choices is the one about increasing the bank's interest rate margin, which confuses cost of capital with pricing power.

Bank capital performs several important roles except:

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