Why is common stock included in bank capital? Capital represents the loss-absorbing capacity of a bank. I do not understand how shares issued in the past provide any indication of a bank's loss-absorbing capacity. I understand that common equity does not carry with it an obligation to repay, but it is not like banks can "draw down" on the value of its outstanding share in the event it experiences severe losses.
Equity/stock/capital does absorb losses. Here is a stylized example:

Ann creates a new bank. She puts in \$100 of her own money. This \$100 is her equity/stock/capital.

She borrows another \$900 (debt). (For simplicity we'll assume that all debt/loans have an interest rate of 0%.)

She has a total of \$1,000. She lends all of it to Bob.

A little later, Bob is able to repay only \$925. So, \$75 was lost on this loan.

This \$75 loss is entirely absorbed by the equity/stock/capital, which now falls from \$100 to \$25.