If lines of credit and others off balance sheet activities do not, by definition, directly affect the balance sheet, how can they influence the level of liquidity risk to which the bank is exposed?
Like your personal line of credit on your credit card, a bank can borrow against their rating for quick access to cash. Any money that is borrowed vs. directly spent is not a bottom-line issue until the bill comes due. At that point, the credit becomes debt and is added to the bottom line. It is considered "liquid" because it can be drawn on at any time; the only limiting factor is current debt.
This question seems to be all about access to income. If a bank has many different ways to access income through lines of credit and other such resources, then they face less risk than if they do not have access to income through different ways.
I find # 4's answer intriguing. From what I understand, one of the major reasons for the financial crisis of 2008 was that credit suddenly dried up, not only for individual borrowers but for institutional borrowers, such as banks. Again, as I understand it, part of the problem was that no bank really had any clear idea of the obligations faced by other banks to which they might consider lending. This massive uncertainty paralyzed the credit system, especially the system of banks loaning to banks.
Essentially the closing of these lines of credit is the root of just about every major financial crisis this country has ever had. When it happens, banks have historically had to put their investment portfolios on the market, which causes their assets to depreciate.
Are we talking about lines of credit that the bank has for itself or lines of credit that it extends to others?
If these are the bank's own lines of credit, the less they have of such things, the more liquidity risk they might face. If they have many lines of credit available to them, they have more ways of getting cash when needed.