Here is the balance sheet of a bank. Required reserves are 10 percent of eposits. Suppose the bank prefers not to change ROE in the face of a liquidity shock. Show that the bank prefers liability adjustment over asset adjustment when there is a sudden $10 million withdrawal of deposits. Assume that the change in ROA after asset adjustment is negligible.
Assets: Reserves $10 million, Loans $90 million, Securities $40 million
Liabilities: Deposits $100 million, Borrowed Funds $30 million, Bank Capital $10 million
a) Show that asset adjustment reduces the size of the balance sheet
b) Show that liability adjustment does not reduce the size of the balance sheet
c) Write out the definition of ROE and show that it is a fraction of ROA and leverage ratio
d) Using a,b,c and given assumptions, show that the bank prefers liability adjustment over asset adjustment for this liquidity shock.