Question

There are two banks, A and B. Bank A has $10 million in reserves, $70 million in loans, $70 million in checkable deposis and $10 million in bank capital. Bank B has $10 million in reserves, $70 million in lona,s $76 million in checkable deposits, and $4 million in bank capital. Suppose that for both banks the return on assets (ROA) is 1 percent. Using the dollar amounts provided, explain the safety-return tradeoff that banks face.

Answer 1

For Bank A

Reserves - $10 Mn

Assets (Loans ) - $70 Mn

Liabilities (Deposits) - $70 Mn

Capital - $10 Mn

For Bank B

Reserves - $10 Mn

Assets (Loans ) - $70 Mn

Liabilities (Deposits) - $76 Mn

Capital - $4 Mn

Clearly for both the banks, return will be same as assets are same =70*0.01 = $ 0.7 Mn

However Liabilities in case of Bank B are greater than that of Bank A. Also the Capital put up by Bank B is lesser than Bank A and hence is at more risk.

ROE (Bank A) = 0.7/10 = 7%

ROE (Bank B) = 0.7/4 = 17.5%

Leverage (Bank A) = 70/10 = 7

Leverage (Bank B) = 70/4 = 17.5

Clearly we can see that for Bank B leverage is significantly higher; hence is the ROE; so Bank B is more at risk than Bank A