Question

3. Give an example of a bank balance sheet with a leverage ratio of 10. If the value of the bank’s assets rises by 5 percent, what happens to the value of the owners’ equity in this bank? How large a decline in the value of bank assets would it take to reduce this bank’s capital to zero?

please refer from the textbook MACROECONOMICS by N Gregory Mankiw

Answer 1

Solution:

3.

The leverage ratio is ratio of book value of core capital to total assets,

where

core capital = book value of equity + qualifying cumulative perpetual preferred stock + minority interests

Assuming that bank has only equity with no preferred stock and minority interests, then leverage ration is given by:

for leverage to be 10, ratio between equity and total assets should be 2:1.

Bank Balance Sheet
Assets	Liabilities & Net Worth
Reserves 20,000	Deposits 70,000
Loans                           50,000	Debt 20,000
Securities 30,000	Capital 10,000

In the above table,

Total Assets = 100,000.

Capital = 10,000

then

Leverage = 10.

If bank assets increase by 5%, to maintain constant leverage, owner's equity should increase in same proportion i.e. by 5%.

Bank Assets should decline by 10% (i.e 10,000) to reduce bank's capital to zero.