Question

Big Bank is a community bank and its balance sheet is reported below.[1] The “total equity/total asset ratio” is 10.00 percent ($10.00/$100.00) and is a very important ratio since bank regulators will shut down a bank when there is not enough capital. Assume bank regulators require the “total equity/total asset ratio” to be at least 8.00 percent at all times and if the ratio falls below 8.00 percent, a bank is immediately shut down.

Balance Sheet (as of 12/31/2019 and in millions)
Assets Assets have a duration of 4.24 years and a yield to maturity of 6.00%.                          Total Assets         $100.00	Liabilities Liabilities have a duration of 1.03 years and a yield to maturity of 3.00%.                         Total Liabilities     $90.00
	Equity                         Total Equity           $10.00

Assume the government releases new economic numbers and there is an immediate parallel shift in the yield curve and all interest rates increase 100 basis points. This means the yield to maturity on Big’s liabilities increases 100 basis points from 3.00% to 4.00% and the yield to maturity on Big’s assets increases 100 basis points from 6.00% to 7.00. Would Big Bank’s total assets increase or decrease in value? Would Big Bank’s total liabilities increase or decrease in value? What is Big Bank’s “total equity/total asset ratio” after interest rates increase? Show your equation with the numbers. Will regulators shut down Big Bank when the interest rates increase?

Increase or decrease in value of total assets
Increase or decrease in value total liabilities
New “total equity/total asset ratio”
Show your equation with numbers
Is Big Bank shut down (yes or no)

Answer 1

	there is an immediate parallel shift in the yield curve and all interest rates increase 100 basis points. This means the yield to maturity on Big’s liabilities increases 100 basis points from 3.00% to 4.00% and the yield to maturity on Big’s assets increases 100 basis points from 6.00% to 7.00.
	Answer
	Calucutlation of volatality for the Assets and Liabilities
	Particulars	Assets	Labilities
	Volatality = Duration/1+YTM
	Duration	4.24	1.03
	1+YTM	1.06	1.03
	Volatality	4	1
	If there is change in the YTM of assets By 1% there will be adverse change in the assets by 4%
	If there is change in the YTM of Laibilities By 1% there will be adverse change in the lailities by 1%
1)	Big Bank’s total assets decrease in value
	There is the Decrease in the value of the Assets By 4%	$                96.00	+100-4%
2)	Big Bank’s total liabilities decrease in value
	There is the Decrease in the value of the Laibilities By 1%	$                89.10	+90-1%
3)	Big Bank’s “total equity/total asset ratio” after interest rates increase
	Total Equity = Total Assets - Total Laibilities
	Total Equity = 96-89.1	$                   6.90
	Total Equity/ Total Asset Ratio = $6.9/$96	7.19%
4)	Will regulators shut down Big Bank when the interest rates increase?
	Regulators will shut down Big Bank Since it has the Total asset and Total equity ratio Below 8%