Question

Question 21

What is the Duration Gap for the bank balance sheet shown below?

Assets	Amount	Duration		Liabilities and Equity	Amount	Duration
Cash	80	0.00		Non-interest deposits	150	0.00
Securities	300	4.00		NOW checking	150	1.50
Loans, net	570	5.00		MMDA	300	0.25
Fed funds sold	0			CDs	170	2.00
Non-earning assets	50			Fed Funds purchased	150	0.00
	$1,000			Equity	80
					$1,000

	A.	3.41 years
	B.	4.05 years
	C.	3.35 years
	D.	5.25 years
	E.	0.70 years

Answer 1

Solution :

The Duration gap is calculated using the formula

Duration Gap = DA – [ (L/A) * DL]

Where

DA =Average duration of Assets ;    DL = Average duration of Liabilities

L = Total Value of Liabilities ; A = Total value of assets

As per the information given in the question we have

L = Total Value of Liabilities and Equity – Value of equity

= $ 1,000 - $ 80 = $ 920

A = Total value of assets = $ 1,000     ;

Calculation of DA =Average duration of Assets

= Summation of ( Value of each asset * Duration ) / Total value of assets

= [ ( $ 80 * 0) + ( $ 300 * 4 ) + ( $ 570 * 5 ) + ( $ 0 * 0 ) + ( $ 50 * 0 )] / $ 1,000

= [ 0 + $ 1,200 + $ 2,850 + 0 + 0 ] / $ 1,000

= $ 4,050 / $ 1,000

= 4.050

Calculation of DA =Average duration of Liabilities

= Summation of ( Value of each Liability * Duration ) / Total value of liabilities

= [ ( $ 150 * 0) + ( $ 150 * 1.50 ) + ( $ 300 * 0.25 ) + ( $ 170 * 2 ) + ( $ 150 * 0 )] / $ 920

= [ 0 + $ 225 + $ 75 + 340 + 0 ] / $ 920

= $ 640 / $ 920

= 0.6957

Applying the above information in the formula we have

= 4.0500 – [ ( 920 / 1000) * 0.6957]

= 4.0500 – [ 0.9200 * 0.6957 ]

= 4.0500 – 0.6400

= 3.4100

Thus the Duration Gap for the bank balance sheet = 3.41 years

The solution is Option A = 3.41 Years