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Question 21 What is the Duration Gap for the bank balance sheet shown below? Assets Amount...


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

Solutions

Expert Solution

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


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