Answer the simple finance related question. Disregard writing on page. 3. (6 poi

Question

Answer the simple finance related question. Disregard writing on page.
3. (6 points) A bank has the following balance sheet (in millions). Its duration of liabilities is 0.377 years. Cash Federal funds Muni S1 20 50 Duration 0 years 0.01 years 2.93 years 4 years Total A 271 Liahilities &equity; Amount Duration Demand deposits S100 Repos CDs 0 years 0.01 years 50 90 De 0.377 years 00/ 2 7 / $31 271 Total L &E; The bank's duration of assets (DA) is Workout: The bank's duration gap (DGAP) is Hint: DGAP-DA-k" DL, where k=L/A. Workout: 3,56 The bank's net worth (i.e., market value of equity) is exposed to interest rate risk. Given the calculated duration gap, will an increase or decrease in interest rate cause a reduction in net worth? Incense

Explanation / Answer

1.

The bank's duration of assets DA = 3.49

Working:

2.

The bank's DGAP is 3.15

DGAP = DA - k*DL = 3.49 - 0.89*0.377 = 3.49 - 0.34 = 3.15

k = L/A, Where L=Total liabilities , A = Total assets.  

k = 241 / 271 = 0.89

3. Increase.

"When the duration of assets is larger than the duration of liabilities, the duration gap is positive. In this situation, if interest rates rise, assets will lose more value than liabilities, thus reducing the value of the firm's equity."

Assets Value Duration Weighted ($million) A B (A x B) Cash           1.00                -                  -   Federal funds         20.00           0.01           0.20 Muni         50.00           2.93      146.50 Loans      200.00           4.00      800.00      271.00      946.70 Weighted average = 946.7/271 3.49

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