3. (6 points) A bank has the following balance sheet (in millions), Its duration

Question

3. (6 points) A bank has the following balance sheet (in millions), Its duration of liabilities is 0.377 years Amount- Duration Cash Federal funds Muni Loans Total A 0 years 0.01 years 2.93 years 4 years DA 20 50 271 20 /2711 Demand deposits $100 Repos CDs 50 90 0 years 0.01 years Di-0.377 years Equity Total L &E; 271 The bank's duration of assets (DA) is Workout: The bank's duration gap (DGAP) is Hint: DGAP-DA-k*Di, where k-LA. 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?rnenese -. Workout

Explanation / Answer

1)

Assign weights to all the assets and multiply those weights with respective durations to arrive at weighted duration. The sum of these weighted durations will be equal to duration of assets

Duration of assets = (1/271) * 0 + (20/271) * 0.01 + (50/271) * 2.93 + (200/270) * 4 = 3.5043 years

2)

Duration Gap = DA - (L/A) * DL = 3.5043 - (240/271) * 0.377 = 3.1704

(L= Total L&E - Equity = 271 - 31 = $240 Mn ) and ( Assets = 271 Mn)

3) Change in networth wrt to assets is given by Change = - Duration gap * Change in rate /(1+ existing rate)

Which will be a negative value given change in rate is positive in case of an increase

Reduction net worth will be caused by an increase in interest rate.

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