Question

Assets Market Value Rate Duration Cash 40,000 160,000 0% 1.8 Bonds 7.50% 3 Commercial Loans 13 % 400,000 Liabilities and Equity Small Time Deposit Large CD's 3.10 % 5.20% 2 100,000 120,000 1.5 Transactions Accour 320,000 2.40 % Equity 60,000 38. Calculate the Bank Duration Gap 39. Calculate the Change in the Banks Economic Value of Equity when interest rates decrease by 1 %. 40. Explain why the Economic Value of Equity changed when interest rate decreased by 1 %

Answer 1

38) Duration GAP = Duration of the Assets - Duration of the Liabilities

Duration GAP = 2.48 - 1.3 =1.18

Assets	Market Value	Duration	Weighted Duration
Cash	40,000	0.00	0
Bonds	1,60,000	1.80	0.48
Commercial Loans	4,00,000	3.00	2
Total Assets	6,00,000		2.48
Liabilities
Small Time Deposits	1,00,000	2.00	0.37
Large CDs	1,20,000	1.50	0.33
Transactions Accounts	3,20,000	1.00	0.59
Total Liabilities	5,40,000		1.30

39) If interest rate decreases by 1%

Total Assets = 600,000

Total Liabilities = 540,000

% Change in asset = - Duration * (%change in interest rate / 1+ interest rate)

% Change in asset = - 2.48 * (-0.1 / 1.1)

% Change in asset = 2.25%

% Change in liabilities = - Duration * (%change in interest rate / 1+ interest rate)

% Change in liabilities = - 1.3 * (-0.1 / 1.1)

% Change in liabilities = 1.18%

New Assets = 600,000 * 1.0225 = 613,500

New Liabilities = 540,000 * 1.0118 = 546,372

Change in equity = Change in Assets - Change in Liabilities = 7,128

40) Economic value of equity changes with change in interest rate because with every change of interest there is change in outflows or inflows of a bank as mots of there assets and liabilities are interest interest bearing. So any change in interest rate directly impact on the inflows and outflows results into change in equity.