b. Duration of Bank\'s Assets and Liabilities. Gap analysis and Duration gap ana

Question

b. Duration of Bank's Assets and Liabilities. Gap analysis and Duration gap analysis ? Interest rate rise from 11% to 15% To compute the income Amount (S milions Durstion CYear) Weighted Duratienear) Cash and Deposits Securities 0.0 0.0000 Less than 1 year 1 to 2 years Greater than 2 years 0.7 1.5 8.5 0.0382 0.0273 .2318 Consumer loans Less than 1 years 1 to 2 years Great than 2 years 0.7 2.0 2.5 0.0 0.3500 0.2727 0.4545 0.0000 15 20 Physical Capital 3745 Average Duration 04 0.1714 Commercial paper Bank loans Less than 1 year 1 to 2 years Greater than 2 years 0.6 1.5 4.0 6.0 0.0286 0.0429 02667 0.5714 .0810 45 Long-term bonds and other long-term debt Average Duration

Explanation / Answer

Duration gap analysis is used for measuring intrest rate risk.

DURgap = DURa - ((L/A) × DUR l)

Where DURgap = Duration gap

DURa = Average duration of assets =1.3745

DURl = Average duration of liabilities = 3.0810

L = Market value of liabilities = $105 mn

A= Market value of assets = $110 mn

Thus putting all values in the formula of duration gap we find

DURgap = 1.3745 - ((105/110) × 3.0810) = -1.5664 yrs

Since it has negative duration gap, it means that a rise in interest rate by 4% will increase the market value of net worth of the firm.

Now calculating the change in the market value of the assets and liabilities.

We use the formula,

% Change in market value of the security = -DUR × (Change in intrest rate (I)/ 1+I)

WHere DUR =Average Duration of assets = 1.3745

I = intrest rate = 11% = 0.11

Change in intrest rate = 0.15 - 0.11 = 0.04

Thus putting all values in the formula we get

% Change in Market value = - 1.3745 × (0.04/(1+0.11)) = -0.055 = - 5.5%

With a total assets of $110 million, the market value of assets fall by $5 million ( $110 million × 0.05 = $5.5 million.

Now,

% Change in market value = - DUR × (Change in intrest rates/ (1+ I))

Where DUR = Average duration of liabilities =3.0810

Chnage in intrest rate = 0.15-0.11 = 0.04

Intrest rate = 0.11

Thus putting all the values in the formula we get,

% change in Market value = -3.0810 × (0.04/(1+0.11)) = -0.11102 = -11.1027 %

Thus with total liabilities of $105 million, the market value of liabilities falls by 11.10 million.

So, the net worth of the bank would rise by

= - 5.5 - (-11.10) = $5.6 million

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