Managing Interest Rate Risk: Duration GAP and Economic ...

[Pages:29]Managing Interest Rate Risk(II): Duration GAP and Economic Value of Equity

Measuring Interest Rate Risk with Duration GAP

Economic Value of Equity Analysis

Focuses on changes in stockholders' equity given potential changes in interest rates

Duration GAP Analysis

Compares the price sensitivity of a bank's total assets with the price sensitivity of its total liabilities to assess the impact of potential changes in interest rates on stockholders' equity.

Duration GAP

Duration GAP Model

Focuses on either managing the market value of stockholders' equity The bank can protect EITHER the market value of equity or net interest income, but not both Duration GAP analysis emphasizes the impact on equity

Compares the duration of a bank's assets with the duration of the bank's liabilities and examines how the economic value stockholders' equity will change when interest rates change.

Steps in Duration GAP Analysis

Forecast interest rates. Estimate the market values of bank assets,

liabilities and stockholders' equity. Estimate the weighted average duration of

assets and the weighted average duration of liabilities.

Incorporate the effects of both on- and offbalance sheet items. These estimates are used to calculate duration gap.

Forecasts changes in the market value of stockholders' equity across different interest rate environments.

Weighted Average Duration of Bank Assets

Weighted Average Duration of Bank Assets (DA)

n

DA wiDai i

Where

wi = Market value of asset i divided by the market value of all bank assets

Dai = Macaulay's duration of asset i n = number of different bank assets

Weighted Average Duration of Bank Liabilities

Weighted Average Duration of Bank Liabilities (DL)

m

DL zjDlj j

Where

zj = Market value of liability j divided by the market value of all bank liabilities

Dlj= Macaulay's duration of liability j m = number of different bank liabilities

Duration GAP and Economic Value of Equity

Let MVA and MVL equal the market values of assets and liabilities, respectively.

If: EVE MVA MVL

and

Duration GAP

DGAP DA - (MVL/MVA)DL

Then:

EVE

-

DGAP

y (1 y)

MVA

where y = the general level of interest rates

To protect the economic value of equity against any change when rates change , the bank could set the duration gap to zero:

Hypothetical Bank Balance Sheet

1

Par

Years

Market

$1,000 % Coup Mat. YTM Value

Assets

Cash

$100

$ 100

Earning assets

3-yr Commercial loan

$ 700 12.00% 3 12.00% $ 700

84 6-yr Treasury bond Total Earning Assets

1

Non-cash earning

Total assets D

a(1ss.1et2s)1

$

$

$

(2981-004.0012)228.00%(184.126)33

$ 1,000

1(7181..010.1010%%2)33$$$

200 900 -

10.00% $ 1,000

700

Liabilities

Interest bearing liabs.

1-yr Time deposit

$ 620 5.00% 1

5.00% $ 620

3-yr Certificate of deposit $ 300 7.00% 3

7.00% $ 300

Tot. Int Bearing Liabs. $ 920

5.65% $ 920

Tot. non-int. bearing

$ -

$ -

Total liabilities

$ 920

5.65% $ 920

Total equity

$ 80

$ 80

Total liabs & equity

$ 1,000

$ 1,000

Dur.

2.69 4.99 2.88

1.00 2.81 1.59

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