THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 370
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338
PA R T I V
The Management of Financial Institutions
The bank manager could have gotten to the answer even more quickly by first calculating what is called a duration gap, which is defined as follows:
DURgap * DURa + a
where
L
, DURl b
A
(5)
DURa * average duration of assets
DURl * average duration of liabilities
L * market value of liabilities
A * market value of assets
Then, to estimate what will happen if interest rates change, the bank manager
uses the DUR gap calculation in Equation 4 to obtain the change in the market value
of net worth as a percentage of total assets. In other words, the change in the market value of net worth as a percentage of assets is calculated as
NW
i
* - DURgap *
A
1 + i
APP LI CAT IO N
(6)
Duration Gap Analysis
Based on the information provided in the previous Application, use Equation 5 to
determine the duration gap for the First Bank and then use equation 6 to determine the change in the market value of net worth as a percentage of assets if interest rates rise from 10% to 11%.
Solution
The duration gap for First Bank is 1.72 years.
DURgap = DURa + a
where
DURa * average duration of assets
L * market value of liabilities
A * market value of assets
DURl * average duration of liabilities
*
*
*
*
L
, DURl b
A
2.70
95
100
1.03
Thus
DURgap * 2.70 + a
95
, 1.03 b * 1.72 years
100
Hence, a rise in interest rates from 10% to 11% would lead to a change in the market value of net worth as a percentage of assets of +1.6%
NW
i
* + DURgap ,
A
1 + i
