THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 369
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CHAPTER 13
A PP LI CATI O N
Banking and the Management of Financial Institutions
337
Duration Analysis
Suppose that a bank s average duration of assets is 2.70 years and its average duration of liabilities is 1.03 years. The bank manager wants to know what happens
when interest rates rise from 10% to 11%. The total asset value is $100 million, and
the total liability value is $95 million. Use Equation 4 to calculate the change in the
market value of the assets and liabilities.
Solution
With a total asset value of $100 million, the market value of assets falls by
$2.5 million ($100 million * 0.025 $2.5 million).
%*P
where
DUR
i
i
duration
change in interest rate
interest rate
DUR
0.11
0.10
*i
1
i
2.70
0.01
0.10
Thus
%*P
0.01
1 0.10
2.70
0.025
2.5%
With total liabilities of $95 million, the market value of liabilities falls by $0.9 million
($95 million * 0.009
$0.9 million).
%*P
where
DUR
duration
i
change in interest rate
i
interest rate
Thus
%*P
1.03
DUR
0.11
0.10
1
0.01
0.10
*i
1
i
1.03
0.01
0.10
0.009
0.9%
The result is that the net worth of the bank would decline by $1.6 million
( $2.5 million [ $0.9 million]
$2.5 million $0.9 million
$1.6 million).
