Managing Interest Rate Risk
Higher interest rates also affect the value of fixed-rate assets and liabilities on the books of the bank and
thus its net worth.
The market value of longer-term assets and liabilities is more profoundly affected by changes in interest
In order to assess the effect of changes in interest rates on a bank’s net worth we need to develop
measures of asset and liability average (weighted) duration.
A measure of net duration is then used to assess how the bank’s net worth responds to changes in interest
In general, the following relationship between changes in interest rates and changes in the measure of net
%△ net worth = - (△ i %) x (DU R) where: DU R represents net duration.
Average duration is a weighted average of individual durations.
The weights reflect the percentage of total assets or total liabilities to third parties that each asset or
i 5%, and the duration of bank assets is 5 years while the duration of liabilities is 3 years.
DU R for the bank is 2 years
% △net worth = -5% x 2 = -10% of total assets (i.e. $10 million).
This is broken down as follows –5 x 5 = -$25 million (decline in asset value)
3 x -5 = -$15 million (decline in liabilities)
For a net decline of $10 million in the bank’s net worth.
It is clear that an increase in the measure of net duration makes the bank more susceptible to changes in
While there are different measures of duration, the principal one is the so-called Macauley duration, which is
calculated as follows:
N cP t
t = time until cash payment is made
cP = Cash payment (interest plus principal) at time t.
i = interest rate (yield to maturity)