Question

4. ) Stillwater Bank reports an average asset duration of 3.25 years and an average liability duration of 1.75 years. Liabilities are $485 million, while assets total $512 million. Suppose that interest rates are 6% but rise to 7.5%. What will happen to Stillwater's net worth if interest rates rise?

Answer 1

When the interest rate increases the bank would like have short term assets and long term liabilities, so that they can earn quick money.

But in this case, due to the increase in the interest rate the net worth of the bank will decrease. This is shown by duration analysis.

Duration analysis:

% ∆ in market value = - %∆ in interest × duration

If interest rate changes by 1.5% i.e (7.5% - 6%)

Asset = -%∆interest rate × duration

= -1.5% × 3.25years

= -4.875%

Change in Asset= -4.875% × $512 million= ($24.96 million)

Liabilities = -%∆interest rate × duration

= -1.5% × 1.75

= -2.625%

Change in liabilities= -2.625% × $485 million = ($12.73 million)

As the value of asset decreases more than that of liabilities, the net worth decreases.

Net worth = Chanhe in asset - change in liabilities

= - $24.96 million - (-$12.73 million)

= -$24.96 million + $12.73 million

= -$12.23 million

Therefore the total net worth decreases by -%12.23 million due to rise in interest rates.