Question

First National Bank Balance sheet

                              Assets            Liabilities

Rate-sensitive    $20 million         $50 million

Fixed-rate           $80 million         $50 million

4) Given the above table and assuming that the average duration of its assets is four years, while the average duration of its liabilities is three years, then a 5 percentage point increase in interest rates will cause the net worth of First National to ________ (increase/decline) by ________ (5% /10%/ 15%/ 20%) of the total original asset value (use duration analysis).

Answer 1

We use duration analysis to estimate the change in net worth. For that we make use of following formula -

Duration Gap = Average duration of Assets - ( Market value of liabilities x duration of liabilities/ market value of assets)

Here as given,

• Avg duration of assets = 4 years
• Avg.duration of liabilities = 3 years
• Total value of liabilities = 50+50=$100 million
• Total value of Assets - 20+80=$100 million

Therefore Duration gap = 4 - (100 x 3/100) = 1 year

To find change in net worth as proportion to total assets following formula is used,

Here change in r = 5%. We assume initial rate to be 10 %.

So required ratio = -1 x 0.05/(1 +0.10) = -4.5% which is approx -5%.

Note: Here we have assumed initial rate to be 10%.

Therefore the net worth of First National Bank will decline by 5 percentage of the total original asset value when interest rate increases by 5 percentage point.