Assume a bank has $200 million of assets with a duration of 2.5, and $190 million of liabilities with a duration of 1.05. If interest rates increase from 5 percent to 6 percent, the net worth as a percentage of assets would ________ by approximately ________.

Question

Quizplus · Accepted Answer

To calculate the change in net worth as a percentage of assets, we need to use a duration gap analysis. The duration gap is the difference between the durations of assets and liabilities. In this case, the duration gap is 2.5 - 1.05 = 1.45 years.

The formula to estimate the change in net worth as a percentage of assets is:
Change in NW/Assets = - Duration Gap x Change in Interest Rates x (Net Worth + Assets/2)

Plugging in the numbers, we get:
Change in NW/Assets = -1.45 x 0.01 x (200 + 190)/2 = -1.38%

Since the answer is negative, the net worth as a percentage of assets would decrease by approximately 1.4% if interest rates increase from 5% to 6%. Therefore the correct answer is D.

Assume a Bank Has $200 Million of Assets with a Duration