A bank has an average asset duration of 5 years and an average liability duration of 3 years.This bank has total assets of $500 million and total liabilities of $250 million.Currently,market interest rates are 10 percent.If interest rates fall by 2 percent (to 8 percent),what is this bank's change in net worth?
A)Net worth will decrease by $31.81 million.
B)Net worth will increase by $31.81 million.
C)Net worth will increase by $27.27 million.
D)Net worth will decrease by $27.27 million.
E)Net worth will not change at all.

Question

Quizplus · Accepted Answer

The bank's net worth will increase due to the positive gap between the duration of assets and liabilities. When interest rates fall, the value of longer-duration assets increases more than the value of shorter-duration liabilities. The change in net worth can be calculated using the formula: ΔNW = ΔR * (DA - DL) * A, where ΔR is the change in interest rates (in decimal form), DA is the duration of assets, DL is the duration of liabilities, and A is the total assets. Here, ΔR = -0.02 (since interest rates fall by 2%), DA = 5 years, DL = 3 years, and A = $500 million. Plugging these values into the formula gives an increase in net worth, which matches option B.

A Bank Has an Average Asset Duration of 5 Years