A bank has $100 million of investment grade bonds with a duration of 9.0 years.This bank also has $500 million of commercial loans with a duration of 5.0 years.This bank has $300 million of consumer loans with a duration of 2.0 years.This bank has deposits of $600 million with a duration of 1.0 year and non-deposit borrowings of $100 million with an average duration of .25 years.What is this bank's duration gap? These are all of the assets and liabilities this bank has.
A)This bank has a duration gap of 14.75 years.
B)This bank has a duration gap of 15.03 years.
C)This bank has a duration gap of 3.55 years.
D)This bank has a duration gap of 3.75 years.
E)This bank has a duration gap of 5.15 years.

Question

Quizplus · Accepted Answer

The duration gap is calculated as the weighted average duration of assets minus the weighted average duration of liabilities. For assets: $$ (100 \times 9) + (500 \times 5) + (300 \times 2) = 900 + 2500 + 600 = 4000 $$ Total assets = $900 million, so weighted average duration of assets = $ \frac{4000}{900} = 4.44 $ years. For liabilities: $$ (600 \times 1) + (100 \times 0.25) = 600 + 25 = 625 $$ Total liabilities = $700 million, so weighted average duration of liabilities = $ \frac{625}{700} = 0.89 $ years. Duration gap = 4.44 - 0.89 = 3.55 years.

A Bank Has $100 Million of Investment Grade Bonds with a Duration