A bank has three assets. It has $75 million invested in consumer loans with a 3-year duration, $39 million invested in T-Bonds with a 16-year duration, and $39 million in 6-month maturity T-Bills. What is the duration of the bank's asset portfolio in years?

Question

Quizplus · Accepted Answer

To find the duration of the bank's asset portfolio, we need to weight the duration of each asset by the proportion of the total value it represents. We can calculate the proportion of total value for each asset by dividing its value by the total value of all assets:

Consumer loans: $75 million / ($75 million + $39 million + $39 million) = 975/1320 
T-Bonds: $39 million / ($75 million + $39 million + $39 million) = 39/132 
T-Bills: $39 million / ($75 million + $39 million + $39 million) = 39/132

Then, we can calculate the weighted average duration by multiplying each asset's proportion by its duration in years:

(975/132) x 3 + (39/132) x 16 + (39/132) x 0.5 = 6.50

Therefore, the answer is C.

A Bank Has Three Assets