A bank has three assets. It has $75 million invested in consumer loans with a three-year duration, $39 million invested in T-bonds with a 16-year duration, and $18 million in six-month maturity T-bills. What is the duration of the bank's asset portfolio in years?

A. 6.50 years

B. 7.38 years

C. 11.51 years

D. 3.95 years

E. 4.83 years

A. 6.50 years

Explanation:

Let C represent consumer loans,

T represent T-bonds and

t represent T-bills

Portfolio duration = wC*dC + wT*dT + wt*dt

w = weight of ...

d = duration of ...

Find the weights;

Total amount invested = 75 + 39 + 18 = 132 mill

wC = 75 / 132 = 0.5682

wT = 39 / 132 = 0.2955

wt = 18 / 132 = 0.1364

Portfolio duration = (0.5682*3) + (0.2955*16) + (0.1364*0.5)

= 1.7046 + 4.728 + 0.0682

= 6.50 years