Abank 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

First set are parallel, second are perpendicular, third are perpendicular, fourth are neither.

*If you can't remember the rules, or want to check your answers, I would type them into a graphing calculator. It will easily tell you which category they're in. (desmos.com)*

Step-by-step explanation:

1. Same slope (6/5) = parallel

2. Reciprocal (flipped) slope, opposite signs

3. Reciprocal (flipped) slope, opposite signs

4. Neither, the slopes aren't the same or flipped

When you flip the slopes (3/4 becomes 4/3) and change a sign, the lines will always be perpendicular.

Hope it helps :)