Original practice · fully worked
Original variant: determine a liability portfolio's target duration
A foundation owes 200,000 in eight years and 300,000 in twelve years. Using a constant annual force of interest of 5%, determine the Macaulay duration that an immunizing asset portfolio must match.
- A
9.205 - B
9.705 - C
10.205 - D
10.705 - E
11.205
Answer and calculation
The present-value-weighted average of years 8 and 12 is 10.205 years, choice C.
Setup
Setup
Discount each liability at the constant force to obtain its current-value weight.
PL=200000e−0.05(8)+300000e−0.05(12)=298707.50 Model
Model
Multiply each present value by its payment time to form the first moment.
ML=8(200000)e−0.4+12(300000)e−0.6 Compute
Compute
Dividing that moment by total liability value gives 10.204745 years.
DL=PLML=10.204745 Answer
Answer
An immunizing asset portfolio must match duration 10.205 years, corresponding to choice C.
DL=10.205 years(C) 