This Exam FM sample reference tests Cash-Flow and Risk Matching. Matching present value and the first moment of liability value yields current investments 223,852 in the five-year zero and 199,410 in the twenty-year zero, choice C.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the simultaneous present-value and duration-moment equations; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the simultaneous present-value and duration-moment equations; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the simultaneous present-value and duration-moment equations; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the simultaneous present-value and duration-moment equations; no distinct standard single-step error producing it is identifiable.
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
Variant answer in brief
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.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
