This Exam FM sample reference tests Redington Immunization Weights. Solving the system gives A = 48,259 and B = 47,630. Therefore A/B = 1.0132. The result agrees with the published answer key, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (0.7307) does not match the checked redington immunization weights result (1.0132); no distinct standard one-step error is identifiable.
BChoice B (0.9670) does not match the checked redington immunization weights result (1.0132); no distinct standard one-step error is identifiable.
CChoice C (1.0000) does not match the checked redington immunization weights result (1.0132); no distinct standard one-step error is identifiable.
EChoice E (1.3686) does not match the checked redington immunization weights result (1.0132); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: face-amount ratio after dollar-duration matching
A liability has present value 200,000 and Macaulay duration 6. Asset A is a four-year zero priced at 0.90 per unit of face; Asset B is a nine-year zero priced at 0.80 per unit. Find the ratio of face amount in A to face amount in B that matches value and duration.
A 0.8889
B 1.0667
C 1.2000
D 1.3333
E 1.5000
Variant answer in brief
The market values are 120,000 and 80,000. Converting each to face amount gives a ratio of 1.3333. The face-amount ratio is 1.3333, corresponding to choice D.
Setup
Setup
First solve for current market values X and Y; duration weights market value, not face amount.
X+Y=200000,4X+9Y=6(200000)
Model
Model
Value and dollar-duration matching give a two-equation system with asset durations 4 and 9.
X=120000,Y=80000
Compute
Compute
The market values are 120,000 and 80,000. Converting each to face amount gives a ratio of 1.3333.
FBFA=Y/0.80X/0.90=1.333333
Answer
Answer
The face-amount ratio is 1.3333, corresponding to choice D.
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.
