Financial mathematics · portfolio risk diagnostic PDF
Exam FM Duration & Immunization: 30 Worked Problems
Turn Macaulay duration, modified duration, convexity, Redington conditions, and cash-flow matching into repeatable exam decisions.
One-time USD 19 purchase for a personalized PDF. The 30 original variants are also included in the complete Financial Mathematics Proof Manual; choose this focused diagnostic for curated practice and a lower entry price.
- New practice problems
- 30
- Pages
- 76
- Time limit
- 150 min
- Price
- $19
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One original Exam FM practice question with full solution
A liability has present value 100, Macaulay duration 5, and convexity 32 at the valuation yield. Which candidate asset portfolio satisfies the Redington value, duration, and strict convexity conditions at that yield?
- PV 98; duration 5; convexity 35
- PV 100; duration 4.8; convexity 36
- PV 100; duration 5; convexity 35
- PV 100; duration 5; convexity 30
- PV 102; duration 5; convexity 40
Only candidate C matches both 100 and 5 and has convexity 35, which is greater than 32. Candidate C is the locally immunized portfolio.
Setup
Write the three local Redington requirements before inspecting the candidates: equal value, equal duration, and strictly greater asset convexity.
Model
A candidate fails if even one of the three quantities misses its required relation.
Compute
Only candidate C matches both 100 and 5 and has convexity 35, which is greater than 32.
Answer
Candidate C is the locally immunized portfolio.
Why the other choices are wrong
- A
- Choice A matches duration and exceeds liability convexity but is underfunded by 2.
- B
- Choice B matches value and exceeds convexity but its duration is short by 0.2.
- D
- Choice D matches value and duration but asset convexity 30 is below liability convexity 32.
- E
- Choice E has sufficient convexity and matching duration but exceeds the liability present value by 2.
Independent answer check
| Primary value | candidate C |
|---|---|
| Primary method | Apply all three Redington conditions to the candidate table. |
| Independent value | candidate C |
| Independent method | Candidate C has zero value and duration mismatch and positive convexity surplus 3. |
| Answer | C · agreement passed |
Contents
Inside the 76-page edition
Candidates preparing in English for the Financial Mathematics (FM) Exam
Table of contents
- 30 original duration and immunization problems
- Macaulay and modified duration
- First-order price change and convexity
- Redington and full immunization
- Portfolio matching with independent checks
What is included
30 verified original variants selected without duplication for this focused diagnostic. Official problem wording is not included.
Verification
Every included result is reproducible
Every selected problem already passed a reproducible calculation, an independent second method, and answer-letter agreement. The compiler rejects any failed check, cross-product duplicate, or official source wording.
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Questions about this edition
Are these official sample questions?
No. Every question is an independently written original variant. Official problem wording is not reproduced.
Are complete solutions included?
Yes. Every problem includes Setup, Model, Compute, and Answer steps plus a concrete explanation for each of the four incorrect choices.
How are the answers checked?
Each answer must agree under a reproducible primary calculation and a distinct independent method before the PDF can build.
Does this overlap the complete proof manual?
Yes. These 30 original variants are selected from the verified variant bank included in the Financial Mathematics Proof Manual. This edition adds a curated focused diagnostic, answer sheet, answer key, and focused purchase price.
Independent publication
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ActuaryProof is not affiliated with, endorsed by, or sponsored by the Society of Actuaries. Exam names are used solely to identify the exams for which these study materials are relevant. All problems and solutions are original works.
Financial Mathematics Duration & Immunization Workbook
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