Exam FM practice problems: Immunization and cash-flow matching

10 problems · Untimed · Worked solution after each answer

Redington immunization, full immunization and exact cash-flow matching of liabilities with bonds. This drill covers topic 5 of the Exam FM syllabus, General Cash Flows, Portfolios and Asset Liability Management (20–30% of the exam).

5a Immunization definitions
5c Immunization and cash-flow matching

Line drawing of a balanced two-pan scale with a stack of certificates on one pan and stacks of coins on the other

Before you start

Every problem has five options, A to E, and one correct answer, as on the real exam. Every value you need is in the problem, so you can work it with an approved calculator; the worked solution shows each step and names the mistake behind the most tempting wrong answer.
Check each answer to see the explanation before moving on. Checked answers cannot be changed.

Study guide: Immunization and cash-flow matching

Redington immunization: PV(assets) = PV(liabilities), equal durations (first derivatives) and asset convexity greater than liability convexity.
Full immunization of a single liability needs one asset cash flow before it and one after, with matching present value and duration.
Exact matching works backward: buy enough of the longest bond to cover the last liability, subtract its coupons from earlier liabilities, and repeat.
Immunization protects against a small parallel shift in a flat yield curve, not against any change.

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Original practice problems written to the published SOA syllabus; not SOA sample questions. Independent preparation, not affiliated with or endorsed by the Society of Actuaries (SOA).