Exam FM practice problems: Duration and convexity

10 problems · Untimed · Worked solution after each answer

Macaulay and modified duration and convexity of a set of cash flows and portfolios, and first-order approximations of price changes. This drill covers topic 5 of the Exam FM syllabus, General Cash Flows, Portfolios and Asset Liability Management (20–30% of the exam).

5a Duration and convexity definitions
5b Duration, convexity and price-change approximations

Line drawing of a plank balanced on a fulcrum with a heavy block near the pivot and a small block at the far end

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: Duration and convexity

Macaulay duration is the present-value-weighted average time of the cash flows; modified duration = Macaulay duration / (1 + i).
First-order modified approximation: P(i₁) ≈ P(i₀)[1 − (i₁ − i₀)·D_mod]. Macaulay approximation: P(i₁) ≈ P(i₀)·((1 + i₀)/(1 + i₁))^D_mac.
A portfolio’s duration is the market-value-weighted average of its holdings’ durations.
A zero-coupon bond’s Macaulay duration equals its term; adding coupons lowers duration.

Create a free account before you start

Create a free account to start. Every drill includes one free attempt. An Exam P and FM pass unlocks both timed practice exams and unlimited drills for both exams.

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).