Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. Modified duration is negative P prime divided by P. Differentiating the year-3 and year-4 discounted terms gives the numerator 1,500 times (1+i) to the −4 minus 4,000 times (1+i) to the −5, which is the expression in choice A.
Independent solution
Setup
Use the definition of modified duration for the given price function.
Model
Differentiate each discounted term; the time-0 amount has zero derivative.
Compute
Negating the derivative gives the displayed numerator over the original price function.
Answer
This derivative ratio is the expression in choice A.
Test the method on unseen problems
30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
A portfolio pays 200 today, 300 at year 2, and 500 at year 5. At a 4% annual effective yield, calculate its modified duration.
The portfolio price is 888.33. Dividing the negative price derivative 2509.18 by that price gives modified duration 2.8246 years, choice E.
Setup
Price the three cash flows at 4%; the time-0 cash flow is included in price but has no duration numerator.
Model
Compute the negative derivative with respect to annual yield.
Compute
The price is 888.330417 and derivative magnitude is 2509.184130, giving 2.82460679 years.
Answer
The modified duration is 2.8246 years, selecting choice E.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 117 Exam FM general cash flows, portfolios, and asset liability management practice problems.
Drill the method: Exam FM Duration and Convexity problems
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam FM solution in one searchable PDF.
