Worked solution · Exam FM
This Exam FM sample reference tests Portfolio Duration under a Common Yield. Bond A is at par, so the common yield is 6%. Its duration is 7.8017 years; the zero prices are 747.26 and 558.39. Weighting all three durations by market value gives 7.4261 years, choice B.
Independent solution
Setup
Because the coupon bond sells at par, its annual effective yield equals its 6% coupon rate.
Model
Compute Bond A's price-weighted timing at this yield.
Compute
Price the two zeroes and use their maturities as durations.
Answer
Market-value weighting gives 7.4261 years, choice B.
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.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A coupon bond has market value 1,000 and Macaulay duration 7.8 years at a common 6% yield. It is combined with a five-year zero-coupon bond to obtain portfolio duration 6.4 years. Determine the zero's maturity value.
The duration equation requires the zero to have present value 1000. Accumulating that value five years at 6% gives maturity value 1338.23, choice D.
Setup
Let Z be the zero's current market value.
Model
Solve the market-value weighted duration equation.
Compute
Convert the zero's present value to its year-5 maturity amount.
Answer
The maturity value is 1338.23, choice D.
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.
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.
