This Exam FM sample reference tests Duration and Convexity. The three zero-coupon positions have market values 14423.10, 19322.80, 26352.30. Their market-value-weighted maturity is 2.1985 years, so the portfolio duration is 2.20 and choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (1.97) does not satisfy the market-value-weighted average of the one-, two-, and three-year zero maturities; no distinct standard one-step error is identifiable.
BChoice B (2.11) does not satisfy the market-value-weighted average of the one-, two-, and three-year zero maturities; no distinct standard one-step error is identifiable.
CChoice C (2.16) does not satisfy the market-value-weighted average of the one-, two-, and three-year zero maturities; no distinct standard one-step error is identifiable.
EChoice E (2.23) does not satisfy the market-value-weighted average of the one-, two-, and three-year zero maturities; no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: long-zero quantity required for a target portfolio duration
A portfolio holds ten one-year zero-coupon bonds priced at 950 each. It may add four-year zero-coupon bonds priced at 800 each. How many four-year bonds are required for the combined portfolio to have Macaulay duration exactly 3.0 years?
A 21.38
B 22.56
C 23.75
D 24.94
E 26.13
Variant answer in brief
The existing short position has value 9,500. Solving the market-value-weighted duration equation for the four-year position gives 23.75 bonds, choice C.
Setup
Setup
The one-year position has market value 10 times 950.
V1=9500
Model
Model
Let n be the number of four-year bonds and impose the target weighted maturity.
3=9500+800n1(9500)+4(800n)
Compute
Compute
Solving the linear equation gives n = 23.7500.
n=23.75000000
Answer
Answer
The portfolio needs 23.75 four-year bonds, selecting choice C.
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