Worked solution · Exam FM
This Exam FM sample reference tests Portfolio Weight for a Target Duration. Bond A has price 1055.50 and Macaulay duration 2.8381 years; the one-year zero has duration 1. Solving the market-value weighted duration equation gives 54.403% in Bond A, choice D.
Independent solution
Setup
Price Bond A and form its time-weighted present-value numerator at 4%.
Model
Divide the timing numerator by price.
Compute
Let w be the fraction of portfolio market value in Bond A. The zero's duration is one year.
Answer
Solving gives 54.4%, choice D.
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Error diagnosis
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Original practice · fully worked
A portfolio places 60% of market value in the three-year 6% coupon bond described by cash flows 60, 60, and 1,060, priced at a 4% yield. The remaining 40% is in a one-year zero. Determine the portfolio's Macaulay duration.
The coupon bond duration is 2.8381 years. Applying the stated 60%-40% market-value mix gives portfolio duration 2.1029 years, choice C.
Setup
Discount the coupon bond cash flows at 4% and calculate its duration.
Model
The one-year zero has Macaulay duration one.
Compute
Use the market-value allocation as the duration weights.
Answer
The portfolio duration is 2.1029 years, choice C.
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