This Exam FM sample reference tests Duration Around Coupon Date. Their ratio is 5.7864/6.0757 = 0.9524. The result agrees with the published answer key, choice C.
How to solve this Duration Around Coupon Date question
Setup
Setup
Use the annuity-due duration identity at 5% for the bond immediately before and immediately after its coupon date. Removing the immediate coupon reduces the first duration measure by one.
d0=a¨8∣0.05=6.7864,d1=d0−1=5.7864
Model
Model
The quantities are d₁ = 5.7864 after the first adjustment and d₂ = 6.0757 for the corresponding seven-period annuity-due.
d2=a¨7∣0.05=6.0757
Compute
Compute
Their ratio is 5.7864/6.0757 = 0.9524.
d1/d2=0.9524
Answer
Answer
The calculation gives 0.95 for duration around coupon date, matching published choice C.
d1/d2=0.9524(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (0.91) does not match the checked duration around coupon date result (0.95); no distinct standard one-step error is identifiable.
BChoice B (0.93) does not match the checked duration around coupon date result (0.95); no distinct standard one-step error is identifiable.
DChoice D (0.97) does not match the checked duration around coupon date result (0.95); no distinct standard one-step error is identifiable.
EChoice E (1.00) does not match the checked duration around coupon date result (0.95); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: post-coupon duration recovered from pre-coupon duration
Immediately before a coupon of 20 is paid, a bond price is 1,020 and its Macaulay duration is 7.0 years. Yield is unchanged across the payment. Calculate Macaulay duration immediately after the coupon.
A 6.43 years
B 6.78 years
C 7.14 years
D 7.50 years
E 7.85 years
Variant answer in brief
Removing the time-0 coupon raises duration to 7.14 years. Post-coupon duration is 7.14 years, so choice C is correct.
Setup
Setup
The immediate coupon contributes zero to the duration numerator but is included in the pre-payment price.
P−=1020,D−=7,P+=1000
Model
Model
Equate the time-weighted present-value numerator immediately before and after payment.
D−P−=D+P+
Compute
Compute
Removing the time-0 coupon raises duration to 7.14 years.
D+=7(1020)/1000=7.1400
Answer
Answer
Post-coupon duration is 7.14 years, so choice C is correct.
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