Explanation:
Let's verify Option A:
Consol Bond Price Calculation:
$100$100 = $3Price of a perpetual bond = Annual coupon payment / Yield
Price = $3 / 0.05 = $60 ✓
Modified Duration Calculation: For a perpetual bond, modified duration = 1 / Yield Modified duration = 1 / 0.05 = 20 years ✓
Both calculations are correct, so Option A is TRUE.
Option B is incomplete in the text, but even if completed, it would likely be false because while a barbell portfolio typically has greater convexity than a bullet portfolio, the barbell doesn't "always" outperform - it depends on yield curve movements and other factors.
Therefore, Option A is the correct answer.
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Which of the following is TRUE?
A
If a consol (perpetual) bond with a $100 face value pays a 3.0% coupon in perpetuity and the yield is 5.0%, the consol's price is $60 and its modified duration is 20 years.
B
Since a BARBELL bond portfolio has greater convexity than a BULLET, the barbell always
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