The market price of a two-year bond is 105% of its nominal value. The annual coupon to be paid in exactly one year is 7%. Its yield-to-maturity (European method) is 4.336%.
a. Calculate its duration.
b. Calculate its simple yield.
c. Calculate its semiannual yield (U.S. method).

Question

Quizplus · Accepted Answer

The Answer is We verify that:

105 = \frac { 7 } { 1 + r } + \frac { 107 } { ( 1 + r ) ^ { 2 } }

with

r = 4.336 \%

a. Macaulay duration

= \frac { 1 } { 105 } \left( \frac { 7 } { 1 + r } + 2 imes \frac { 107 } { ( 1 + r ) ^ { 2 } } ight) = 1.936

Duration: D = 1.936/1.04336 =1.86.
b. Simple yield

= \frac { 1 } { 105 } \left( 7 \% + \frac { 100 - 105 } { 2 } \% ight) = 4.286 \%

c.

105 = \frac { 7 } { \left( 1 + \frac { r ^ { \prime } } { 2 } ight) ^ { 2 } } + \frac { 107 } { \left( 1 + \frac { r ^ { \prime } } { 2 } ight) ^ { 4 } }

or

\left( 1 + \frac { r ^ { t } } { 2 } ight) ^ { 2 } = 1 + r

where r' is the semiannual yield (U.S. YTM) and r is the annual yield (European YTM).
r' = 4.29%.

The Market Price of a Two-Year Bond Is 105% of Its