Answer:
the bond with the greater yield is the semi-annual coupon bond trading in the United States.
Step-by-step explanation:
To determine which bond has the greater yield, we need to compare the effective annual yields of both bonds.
For the semi-annual coupon bond trading in the United States with a YTM (yield to maturity) of 6.25%, the semi-annual yield is simply the YTM divided by 2, since it pays coupons twice a year. Therefore, the semi-annual yield is 6.25% / 2 = 3.125%.
To calculate the effective annual yield of the semi-annual coupon bond, we use the formula:
1
+
Effective Annual Yield
=
(
1
+
Semi-Annual Yield
)
2
1+Effective Annual Yield=(1+Semi-Annual Yield)
2
Let's substitute the value of the semi-annual yield into the formula:
1
+
Effective Annual Yield
=
(
1
+
0.03125
)
2
1+Effective Annual Yield=(1+0.03125)
2
Simplifying the equation:
1
+
Effective Annual Yield
=
1.0312
5
2
1+Effective Annual Yield=1.03125
2
1
+
Effective Annual Yield
=
1.063416015625
1+Effective Annual Yield=1.063416015625
Effective Annual Yield
=
1.063416015625
−
1
Effective Annual Yield=1.063416015625−1
Effective Annual Yield
=
0.063416015625
Effective Annual Yield=0.063416015625 or 6.3416%.
For the annual coupon bond traded in Europe with a YTM of 6.3%, the yield is already given as an annual yield, so the effective annual yield is simply 6.3%.
Comparing the effective annual yields, we find that the semi-annual coupon bond in the United States has an effective annual yield of 6.3416%, while the annual coupon bond in Europe has an effective annual yield of 6.3%.
Therefore, the bond with the greater yield is the semi-annual coupon bond trading in the United States.