8.2 Fill in the missing items in the following table, using the Law of One Price
ID: 1167839 • Letter: 8
Question
8.2 Fill in the missing items in the following table, using the Law of One Price. Assume all these bonds have the same risk, the yield curve is flat, and any coupon payments are paid annually. (10 marks)
Bond #
1
2
3
4
1-year
strip bond
2-year
strip bond
2-year
6% coupon bond
2-year
7% coupon bond
Time 0 cash flow (i.e., Purchase
Price for the bond)
–950
?
?
?
Time 1 cash flow
+1000
0
+60
+70
Time 2 cash flow
0
+1000
+1060
+1070
Yield
?
?
5.50%
?
Bond #
1
2
3
4
1-year
strip bond
2-year
strip bond
2-year
6% coupon bond
2-year
7% coupon bond
Time 0 cash flow (i.e., Purchase
Price for the bond)
–950
?
?
?
Time 1 cash flow
+1000
0
+60
+70
Time 2 cash flow
0
+1000
+1060
+1070
Yield
?
?
5.50%
?
Explanation / Answer
Bond 1:
Yield = (1000 - 950)/950 * 100 = 5.26%
Bond 2:
Assume that the annual yield is 5.5%
Let the Time 0 cashflow be x.
then,
1000 = x * (1+5.5%)(1+5.5%) = x *1.055*1.055 = 1.113025x
x = 1000/1.113025 = 898.45
Bond 3:
Assume that the time 0 cashflow be y.
Then,
y = 60/(1+5.5%) + 1060/(1+5.5)^2
= 60/1.055 + 1060/1.113025 = 56.872 + 952.360 = 1009.232
Bond 4:
Assume that the time 0 cashflow be z.
Then,
y = 70/(1+5.5%) + 1070/(1+5.5)^2
= 70/1.055 + 1070/1.113025 = 66.351 + 961.344 = 1027.70
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