8.2 Assume all these bonds have the same risk, the yield curve is flat, and any
ID: 2670430 • Letter: 8
Question
8.2
Assume all these bonds have the same risk, the yield curve is flat, and any coupon payments are paid annually.
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
=-1000/(1+5.5%)^2
=-898.45
=-(+60/(1+5.5%) +1060/(1+5.5%)^2)
=-1009.23
=-(+70/(1+5.5%) +1070/(1+5.5%)^2)
=-1027.69
Time 1 cash flow
+1000
0
+60
+70
Time 2 cash flow
0
+1000
+1060
+1070
Yield
=(1000-950)/950
=0.0526
5.26%
5.50%
5.50%
5.50%
Comment
Yield would be same as that for 2 year coupon bond
Yield would be same as that for 2 year coupon bond
Above table has already been filled in. Data is to be used to answer question 8.3 below
8.3
A.
You are considering two investments from the bonds listed in question 8.2. Show that the cash flows from the following two investments would be identical.
i.
60 units of Bond #1 + 1060 units of Bond #2, and
ii.
1000 units of Bond #3.
B.
How many units of Bond #1 and #2 would you need to replicate the cash flows of 1000 units of Bond #4?
C.
i.
If the yield of Bond #3 is 5.5%, what would it cost to buy 1000 units of Bond #3?
ii.
What would it cost to buy 60 units of Bond #1?
iii.
From part A. above, infer the value of 1060 units of Bond #2.
iv.
What is the value of one unit of Bond #2? Yield of Bond #2?
D.
What's the value of 1000 units of Bond #4? Yield?
E.
What have you learned about the Law of One Price from questions 8.2 and 8.3?
8.2
Assume all these bonds have the same risk, the yield curve is flat, and any coupon payments are paid annually.
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
=-1000/(1+5.5%)^2
=-898.45
=-(+60/(1+5.5%) +1060/(1+5.5%)^2)
=-1009.23
=-(+70/(1+5.5%) +1070/(1+5.5%)^2)
=-1027.69
Time 1 cash flow
+1000
0
+60
+70
Time 2 cash flow
0
+1000
+1060
+1070
Yield
=(1000-950)/950
=0.0526
5.26%
5.50%
5.50%
5.50%
Comment
Yield would be same as that for 2 year coupon bond
Yield would be same as that for 2 year coupon bond
Above table has already been filled in. Data is to be used to answer question 8.3 below
8.3
A.
You are considering two investments from the bonds listed in question 8.2. Show that the cash flows from the following two investments would be identical.
i.
60 units of Bond #1 + 1060 units of Bond #2, and
ii.
1000 units of Bond #3.
B.
How many units of Bond #1 and #2 would you need to replicate the cash flows of 1000 units of Bond #4?
C.
i.
If the yield of Bond #3 is 5.5%, what would it cost to buy 1000 units of Bond #3?
ii.
What would it cost to buy 60 units of Bond #1?
iii.
From part A. above, infer the value of 1060 units of Bond #2.
iv.
What is the value of one unit of Bond #2? Yield of Bond #2?
D.
What's the value of 1000 units of Bond #4? Yield?
E.
What have you learned about the Law of One Price from questions 8.2 and 8.3?
Explanation / Answer
8.3
A.
You are considering two investments from the bonds listed in question 8.2. Show that the cash flows from the following two investments would be identical.
i.
60 units of Bond #1 + 1060 units of Bond #2, and
ii.
1000 units of Bond #3.
B.
How many units of Bond #1 and #2 would you need to replicate the cash flows of 1000 units of Bond #4?
C.
i.
If the yield of Bond #3 is 5.5%, what would it cost to buy 1000 units of Bond #3?
ii.
What would it cost to buy 60 units of Bond #1?
iii.
From part A. above, infer the value of 1060 units of Bond #2.
iv.
What is the value of one unit of Bond #2? Yield of Bond #2?
D.
What's the value of 1000 units of Bond #4? Yield?
E.
What have you learned about the Law of One Price from questions 8.2 and 8.3?
8.3
A.
You are considering two investments from the bonds listed in question 8.2. Show that the cash flows from the following two investments would be identical.
i.
60 units of Bond #1 + 1060 units of Bond #2, and
ii.
1000 units of Bond #3.
B.
How many units of Bond #1 and #2 would you need to replicate the cash flows of 1000 units of Bond #4?
C.
i.
If the yield of Bond #3 is 5.5%, what would it cost to buy 1000 units of Bond #3?
ii.
What would it cost to buy 60 units of Bond #1?
iii.
From part A. above, infer the value of 1060 units of Bond #2.
iv.
What is the value of one unit of Bond #2? Yield of Bond #2?
D.
What's the value of 1000 units of Bond #4? Yield?
E.
What have you learned about the Law of One Price from questions 8.2 and 8.3?
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