Question

8.2 The Law of One Price implies that financial instruments with the same risk and the same cash flows at the same time should have the same price.

You are given the following table containing incomplete information on four different bonds. Assume that all these bonds have the same risk, 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
Purchase price ($xxxx.xx)	-950.00
Time 1 cash flow	+1000.00	0	+60.00	+70.00
Time 2 cash flow	0	+1000.00	+1060.00	+1070.00
yield to maturity (xx.xx%)			5.50%

e. How many units of Bond #1 and #2 would you need to replicate the future cash flows of 1000 units of Bond #4?

f. Using your answer to part e above, determine the following:

i. What’s the value of 1000 units of Bond #4?

ii. What’s the yield of Bond 4?

g. Fill in the missing information in the given table: (1 mark)

Answer 1

From Bond#1 , Spot rate for 1 year s1 is given by

950 = 1000/(1+s1)

= > s1 = 0.05263158

From Bond#3,

Price of Bond #3 = 60/1.055+1060/1.055^2 = 1009.2316

Also, Price of Bond #3 = 60/(1+s1) + 1060/(1+s2)^2

=> 1009.2316 = 60/1.05263158 +1060/(1+s2)^2

=> s2 = 0.05507088

So, price of Bond#2 = 1000/1.05507088^2 = $898.33

e.) 1000 units of Bond #4 would provide a cash flow of $70000 at time 1 and $1070000 at time 2

So, one would require 70 units of Bond #1 and 1070 units of Bond#2 to replicate the cashflows of 1000 units of Bond #4

f) i) Value of 1000 units of Bond#4 = value of 70 units of Bond#1+ 1070 units of Bond#2

= 70*950+1070*898.33

=$1027714.92

Value of 1 unit of Bond#4 = $1027.71

ii) Yield of Bond#4 (y) is given as

70/(1+y)+ 1070/(1+y)^2 = 1027.71

From Solver in Excel , y = 0.05499 or 5.50%

g) YTM of bond 1 = s1 =0.05263 = 5.26%

  YTM of bond 2 = s2 =0.05507088 = 5.51%

Price of Bond 2 =$898.33 (calculated above)

Price of Bond 3 =$1009.23 (calculated above)

Price of Bond 4 =$1027.71 (calculated above)

YTM of Bond 4 =5.50% (calculated above)