8.3 A. You are considering two investments from the bonds listed in question 8.2

Question

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 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 # 4 2-year 7% coupon bond 1-year strip bond 2-year strip bond 2-year 696 coupon Time 0 cash flow (i.e., Purchase Price for the bond) Time 1 cash flow Time 2 cash flow Yield -950 +70 +60 +1060 5. 5090 +1000 +1000 +1070 Bond # 1-year strip bond 2-year strip bond | 2-year 6% coupon bond | 2-year 6% coupon bond 3 Time O cash flow(i.e., Purchase -950 Price for the Time 1 cash flow Time 2 cash flow 1000 70 1000 1060 1070 (86/-83)-1 -88 Bond # 1-year strip 2-year 2-year 6% 2-year 6% bond strip bond Coupon bond c 3 Time 0 cash flow (i.e., Purchase-950 902.50 $1,009.23 1,027.69 Price for the Time 1 cash flow Time 2 cash flow Yield 1000 1000 5.26% 1060 5.50% 1070 5.50% 8 5.26%

Explanation / Answer

Answer:

A.

i. 60 units of bond -1 + 1060 units of bond-2 = 60 x $1000 + 1000 x $1060 =

                                                                         = $60000 + $1060000

                                                                         = $1120000

ii. 1000 units of bond-3 = 1000 x $1120 = $1120000

B.

If 60 B-1 and 1060 B-2 replicate 1000 B-3 then the only difference between B-3 and B-4 is the amount of the coupon.

C.

i. If the yield of Bond-3 is 5.5%, what would it cost to buy 1000 units of Bond-3

The cost of the bond-3 will be:

Cost = 1000 x $1120 = $1120000

ii. What would it cost to buy 60 units Bond-1

The cost to buy 60 units = 60 x $1000 = $60000

iii. From part A.

Value of Bond-2 = 1000 x $1060 = $1060000

iv. Value of 1 bond-2 = 1 x $100 = $100

and Bond-2 yield = 5.5%

D.

What is the value of 1000 units of Bond-4

Value = 1000 x $1027.69 = $1027690

E.

The theory that the price of a given security, commodity or asset will have the same price when exchange rates are taken into consideration. The law of one price is another way of stating the concept of purchasing power parity.

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