4. All zero coupon bonds have a face value of $100. A one-year zero-coupon bond

Question

4. All zero coupon bonds have a face value of $100. A one-year zero-coupon bond trades at $95. A two-year zero-coupon bond trades at $96. A three-year zero-coupon bond trades at $97. Answer the following questions:

(a) Construct a replicating portfolio from the three zero-coupon bonds above to replicate cash flows of a 7% annual coupon bond with a face value of $100.

(b) What is the equilibrium price of the 7% annual coupon bond given in part (a)?

(c) If the 7% annual coupon bond is trading at a price of $110, show how you can make an arbitrage profit

Explanation / Answer

Zero Coupon Bond

1 Year Zero

2 Year Zero

b.

discounted value of its cash flows =  

by selling the coupon bond and buying the zero coupon bond portfolio.

a.Replicating portfolio of a 7% annual coupon bond with a face value of $100 from the three zero-coupon bonds

Zero Coupon Bond

Price of Zero to be replicated Cash flow of 7%Coupon bond Cost

1 Year Zero

95 7 95/100*7= 6.65

2 Year Zero

96 7 96/100*7= 6.72 3 Year Zero 97 107 97/100*107= 103.79 Total Cost 117.16

b.

The equilibrium price of the 7% annual coupon bond is the

discounted value of its cash flows =  

$117.16

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