Given the following spot rates on 1-year to 4-year zero coupon bonds: Year Spot

ID: 2819798 • Letter: G

Question

Given the following spot rates on 1-year to 4-year zero coupon bonds: Year Spot Rate 1 8.0% 2 8.5% 3 9.0% 4 9.5%

1- What is the equilibrium price of a four-year, 9% coupon bond paying a principal of $100 at maturity and coupons annually?

2- If the market prices the four-year bond such that it yields 10%, what is the bond’s market price?

3- What would arbitrageurs do given the prices you determined in (a) and (b)? What impact would their actions have on the market price?

4- What would arbitrageurs do if the market price exceeded the equilibrium price? What impact would their actions have on the market price?

1.) Calculation of eqilibrium price

coupon rate 9%,Coupon payment annually = 100*9/100 = 9 $

Spot rates S1 = 18% ,S2 = 28.5%, S3 =39%, S4 = 49.5%,Coupon Amount C = 9 $,F =Maturity amount

Equilibrium price P0 = C / (1 +S1)1 + C / (1 +S2)2 + C / (1 +S3)3 + (C + F)/ (1 +S4)4

= 9 / (1+ 0.18) + 9 / ( 1 + 0.285)2 + 9 / ( 1 + 0.39)3 + (9 +100)/ ( 1 + 0.495)4

= 38.249$

Equilibrium price of 4 years is 38.249$

2.)Market price of 4 years 9% Coupon bond = 100 $,

Arbitrage:

1 Year Zero with F= 100, P0 = 9/(1+0.18) = 7.627$

2 Year Zero with F=100, P0 = 9 /(1+0.285)2 = 5.45 $

3 Year Zero with F= 100, P0 = 9 /(1+0.39)3 = 3.351 $

4 Year Zero with F= 100, P0 = 109 /(1+0.495)4 = 21.82 $

Market price = 8/ ( 1+0.1) +100/ (1+0.1)4 = 76.483 $

3.)

Arbitrages:

1 Year Zero with F= 100, P0 = 9/(1+0.18) = 7.627$

2 Year Zero with F=100, P0 = 9 /(1+0.285)2 = 5.45 $

3 Year Zero with F= 100, P0 = 9 /(1+0.39)3 = 3.351 $

4 Year Zero with F= 100, P0 = 109 /(1+0.495)4 = 21.82

4.)equilibrium bond price arbitrage when bond is underpriced,

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