Question

The price of one-year bond (A) with zero coupon and face value $ 1000 is $ 961.5. The price of two-year bond (B) with zero coupon and face value $ 1000 is $ 907. Consider a third bond (C), a two-year bond with $ 100 coupon paid annually and face value of $ 1000.

(i) What must be the price of bond C so that the Law of One Price holds. Explain where you use LOOP.

(ii) Suppose that the price of bond C is $ 1000. Construct an arbitrage portfolio of bonds (assuming that bonds can be sold short at the same prices).

(iii) Find yield-to-maturity of each bond.

Answer 1

For bond A :

Face Value = $1000

Price = $961.5

We know that For simple 1 year bond, PV = FV/(1+i)

961.5=1000/(1+i)

YTM=i=4%

• For bond B:

Maturity Time = 2 yrs

FV=$1000

price= $907

PV= FV/(1+i)^n

907=1000/(1+i)^2

YTM=i=5%

• For bond C:

It is a 2 yr bond so as per LOOP, its price must be same as that of bond B

now, for 2 yr coupon bond,

PV=c/(1+i)+c/(1+i)^2+FV/(1+i)^2

907=100/(1+i)+100/(1+i)^2+1000/(1+i)^2

i=15.85%

• Now if the price of bond C is $ 1000

1000=100/(1+i)+100/(1+i)^2+1000/(1+i)^2

i=10%

as there is a difference in prices of bond B and C despite the face that they are both 2 yr maturity bonds one can buy Bond B and sell bond C