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.
For bond A :
Face Value = $1000
Price = $961.5
We know that For simple 1 year bond, PV = FV/(1+i)
Maturity Time = 2 yrs
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,
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
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