Question

Suppose the price of the two-year pure discount bond with a $2,500 face value is only $1,900. Is there an arbitrage opportunity? Is yes, how would you structure a trade that has zero cash-flow in years 1 and 2 and a positive cash-flow only in year 0 (i.e. now).

(a) What must the price of a two-year pure discount bond with a $2,500 face value be in order to avoid arbitrage?

(b) Suppose the price of the two-year pure discount bond with a $2,500 face value is only $1,900. Is there an arbitrage opportunity? Is yes, how would you structure a trade that has zero cash-flow in years 1 and 2 and a positive cash-flow only in year 0 (i.e. now).

Answer 1

a.

Here in the question the interest rate is not given.

Lets assume that the market interest rate is 12%

Hence price of two year pure discount ( Deep discount) Bond should be =

= $ 2500/ (1+12%)^2

=$2500/1.2544

=$1993 in order to avoid the arbitrage

b.

Yes there will be an arbitrage opportunity because the fair price of the bond today should be $ 1993 But its actual price quoted in the market is $1900.

suppose 1 year zero coupon bond $ 50 is trading at $ 44.64 ( i.e. $50/(1+12%) =$44.64)

and 2 year 25% coupon bond having par value $1000 is selling at $1219.71 (i.e ($250/(1+12%)) +($1250/(1+12%^2)

Bond	position	CF at 0	CF at 1	CF at 2
1­yr, Zero Coupon, $50 Par, sells for $44.64	Buy 10 bonds	-446.40	+500 ( by redemption)	---
2­year, 25% coupon, $1,000 Par, sells for $1,219.71	sell 2 bonds	+2439.42	-500 (interest payment)	-2500 (redemption)
2­yr,ZeroCoupon,$2,500 par sells at $ 1900	buy 1 bond	-1900	0	+2500
	cash flow	+93.02	0	0