Question

Suppose a one-year pure discount bond (zero-coupon bond) is trading at £950, and a two-year pure discount bond is trading at £905. Assuming no market frictions, if a twoyear coupon bond with 5-percent coupon rate is trading at £992, describe explicitly how investors should trade to enjoy arbitrage profits. All bonds are riskless and have a face value of £1000

Answer 1

1 year rate=1000/950-1=5.2632%

2 year rate=(1000/905)^(1/2)-1=5.1177%

Intrinsic value of the bond=1000*5%/1.052632+1000*5%/1.051177^2+1000/1.051177^2=997.7494

As the bond is trading at 992 that is less than intrinsic value of 997.7494, one should buy the bond

Buy bond at 992

Sell 1 year bond with face value of 50

Sell 2 year bond with face value of 1050

Cash flow at t=0: -992+950/1000*50+1050/1000*992=97.1

Cash flow at t=1: -50+50=0

Cash flow at t=2: -1050+50+1000=0