Question

The yield to maturity (YTM) on 1-year zero-coupon bonds is 7% and the YTM on 2-year zeros is 8%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 14% (paid annually) is 7.9%. a. What arbitrage opportunity is available for an investment banking firm? The arbitrage strategy is to buy zeros with face values of $ 140 and $ 1140 , and respective maturities of one year and two years. b. What is the profit on the activity? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

(a) The arbitrage strategy is to buy zeros with face values of $140 and $1,140 and respective maturities of one and two years, and simultaneously sell the coupon bond.

(b) The profit on the activity equals $0.72 on each bond.

Step-by-step explanation:

The price of the coupon bond = 140 × PV(7.9%, 2) + 1000 × PV(7.9%, 2)

= 140 × (1-(1/1.079)^2)/0.079 + 1,000/1.079^2

= $1,108.93

If the coupons were withdrawn and sold as zeros individually, then the coupon payments could be sold separately on the basis of the zero maturity yield for maturities of one and two years.

[140/1.07] + [1,140/1.08^2] = $1,108.21.

The arbitrage strategy is to buy zeros with face values of $140 and $1,140 and respective maturities of one and two years, and simultaneously sell the coupon bond.

The profit on the activity equals $0.72 on each bond.