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 11% (paid annually) is 7.5%.

a. What arbitrage opportunity is available for an investment banking firm?

The arbitrage strategy is to buy zeros with face values of $  and $  , 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

The price of the coupon bond, based on its yield to maturity, is:

[$110 ×Annuity factor (7.5%, 2)] + [$1,000 × PV factor (7.5%, 2)]

= $1,062.84

If the coupons were stripped and sold separately as zeros, then, based on the yield to maturity of zeros with maturities of one and two years, respectively, the coupon payments could be sold separately for:

[$110 / 1.07] + [$1,110 / 1.08²] = $102.80 + $951.65 = $1,054.45

The arbitrage strategy is to buy zeros with face values of $110 and $1,110, and respective maturities of one year and two years, and simultaneously sell the coupon bond. The profit equals $8.39 on each bond.