Question

The yield to maturity (YTM) on 1-year zero-coupon bonds is 5% and the YTM on 2-year zeros is 6%. The yield to maturity on 2-year-maturity coupon bonds with coupon rate of 12% (paid annually) is 5.8%. What arbitrage opportunity is available for an investment banking firm? What is the profit on the activity?

Answer 1

Answer:

A]

The price of the coupon bond, based on its YTM, is:
Using Calculator,

N = 2, I/Y = 5.8, PMT = -120, FV = -1000 and Compute PV = $1113.99

If the coupons were stripped and sold separately as zero-coupon bonds, then based on the YTM of zero-coupon bonds with maturities of one and two years, the coupon payments could be sold separately for
[120/1.05] + [1,120/(1.06)²] = $1,111.08.

B]

The arbitrage strategy is to:
Buy zero-coupon bonds with face values of $120 and $1,120 and respective maturities of 1 and 2 years
Simultaneously sell the coupon bond.
The profit equals $2.91 on each bond.