Question

The yield to maturity (YTM) on 1-year zero-coupon bonds is 8% and the YTM on 2-year zeros is 9%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 11% (paid annually) is 8.5%.
Required:
a. What arbitrage opportunity is available for an investment banking firm?
b. What is the profit on the activity?

Answer 1

Answer:

Arbitrage opportunity may exists as the ZCBs selling at different price at same time due to change in their YTM .

The PV of 100 face value zcb with different ytm are different , in this case.

for one year maturity with face value 100 current price = fv/ pv at 8% = 92.59

for Two year maturity with face value 100 current price = fv / Pv at 9% for two years = 84.167 , if the bond holder sell the bond after 1 year only, the price = 91.74 .

a) The arbitrage opportunity exist with buy two bond with face value 100 with maturity of 1 year and face value 110 with maturity of 2 years.

b) profit 0.01 , as difference between PV of both bond at their YTM rate.