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 rates of 15% (paid annually) is 5.2%.

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

b. What is the profit on the activity? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Price of 2 year , 15% coupon bond is computed as follows:

Assuming Face value = 1000

Coupon = Coupon Rate * Face Value = 15%*1000 = 150

Price = Coupon / (1+YTM)^1 + (Coupon +Face Value) / (1+YTM)^2

Price = 150/ 1.052 + (150+1000) / 1.052^2

Price = 142.59 + 1039.12

Price = $1181.71

Price of bond using YTM of zero coupon bond of 1 year (5%) and YTM of zero coupon bond of 2nd year (6%)

Price = Coupon / (1+YTM first year)^1 + (Coupon +Face Value) / (1+YTM second year)^2

Price = 150/ 1.05 + (150+1000) / 1.06 ^2

Price = 142.85 + 1023.496

Price = $1166.353

Answer 1) Arbitrage is making risk less profit on transactions which arises due to mispricings. Here, the arbitrage strategy will be to buy zero coupon bonds with face value of 150 and 1150 with maturities of 1 year and 2 years respectively. At the same time, we will short sell a 15% zero coupon bond of 2 years.

Answer 2)

Profit =Price of 15% coupon bond - Price of Zero Coupon Bond using 1 year and 2 year YTM rates

Profit = 1181.71 - 1166.353

Profit = $15.35