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 10% (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

	Let Face Value of 10% Bond be $100.
a)	Price of a 2 Years 10% Bond
	= [Coupon / (1+YTM)^1] + [(Coupon+Maturity Value) / (1+YTM)^2]
	Where,
	Coupon = Face Value*Coupon Rate = $1000*10% = $100
	YTM = 7.5%
	Price of a 2 Years 10% Bond
	= [Coupon / (1+YTM)^1] + [(Coupon+Maturity Value) / (1+YTM)^2]
	= [$100 / (1+7.5%)^1] + [($100+$1000) / (1+7.5%)^2]
	= [$100 / (1.075)^1] + [($1100) / (1.075)^2]
	= [$100 / 1.075] + [($1100) / 1.155625]
	= $93.02 + $951.87
	= $1044.89
	Price of a 2 Years 10% Bond using YTM of Zero Coupon Bonds
	= [Coupon / (1+YTM)^1] + [(Coupon+Maturity Value) / (1+YTM)^2]
	Where,
	YTM of 1 Year Zero Coupon Bond =7%
	YTM of 2 Year Zero Coupon Bond =8%
	Price of a 2 Years 10% Bond
	= [Coupon / (1+YTM)^1] + [(Coupon+Maturity Value) / (1+YTM)^2]
	= [$100 / (1+7%)^1] + [($100+$1000) / (1+8%)^2]
	= [$100 / (1.07)^1] + [($1100) / (1.08)^2]
	= [$100 / 1.07] + [($1100) / 1.1664]
	= $93.46 + $943.07
	= $1036.53
	Therefore, arbitrage strategy will be buy zero coupon bonds
	with face value of $100 and $1100 with maturities of 1 year
	and 2 years respectively and simultaneously sell a
	10% Coupon Bond.
b)	Profit on activity
	= Price of 10% Coupon Bond - Price of Bond using YTM of Zero Coupon Bond
	= $1044.89 - $1036.53
	= $8.36
	Profit on each Bond = $8.36