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 9% (paid annually) is 5.9%. a. What arbitrage opportunity is available for an investment banking firm? The arbitrage strategy is to buy zeros with face values of $ D and $C , 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.) Profit Profit each bond |

Answer 1

a To formulate arbitrage Strategy we first need to find out following 2 prices 0 Calculation of Price of 9% Coupon Rate Bond Where, Face Value = $1000 Coupon = $1000X9% = $90 YTM=r= 5.9% = 0.059 na no. of Year Price of a g% Coupon Rate Bond Coupon Coupont Maturity Value (1+r)" (1+r)nti $90 $ 90+ $1000 (1+0.059) T-(1+0.0592 $90 logo (1+0.055) (1+0.059)

= $84.99 + $ 97).93 $ 1056.92 ② Calculation of Price of a Bond using yTm of a Zero Coupon Bord for Year 1 is 5%. & for Year 2 is 6% - - Price of a Bond $ 90 $90+ $1000 (1+o.os). (140.06)2 $90 $ logo 1.05 WÁDK) 11.062 $85.71 + $ 970-10 - $1055.81 Therefore the arbitrage Strategy will be buy zeros with face value of $90 a $1090 with maturities of Tear & 2 Tear respectively & simultaneously sell a 9% Coupon Bond. 6 Profit on activity = Price of 9% Coupon Rate Bond - Price of Bond using YTM of Zero Coupon Bond = $ 1056.92 (-) $1055.8) = $ 1.11 Profit = $1.11 each bond