Question

A 6% annual coupon corporate bond with two years remaining to maturity is trading at a price of 100.125. The two-year, 4% annual payment benchmark bond is trading at a price of 100.750. The one year and two-year government spot rates are 2.10% and 3.635%, respectively, stated as effect annual rates. 1. Calculate G spread, the spread between the yield to maturity on the corporate bond and government bond having same maturity. 2. Demonstrate that the Z-spread is 234.22 Please give a step by step solution to the math and not just the answer

Answer 1

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7415 Calculation of corporate yield bond 416 7417 Coupon payment 6-100 6/100 418 7419 Remaining maturity period 7420 FV 100 100.125 421 PV 7422 Now as per equation 7423 LHS RHS 100.125 424 425 426 427 6/ (1+r)1+6/ (1+r)A2 100/ (1+r)*2 6 0.94 5.66392538 6 0.89 5.34685677 100 0.89 89.1142796 5.933599% 7428 Yield as per govt bonds 100.125062 429 7430 Coupon payments 7431 Remaining maturity period 7432 FV 7433 PV -100 4/100 100 100.75 434 435 7436 LHS RHS 100.75 4/ (1+r)1+4/ (1 r)*2+100/(1+r)A2 40.97 4 0.93 1000.93 3.86 3.73 93.16 437 3.60% 438 7439 G-Spread is 7440 7441 G-Spread 7442 7443 Part B: Z-spread 2.328995%-+B7428-B7439 100.75 232.73 bps 444 Coupon rate 7445 One year rate 7446 two year spot rate 7447 z spread 7448 2.10% given 3.64% given 2.3422% given 449 PV 100.1250+B7449/(1+B7450+B7454)+ B7449/1+B7452+B7454) 2) 100/((1+B7452+B7454)A2)