## fixed income

Posts: 9
Joined: Fri Aug 05, 2016 5:52 am

### fixed income

1-, 2-, and 3-year spot rates on Treasuries are 40/0,8.1670/0, and 12.3770/0, respectively. Consider a 3-year, 90/0annual coupon corporate bond trading at 89.464. The YTM is 13.500/0, and the YTM of a 3-year Treasury is 120/0.Compute the G-spread and the Z-spread of the corporate bond.
G-spread = YTMBond - YTMTreasury = 13.50 - 12.00 = 1.500/0.
To compute the Z-spread, set the present value of the bond's cash flows equal to today's market price. Discount each cash flow at the appropriate zero-coupon bond spot rate plus a fixed spread ZS. Solve for ZS in the following equation and you have the Z-spread: 89.464 = 9 + 9 + 109 => (1.04 +ZS)l (1.08167 +ZS)2 (1.12377 +ZS)3
ZS = 1.67% or 167 basis points
Note that this spread is found by trial-and-error. In other words, pick a number "ZS," plug it into the right-hand side of the equation, and see if the result equals 89.464. If the right-hand side equals the left, then you have found the Z-spread. If not, adjust "zs" in the appropriate direction and recalculate

edupristine
Finance Junkie
Posts: 947
Joined: Wed Apr 09, 2014 6:28 am

### Re: fixed income

Hi Azhar

You can solve this in excel by putting the sum formula. As you can put ZS value at the right hand side of the equation and then see if the result is 89.465.