Z-spread
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The Z-spread (or ZSPRD) of a bond is the number of basis points one needs to add to the Treasury spot rates yield curve, so that the NPV of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (after accounting for accrued interest). The spread is calculated iteratively and improves the accuracy of the value calculation as it uses the entire yield curve to value the cash flows.
If you calculate the present value of all future cash flows for a bond using prevailing spot rates, you may discover that the price you calculate is greater than the price observed in the market. This difference arises because the market price incorporates additional factors such as liquidity and credit risk. The Z-spread quantifies the impact of these additional factors. It is the spread you need to add to the curve you are discounting with in order to generate a price that matches the market price.
Conventionally, the zero rates are determined from the Treasury curve, with semi-annual compounding.
Example
Assume that a bond has three cash flows: $5 on 1/1/2009; $5 on 1/1/2010; and $105 on 1/1/2011.
The corresponding zero rates (compounded semiannually) are 4.5% on 1/1/2009, 4.7% on 1/1/2010 and 5% on 1/1/2011.
Assuming that the accrued interest is 0, and the Z-spread is 50 basis points, the price of this bond on 1/1/2008, P, is given by:
See also
References
- Frank J. Fabozzi, The Handbook of Fixed Income Securities, 7th edition; McGraw-Hill; 2005
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