# Z-spread > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Z-spread > Markdown URL: https://mediated.wiki/source/Z-spread.md > Source: https://en.wikipedia.org/wiki/Z-spread > Source revision: 1242546039 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Z bonds The **Z-spread**, **ZSPRD**, **zero-[volatility](/source/Volatility_(finance)) spread,** or **yield curve spread** of a [bond](/source/Bond_(finance)) is the [parallel shift](/source/Vertical_translation) or [spread](/source/Yield_spread) over the [zero-coupon](/source/Zero-coupon_bond) [Treasury](/source/Treasury_security) [yield curve](/source/Yield_curve) required for [discounting](/source/Discounting) a predetermined cash flow schedule to arrive at its present [market](/source/Market_(economics)) [price](/source/Price). The Z-spread is also widely used in the [credit default swap](/source/Credit_default_swap) (CDS) market as a measure of [credit spread](/source/Credit_spread_(bond)) that is relatively insensitive to the particulars of specific [corporate](/source/Corporate_bond) or [government bonds](/source/Government_bond). Since the Z-spread uses the entire yield curve to value the individual cash flows of a bond, it provides a more realistic valuation than an [interpolated yield spread](/source/I-spread) based on a single point of the curve, such as the bond's final [maturity date](/source/Maturity_date) or [weighted-average life](/source/Weighted-average_life). However, the Z-spread does not incorporate variability in cash flows, so a fuller valuation of an [interest-rate](/source/Interest_rate)-dependent security often requires the more realistic (and more complicated) [option-adjusted spread](/source/Option-adjusted_spread) (OAS). ## Definition The Z-spread of a [bond](/source/Bond_(finance)) is the number of [basis points](/source/Basis_point) (bp, or 0.01%) that one needs to add to the Treasury yield curve (or technically to Treasury [forward rates](/source/Forward_rate)) so that the [Net present value](/source/Net_present_value) of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (including [accrued interest](/source/Accrued_interest)). The spread is calculated iteratively. For a [mortgage-backed security](/source/Mortgage_backed_security), a projected [prepayment](/source/Prepayment_of_loan) rate tends to be stated; for example, the [PSA](/source/PSA_prepayment_model) assumption for a particular MBS might equate a particular group of mortgages to an 8-year [amortizing](/source/Amortization_(business)) bond with 6% mortality per annum. This gives a single series of nominal cash flows as if the MBS were a riskless bond. If these payments are discounted to [net present value](/source/Net_present_value) (NPV) with a riskless zero-coupon Treasury yield curve, the sum of their values will tend to *overestimate* the market price of the MBS. This difference arises because the MBS market price incorporates additional factors such as [liquidity](/source/Market_liquidity) and [credit risk](/source/Credit_risk) and [embedded option](/source/Embedded_option) cost. ## Benchmark for CDS basis The Z-spread is widely used as the "cash" benchmark for calculating the CDS basis. The CDS basis is commonly the CDS fee minus the Z-spread for a fixed-rate cash bond of the same issuer and maturity. For instance, if a corporation's 10-year CDS is trading at 200 bp and the Z-spread for the corporation's 10-year cash bond is 287 bp, then its 10-year CDS basis is –87 bp. ## Example Assume that on 7/1/2008: - A bond has three future cash flows: $5 on 7/1/2009; $5 on 7/1/2010; $105 on 7/1/2011. - The corresponding zero-coupon Treasury rates ([compounded](/source/Compound_interest) semi-annually) are: 4.5% for 7/1/2009; 4.7% for 7/1/2010; 5.0% for 7/1/2011. - The bond's accrued interest is 0. - The Z-spread is 50 bp. Then the price *P* of this bond on 7/1/2008 is given by: - P = 5 ( 1 + 4.5 % + 50 b p 2 ) ( 2 × 1 ) + 5 ( 1 + 4.7 % + 50 b p 2 ) ( 2 × 2 ) + 105 ( 1 + 5.0 % + 50 b p 2 ) ( 2 × 3 ) = 98.50 , {\displaystyle {\begin{aligned}P&={\frac {5}{(1+{\frac {4.5\%+50\mathrm {bp} }{2}})^{(2\times 1)}}}+{\frac {5}{(1+{\frac {4.7\%+50\mathrm {bp} }{2}})^{(2\times 2)}}}+{\frac {105}{(1+{\frac {5.0\%+50\mathrm {bp} }{2}})^{(2\times 3)}}}\\&=98.50,\\\end{aligned}}} where (for simplicity) the calculation has ignored the slight difference between parallel shifts of spot rates and forward rates. ## See also - [Asset swap spread](/source/Asset_swap_spread) - [I-spread](/source/I-spread) - [Option-adjusted spread](/source/Option-adjusted_spread) - [Yield to maturity](/source/Yield_to_maturity) ## References - Frank J. Fabozzi, *The Handbook of Fixed Income Securities*, 7th edition. McGraw-Hill, 2005. v t e Bond market Bond Debenture Fixed income Types of bonds by issuer Agency bond Corporate bond Senior debt Subordinated debt Distressed debt Government bond Infrastructure bond Municipal bond Global bond Types of bonds by payout Accrual bond Auction rate security Commercial paper Consol Convertible bond Contingent Reverse Exchangeable bond Extendible bond Fixed rate bond Floating rate note Inverse Inflation-indexed High-yield debt Lottery bond Perpetual bond Zero-coupon bond Bond options Callable bond Convertible bond Embedded option Exchangeable bond Extendible bond Puttable bond Bond valuation Clean price Convexity Coupon Credit spread Current yield Dirty price Duration I-spread Mortgage yield Nominal yield Option-adjusted spread Risk-free bond Weighted-average life Yield curve Yield spread Yield to maturity Z-spread Securitized products Asset-backed security Collateralized debt obligation Collateralized mortgage obligation Commercial mortgage-backed security Mortgage-backed security Institutions Commercial Mortgage Securities Association (CMSA) International Capital Market Association (ICMA) Securities Industry and Financial Markets Association (SIFMA) --- Adapted from the Wikipedia article [Z-spread](https://en.wikipedia.org/wiki/Z-spread) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Z-spread?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.