# Zero-Volatility Spread (Z-Spread) By [yui](https://paragraph.com/@yui) · 2022-07-28 --- What Is the Zero-Volatility Spread (Z-Spread)? ---------------------------------------------- The Zero-volatility spread (Z-spread) is the constant spread that makes the price of a security equal to the present value of its cash flows when added to the yield at each point on the [spot rate Treasury curve](https://www.investopedia.com/terms/s/spot_rate_yield_curve.asp) where cash flow is received. In other words, each cash flow is discounted at the appropriate Treasury spot rate plus the Z-spread. The Z-spread is also known as a static spread. Formula and Calculation for the Zero-Volatility Spread ------------------------------------------------------ To calculate a Z-spread, an investor must take the Treasury spot rate at each relevant maturity, add the Z-spread to this rate, and then use this combined rate as the discount rate to calculate the price of the bond. The formula to calculate a Z-spread is: \\begin{aligned} &\\text{P} = \\frac { C\_1 }{ \\left ( 1 + \\frac { r\_1 + Z }{ 2 } \\right ) ^ {2n} } + \\frac { C\_2 }{ \\left ( 1 + \\frac { r\_2 + Z }{ 2 } \\right ) ^ {2n} } + \\frac { C\_n }{ \\left ( 1 + \\frac { r\_n + Z }{ 2 } \\right ) ^ {2n} } \\\\ &\\textbf{where:} \\\\ &\\text{P} = \\text{Current price of the bond plus any accrued interest} \\\\ &C\_x = \\text{Bond coupon payment} \\\\ &r\_x = \\text{Spot rate at each maturity} \\\\ &Z = \\text{Z-spread} \\\\ &n = \\text{Relevant time period} \\\\ \\end{aligned}​P=(1+2_r_1​+_Z_​)2_nC_1​​+(1+2_r_2​+_Z_​)2_nC_2​​+(1+2_rn_​+_Z_​)2_nCn_​​where:P=Current price of the bond plus any accrued interest_Cx_​=Bond coupon payment_rx_​=Spot rate at each maturity_Z_\=Z-spread_n_\=Relevant time period​ For example, assume a bond is currently priced at $104.90. It has three future cash flows: a $5 payment next year, a $5 payment two years from now and a final total payment of $105 in three years. The Treasury spot rate at the one-, two-, and three- year marks are 2.5%, 2.7% and 3%. The formula would be set up as follows: \\begin{aligned} \\$104.90 = &\\ \\frac { \\$5 }{ \\left ( 1 + \\frac { 2.5\\% + Z }{ 2 } \\right ) ^ { 2 \\times 1 } } + \\frac { \\$5 }{ \\left ( 1 + \\frac { 2.7\\% + Z }{ 2 } \\right ) ^ { 2 \\times 2 } } \\\\ &+ \\frac { \\$105 }{ \\left ( 1 + \\frac { 3\\% + Z }{ 2 } \\right ) ^ {2 \\times 3 } } \\end{aligned}$104.90=​ (1+22.5%+_Z_​)2×1$5​+(1+22.7%+_Z_​)2×2$5​+(1+23%+_Z_​)2×3$105​​ With the correct Z-spread, this simplifies to: \\begin{aligned} \\$104.90 = \\$4.87 + \\$4.72 + \\$95.32 \\end{aligned}$104.90=$4.87+$4.72+$95.32​ This implies that the Z-spread equals 0.25% in this example. ### KEY TAKEAWAYS * The zero-volatility spread of a bond tells the investor the bond's current value plus its cash flows at certain points on the Treasury curve where cash-flow is received. * The Z-spread is also called the static spread. * The spread is used by analysts and investors to discover discrepancies in a bond's price. What the Zero-Volatility Spread (Z-spread) Can Tell You ------------------------------------------------------- A Z-spread calculation is different than a nominal spread calculation. A nominal spread calculation uses one point on the Treasury yield curve (not the spot-rate Treasury yield curve) to determine the spread at a single point that will equal the present value of the security's cash flows to its price. The Zero-volatility spread (Z-spread) helps analysts discover if there is a discrepancy in a bond's price. Because the Z-spread measures the spread that an investor will receive over the entirety of the Treasury yield curve, it gives analysts a more realistic valuation of a security instead of a single-point metric, such as a bond's [maturity date](https://www.investopedia.com/terms/m/maturitydate.asp). Learn the Basics of Trading and Investing Looking to learn more about trading and investing? 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