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 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.

BREAKING DOWN 'Zero-Volatility Spread - Z-spread'

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.

Zero-Volatility Spread Calculation

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.

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 components that go into a Z-spread calculation are as follows:

P = the current price of the bond plus any accrued interest

C(x) = bond coupon payment

r(x) = the spot rate at each maturity

Z = the Z-spread

T = the total cash flow received at the bond's maturity

n = the relevant time period

The generalized formula is:

P = {C(1) / (1 + (r(1) + Z) / 2) ^ (2 x n)} + {C(2) / (1 + (r(2) + Z) / 2) ^ (2 x n)} + {C(n) / (1 + (r(n) + Z) / 2) ^ (2 x n)}

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:

$104.90 = $5 / (1 +(2.5% + Z) / 2) ^ (2 x 1) + $5 / (1 +(2.7% + Z) / 2) ^ (2 x 2) + $105 / (1 +(3% + Z) / 2) ^ (2 x 3)

With the correct Z-spread, this simplifies to:

$104.90 = $4.87 + $4.72 + $95.32

This implies that the Z-spread equals 0.5% in this example.

  1. Static Spread

    The constant yield spread which when added to the point on the ...
  2. Nominal Yield Spread

    The spread, expressed in percent or basis points, that when added ...
  3. Yield Spread

    A yield spread is the difference between yields on differing ...
  4. Note Against Bond Spread - NOB

    A spread within futures contracts created by offsetting positions ...
  5. Treasury Bond - T-Bond

    A treasury bond is a marketable, fixed-interest U.S. government ...
  6. Treasury Yield

    Treasury yield is the return on investment, expressed as a percentage, ...
Related Articles
  1. Investing

    Understanding Bond Prices and Yields

    Understanding this relationship can help an investor in any market.
  2. Investing

    Interest Rates And Your Bond Investments

    By understanding the factors that influence interest rates, you can learn to anticipate their movement and profit from it.
  3. Trading

    Trading Calendar Spreads in Grain Markets

    Futures investors flock to spreads because they hold true to fundamental market factors.
  4. Insights

    Understanding The Treasury Yield Curve Rates

    Treasury yield curves are a leading indicator for the future state of the economy and interest rates.
  5. Trading

    S&P 500 Options On Futures: Profiting From Time-Value Decay

    Writing bull put credit spreads are not only limited in risk, but can profit from a wider range of market directions.
  6. Financial Advisor

    Top 4 Treasurys ETFs (SHY, IEI)

    Learn about the specifics of the top four U.S. Treasury ETFs and how investors can buy ETFs that invest in bonds along the yield curve.
  7. Investing

    The Bank Stocks Have Come Too Far Too Fast

    The bank sector has been buoyed by expectations of higher interest rates, but the rally justified?
  8. Investing

    Bond Yield Curve Holds Predictive Powers

    This measure can shed light on future economic activity, inflation levels and interest rates.
  9. Investing

    Get Active In Your Bond Portfolio

    Find out why being a couch potato with your bonds actually could be mashing your results.
  1. What is the difference between an option-adjusted spread and a Z-spread in reference ...

    Learn about the difference between the Z-spread and option-adjusted spread valuations of future cash flows for bonds, and ... Read Answer >>
  2. What is the difference between the Daily Treasury Long-Term Rates and the Daily Treasury ...

    Find out more about the daily Treasury long-term rates, daily Treasury yield curve rates and the difference between these ... Read Answer >>
  3. What is the difference between yield to maturity and the spot rate?

    Find out how yield to maturity and spot rate calculations use different discount rates to determine the present market value ... Read Answer >>
  4. How do I calculate yield to maturity in Excel?

    Learn how to calculate a bond's yield to maturity in Microsoft Excel, which is one of the best methods of comparing bonds ... Read Answer >>
  5. What is the difference between yield to maturity and the yield to call?

    Determining various the various yields that callable bonds can provide investors is an important factor in the bond purchasing ... Read Answer >>
Hot Definitions
  1. Diversification

    Diversification is the strategy of investing in a variety of securities in order to lower the risk involved with putting ...
  2. Liquidity

    Liquidity is the degree to which an asset or security can be quickly bought or sold in the market without affecting the asset's ...
  3. Federal Funds Rate

    The federal funds rate is the interest rate at which a depository institution lends funds maintained at the Federal Reserve ...
  4. Call Option

    An agreement that gives an investor the right (but not the obligation) to buy a stock, bond, commodity, or other instrument ...
  5. Standard Deviation

    A measure of the dispersion of a set of data from its mean, calculated as the square root of the variance. The more spread ...
  6. Entrepreneur

    An entrepreneur is an individual who founds and runs a small business and assumes all the risk and reward of the venture.
Trading Center