## DEFINITION of Static Spread

The static spread is the constant yield spread above the spot rate Treasury curve which equates the price of the bond to the present value of its cash flows. In other words, each cash flow is discounted at the appropriate Treasury spot rate plus the static spread.

The static spread is also known as a zero-volatility spread or Z-spread.

## BREAKING DOWN Static Spread

The yield spread is the difference in yields between two yield curves. The yields on a yield curve which includes Treasury bills, notes, and bonds, are called the Treasury spot rates. The spread is the amount of yield that will be received from a non-Treasury bond above the yield for the same-maturity Treasury bond. For example, an investor is comparing the Treasury yield curve to a corporation’s yield curve. The interest rate on 2-year T-notes is 2.49% and the yield on the comparable 2-year corporate bond is 3.49%. The yield spread is the difference between both rates, which is, 1% or 100 basis points. The spread is said to be constant because it is the same for any period.

A constant or static spread of 100 basis points means that adding 100 basis points to the Treasury spot rate that applies to the bond's cash flow (interest payments and principal repayment) will make the price of the bond equal the present value of its cash flows. Each cash flow is discounted at a rate equal to the Treasury spot rate that applies to the cash flow's period plus 100 basis points.

In effect, the present value of the non-Treasury bond uses a different discount factor for each cash flow. The same spread is added to all risk-free spot rates. The derived value is a static spread above all the different Treasury yields if the security is held to maturity.

Static spread is calculated by trial-and-error. An analyst or investor would have to try different numbers to figure out which number when added to the present value of the non-Treasury security's cash flows, discounted at the Treasury spot rate, will equal the price of the security in question. For example, take the spot curve and add 50 basis points to each rate on the curve. If the two-year spot rate is 2.49%, the discount rate you would use to find the present value of that cash flow would be 2.99% (calculated as 2.49% + 0.5%). After you have calculated all the present values for the cash flows, add them up and see whether they equal the bond's price. If they do, then you have found the static spread; if not, you have to go back to the drawing board and use a new spread until the present value of those cash flows equals the bonds price.

The static spread differs from the nominal spread in that the latter is calculated on one point on the Treasury yield curve, while the former is calculated using a number of spot rates on the curve. This translates to discounting each cash flow using its period to maturity and a spot rate for that maturity.

Static or Z-spread calculations are frequently used in mortgage-backed securities (MBS) and other bonds with embedded options. An option adjusted spread (OAS) calculation, which is frequently used to value bonds with embedded options, is essentially a static spread calculation based on multiple interest rate paths and the prepayment rates associated with each interest rate path. The static spread is also widely used in the credit default swap (CDS) market as a measure of credit spread that is relatively insensitive to the particulars of specific corporate or government bonds.