While you don’t apply a Z-spread to your morning toast, it is a useful tool for pricing a bond. A bond’s yield is the annual interest it pays divided by its purchase price. When you plot yields against different maturity periods, you get a yield curve. When you compare two yield curves, you get a yield spread.

#### Tips

A zero-volatility spread can be defined as the amount of yield an investor can expect to receive from a non-treasury bond compared to a treasury bond.

## Treasury Yield Curve

The most basic yield curve plots the yields of Treasury bills, notes and bonds against their times until maturity. These yields are known as the Treasury spot rates. Treasury debt is considered risk-free, so all other bonds of a similar maturity yield more than does Treasury debt. For example, suppose the Treasury yield curve shows that a five-year Treasury note is yielding 4.5 percent if held to maturity. A five-year note from XYZ Corporation that yields 5.5 percent creates a spread of 1 percent, or 100 basis points, above the five-year Treasury spot rate.

## Zero-Volatility Spread

The zero-volatility spread, or Z-spread, is the amount of yield you’ll receive from a non-Treasury bond above the yield for the same-maturity Treasury bond. Finding the Z-spread requires computing the present value of the cash flows – interest payments and repayment of principal – from a non-Treasury bond. The discount factor of a present value calculation determines the amount of interest you would earn if you received a future cash flow today, and held it until the actual cash flow date. The price of the bond is equal to the sum of the present values of its cash flows.

## The Z-Spread is Static

The Z-spread for a particular bond is static – the spread above the Treasury yield is the same for any period. For example, a Z-spread of 100 basis points means that 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 other words, the present value of the non-Treasury bond uses a different discount factor for each cash flow. The correct solution provides a constant, or static, spread above all the different Treasury yields from today until maturity. In practice, a computer program calculates this quickly.

## Try, Try Again

Finding the correct Z-spread value takes trial and error. You plug in a spread and apply it to each different Treasury spot rate corresponding to each cash flow. For example, the Treasury curve might show the spot rates for one-year, three-year and five-year Treasury debt to be 3.15, 4.25 and 4.50 percent respectively. Adding a 50 basis point spread gives you yields of 3.65, 4.75 and 5.00 percent. You apply the 3.65 percent discount to the XYZ interest payment that is one year out.

Similarly, apply a 4.75 percent discount to the interest payment three years out and a 5.00 percent discount to the cash flows – interest and principal repayment – that will occur at maturity, five years out. In reality, you apply the appropriate discount rate to each semi-annual cash flow, not just to the three in this example. The result is a present value greater than the XYZ note’s current price. Only by repeating the process do you eventually find that a 100 basis point spread gives you the correct present value.

References

- U.S. Department of the Treasury: Daily Treasury Yield Curve Rates
- InvestorWords: Z-Spread
- Finance Train: Z-Spread: Definition and Calculation
- Office of the Comptroller of the Currency. "Embedded Options and Long-Term Interest Rate Risk: Interest Rate Risk." Accessed May 6, 2020.
- Bank of America Merrill Lynch. "The Fixed Income Digest -- Educational Series," Page 10. Accessed May 6, 2020.
- CFA Institute. "Introduction to Fixed-Income Valuation." Accessed May 6, 2020.
- Frank J. Fabozzi. "Fixed Income Securities," Page 75. John Wiley and Sons, 2008. Accessed May 6, 2020.

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