Understanding 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.
Key Insights
- The zero-volatility spread of a bond provides insight into its current value, along with its cash flows at certain points on the Treasury curve where they are received.
- The Z-spread, also called the static spread, helps analysts and investors discover discrepancies in bond prices.
- Utilizing the Z-spread allows for more accurate bond valuation across different maturities.
Formula and Calculation for the Zero-Volatility Spread
To calculate a Z-spread, you 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 bond’s price. The formula to calculate a Z-spread is:
P = C1 / (1 + (r1 + Z) / 2)^(2*n) + C2 / (1 + (r2 + Z) / 2)^(2*n) + ... + Cn / (1 + (rn + Z) / 2)^(2*n)
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
Practical 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 rates at the one-, two-, and three-year marks are 2.5%, 2.7%, and 3% respectively. The formula would be set up as follows:
$104.90 = $5 / (1 + (2.5% + Z) / 2)^(2*1) + $5 / (1 + (2.7% + Z) / 2)^(2*2) + $105 / (1 + (3% + Z) / 2)^(2*3)
After calculating, the simplified equation would reveal that the Z-spread equals 0.25% in this example.
What the Zero-Volatility Spread (Z-Spread) Can Reveal
A Z-spread calculation diverges from a nominal spread calculation, which uses a single point on the Treasury yield curve (as opposed to the spot-rate Treasury yield curve) to determine the spread that will equal the present value of the security’s cash flows to its price.
The Zero-volatility spread (Z-spread) allows analysts to discover discrepancies in a bond’s price. Because the Z-spread measures the spread that an investor will receive over the entire Treasury yield curve, it provides a more realistic valuation of a security, in contrast to a single-point metric such as a bond’s maturity date.
Related Terms: Nominal Spread, Treasury Yield Curve, Maturity Date, Bond Valuation, Spot Rate.
