Zero-Volatility Spread (Z-Spread)

What Is the Zero-Volatility Spread (Z-Spread)?

The Zero-volatility spread (Z-spread) is the steady spread that makes the price of a security equivalent to the current value of its cash flows when added to the yield at each point on the spot rate Treasury curve where cash flow is received. All in all, each cash flow is discounted at the fitting Treasury spot rate plus the Z-spread. The Z-spread is otherwise called a static spread.

Formula and Calculation for the Zero-Volatility Spread

To compute a Z-spread, an investor must take the Treasury spot rate at each pertinent maturity, add the Z-spread to this rate, and afterward utilize this combined rate as the discount rate to work out the price of the bond. The formula to work out a Z-spread is:
$\begin &\text = \frac { \left ( 1 + \frac { r_1 + Z }{ 2 } \right ) ^ {2n} } + \frac { \left ( 1 + \frac { r_2 + Z }{ 2 } \right ) ^ {2n} } + \frac { \left ( 1 + \frac { r_n + Z }{ 2 } \right ) ^ {2n} } \ &\textbf \ &\text = \text \ &C_x = \text \ &r_x = \text \ &Z = \text \ &n = \text \ \end$
For instance, expect a bond is currently priced at $104.90. It has three future cash flows: a $5 payment next year, a $5 payment a long time from now and a last total payment of $105 in three years. The Treasury spot rate at the one-, two-, and three-year points are 2.5%, 2.7% and 3%. The formula would be set up as follows:
$\begin $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 { $105 }{ \left ( 1 + \frac { 3% + Z }{ 2 } \right ) ^ {2 \times 3 } } \end$
With the right Z-spread, this rearranges to:
$\begin $104.90 = $4.87 + $4.72 + $95.32 \end$
This suggests that the Z-spread equals 0.25% in this model.

What the Zero-Volatility Spread (Z-spread) Can Tell You

A Z-spread calculation is not quite the same as a nominal spread calculation. A nominal spread calculation utilizes one point on the Treasury yield curve (not the spot-rate Treasury yield curve) to decide the spread at a single point that will rise to the current value of the security's cash flows to its price.

The Zero-volatility spread (Z-spread) assists analysts with discovering in the event that there is an error in a bond's price. Since the Z-spread measures the spread that an investor will receive over the entirety of the Treasury yield curve, it provides analysts with a more practical valuation of a security rather than a single-point metric, for example, a bond's maturity date.

Features

The Z-spread is likewise called the static spread.
The spread is involved by analysts and investors to discover disparities in a bond's price.
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.