The Z-spread, also referred to as the Z-spread or zero volatility spread addresses a limitation shared by the traditional credit spread, G-spread, and I-spread.
Each of these measures compares the yield to maturity of a corporate bond to a single benchmark rate at a specific maturity.
By doing so, they overlook the broader structure of the yield curve and the variations in interest rates across different maturities.
In reality, interest rates vary by maturity forming a yield curve that reflects market expectations about future rate changes.
As a result, the cashflow structure of a bond, such as the timing and size of coupon payments affects its value.
However, yield to maturity calculations assume a flat yield curve, which implies that the same interest rate applies to all cash flows regardless of their timing.
This means yield to maturity, or YTM does not account for variations in cashflow patterns across different maturities.
The Z-spread adjusts for this by adding a constant spread across the entire yield curve.
This constant spread represents the credit risk premium applied over each point on the curve to discount the bonds cash flows.
The Z-spread calculation therefore considers how changes in spot or zero coupon interest rates at various maturities affect the present value of each cash flow, thereby providing a more comprehensive measure of credit risk that reflects the bond specific cash flow structure.
Let's look at an example using the Deutsche Telecom bond with a YTM of 2.432% and various cash flows.
The Z-spread can generally be calculated using either government bond yields or swap rates as a base curve.
In our example, we use the swap curve because it provides a unified benchmark for euro denominated bonds.
Additionally, swap rates are often preferred because they are par rates representing rates at which fixed for floating swaps are priced at par, providing a consistent reference across maturities.
Now, let's walk through the table.
The first column lists the bonds cash flows, while the second column shows the spot or zero coupon rates derived from the swap curve.
We use zero coupon rates as they reflect the exact present value of cash flows without reinvestment assumptions, allowing for precise discounting of each of the bonds cash flows according to its timing.
If we were to discount the bonds cash flows using the unadjusted zero coupon curve based on our benchmark swap rates, we Would arrive at a theoretical clean price of around 1060.1%.
This is effectively the price the bond would have if it were credit risk free, but which is too high for our credit risky corporate bond, which has a market price of 104.08%.
This discrepancy indicates that a credit risk adjustment or spread needs to be applied to each of the differing zero coupon rates so that the present value of all cash flows aligns with the actual market price of the bond.
The amount that needs to be added is determined through trial and error.
At the end of this process, a Z-spread of 0.447% has been identified.
By adding a Z-spread of 0.447% across the entire zero coupon curve, we increase the discount rates applied to each cash flow, effectively adjusting for the credit risk of the corporate bond.
This constant spread ensures that the present value of all cash flows aligns with the bond's observed clean price, incorporating both the bond's cash flow structure, and the shape of the yield curve.
Although this approach is more involved than the I-spread, it provides a more precise measure of credit risk compared to a single maturity benchmark.
