## Option-Adjusted – OAS vs. Zero-Volatility Spread – Z-Spread: An Overview

Both the option-adjusted (OAS) and the zero-volatility spread (Z-spread) are useful to calculate the value of a security. In general, a spread represents the difference between the two measurements. The OAS and Z-spread help investors compare the yield of two different fixed-income offerings that have embedded options. Embedded options are provisions included with some fixed-income securities that allow the investor or the issuer to do specific actions, such as calling back the issue.

As an example, mortgage-backed securities (MBS) often have embedded options due to the prepayment risk associated with the underlying mortgages. As such, the embedded option can have a significant impact on the future cash flows and the present value of the MBS.

An option-adjusted spread compares the yield or return of a fixed-income product to the risk-free rate of return on the investment. The risk-free rate is theoretical and shows the value of an investment with all possible risk dynamics removed. Most analysts use U.S. Treasurys as the basis of the risk-free return.

The zero-volatility spread provides the analyst with a way to evaluate a bond's pricing. It is the consistent spread—or difference—between the present cash flow value and the U.S. Treasury spot rate yield curve. Z-spread is also known as the static spread because of the consistent feature.

The nominal spread is the most basic type of spread concept. It measures the difference in the basis points between a risk-free U.S. Treasury debt instrument and a non-Treasury instrument. This spread difference is measured in basis points. The nominal spread only provides the measure at one point along the Treasury yield curve, which is a significant limitation.

## Option-Adjusted Spread

Unlike the Z-spread calculation, the option-adjusted spread takes into account how the embedded option in a bond can change the future cash flows and the overall value of the bond. These enclosed options can include allowing the issuer to call back the debt offering early or the investor to convert the bond into underlying company shares or demand early redemption.

The embedded option's cost is calculated as the difference between the option-adjusted spread at the expected market interest rate and the Z-spread. The base calculations for both spreads are similar. However, the option-adjusted spread will discount the bond's value due to any options included in the issue. This calculation allows an investor to determine if the listed price of a fixed-income security is worthwhile due to the risks associated with the added options.

The OAS adjusts the Z-spread to include the value of the embedded option. It is, therefore, a dynamic pricing model that is highly dependent on the model being used. Also, it allows for the comparison using the market interest rate and the possibility of the bond being called early—known as prepayment risk.

The option-adjusted spread considers historical data as the variability of interest rates and prepayment rates. These factors' calculations are complex since they attempt to model future changes in interest rates, prepayment behavior of mortgage borrowers, and the probability of early redemption. More advanced statistical modeling methods such as Monte Carlo analysis are often used to predict prepayment probabilities.

## Z-Spread

The zero-volatility spread provides the difference in basis points along the entire Treasury yield curve. The Z-spread is the uniform measurement comparing the bond's price equal to its present cash flow value against each point of maturity for the Treasury yield curve. Therefore, the bond's cash flow is discounted against the Treasury curve's spot rate. The complex calculation includes taking the spot rate at a given point in the curve and adding the z-spread to this number. However, the Z-spread does not include the value of embedded options in its calculation which can impact the present value of the bond.

Mortgage-backed securities often include embedded options, since there is a significant risk of prepayment. Mortgage borrowers are more likely to refinance their mortgages if interest rates go down. The embedded option means the future cash flows are alterable by the issuer since the bond can be called. The issuer may use the embedded option if interest rates drop. The call allows the issuer to call the outstanding debt, pay it off and reissue it at a lower interest rate. By being able to reissue the debt at a lower interest rate, the issuer can reduce the cost of capital.

Investors in bonds with embedded options, therefore, take on more risk. If the bond is called, the investor will likely be forced to reinvest in other bonds with lower interest rates. Bonds with embedded call options often pay a yield premium over bonds with similar terms. Thus, the option-adjusted spread is helpful to understand the present value of debt securities with embedded call options.

### Key Takeaways

- The option-adjusted spread (OAS) considers how a bond's embedded option can change the future cash flows and the overall value of the bond.
- The option-adjusted spread adjusts the Z-spread to include the embedded option's value.
- The zero-volatility spread (Z-spread) provides the difference in basis points along the entire Treasury yield curve.
- The analyst will use OAS and Z-spread to compare debt securities for value.