Adjusted annualized spread

What Is Adjusted Annualized Spread?

The Adjusted Annualized Spread, commonly known as the Option-Adjusted Spread (OAS), is a key measure in fixed income analysis that quantifies the yield difference between a bond with embedded options and a comparable benchmark, typically a U.S. Treasury security. It represents the additional yield an investor receives for holding a bond that contains provisions, such as call or put options, while attempting to strip out the value attributed to these options. This concept falls under the broader financial category of bond valuation. By adjusting for the impact of these embedded options, the Adjusted Annualized Spread provides a more accurate reflection of the compensation for risks inherent in the bond, primarily credit risk and liquidity risk. It aims to isolate the spread component that is purely attributable to the bond's fundamental characteristics rather than the probabilistic outcomes of its embedded features.³⁷

History and Origin

The concept of credit spreads, which is foundational to the Adjusted Annualized Spread, has historical roots dating back to the emergence of corporate bonds. While government bonds, often considered risk-free, have existed for centuries, corporate bonds first appeared with entities like the Dutch East India Company in the 1600s.³⁶ Initially, the difference in yield between a corporate bond and a U.S. Treasury bond was informally used to gauge credit risk. By the 1960s, this practice was fully integrated into bond relative-value analysis.³⁵

However, as fixed-income markets grew in complexity, particularly with the introduction of bonds featuring embedded options, simpler spread measures proved insufficient. In the 1980s and 1990s, new approaches evolved to derive credit spreads that accounted for these complexities.³⁴ The Zero-Volatility Spread (Z-spread) emerged as a fixed spread added to the risk-free yield curve to match a bond's price.³², ³³ However, the Z-spread did not account for the impact of interest rate volatility on the embedded options themselves. This limitation led to the development of the Option-Adjusted Spread (OAS), which sought to remove the value of these options from the Z-spread, providing a truer measure of the credit and liquidity components of the yield spread.³¹ This advancement was enabled by the concurrent development of term structure models that could value such options.³⁰

Key Takeaways

• The Adjusted Annualized Spread, or Option-Adjusted Spread (OAS), quantifies the yield premium of a bond with embedded options over a benchmark, adjusting for the value of those options.²⁹
• It is a more sophisticated measure than the nominal spread or Z-spread for evaluating bonds with complex features like call options or put options.²⁸
• OAS aims to isolate the compensation for credit and liquidity risks, making it easier to compare bonds with differing embedded option characteristics.²⁶, ²⁷
• A higher OAS generally suggests that a bond is undervalued relative to its risk, while a lower OAS indicates it may be overvalued.²⁵
• The calculation of OAS involves complex modeling, often using binomial or Monte Carlo simulations to project cash flows under various interest rate scenarios.

Formula and Calculation

The calculation of the Adjusted Annualized Spread (OAS) is an iterative and complex process, as it involves removing the theoretical cost of an embedded option from a bond's yield spread. Conceptually, it is often expressed in relation to the Z-spread and the value of the embedded option.

Where:

• OAS (Option-Adjusted Spread): The spread that remains after adjusting for the embedded option's value.
• Z-Spread (Zero-Volatility Spread): The constant spread that, when added to each point on the benchmark spot rate curve, equates the present value of the bond's cash flows to its market price, assuming no interest rate volatility and no embedded options.²⁴
• Option Cost: The value attributed to the embedded option (e.g., call or put). This cost is subtracted for issuer-favorable options (like a callable bond) because the investor requires less compensation for the non-option risk, as the option benefits the issuer. It is added for investor-favorable options (like a putable bond) because the investor benefits from the option and thus requires greater compensation for the non-option risk.²³

The actual computation of OAS typically involves:

1. Constructing an Interest Rate Tree: This models future interest rate paths, accounting for interest rate volatility.
2. Valuing the Bond: Under each path of the interest rate tree, the bond's cash flows are determined, considering how the embedded option would be exercised (e.g., if a bond is called or put).
3. Iterative Adjustment: The OAS is the constant spread that, when subtracted from (or added to) the interest rates at each node of the tree, makes the calculated arbitrage-free value of the bond equal to its current market price.²² This trial-and-error procedure is often performed using specialized financial software.

Interpreting the Adjusted Annualized Spread

Interpreting the Adjusted Annualized Spread (OAS) is crucial for evaluating fixed-income securities, especially those with embedded options. The OAS represents the compensation an investor receives for holding a bond's inherent credit and liquidity risks, after accounting for the influence of any embedded features.²¹

A higher Adjusted Annualized Spread, relative to comparable bonds, generally indicates that the bond is offering more compensation for its non-option risks. For an investor, a higher OAS for a bond with similar credit risk and maturity suggests that the bond might be undervalued or "cheap" compared to others in the market.²⁰ Conversely, a lower OAS could signal that the bond is relatively overvalued or "expensive." Analysts often compare the OAS of different bonds to assess their relative value.¹⁹

It's important to remember that the OAS is a model-dependent measure. Its accuracy relies on the assumptions made in the interest rate model and the volatility estimates used. Changes in these assumptions can lead to different OAS values for the same bond. Therefore, investors and analysts typically use the OAS in conjunction with other metrics and a thorough understanding of the bond's structure and the issuer's financial health.

Hypothetical Example

Consider two hypothetical corporate bonds, Bond A and Bond B, both with a 5-year maturity and issued by companies with similar credit ratings.

• Bond A: A plain vanilla (option-free) corporate bond, yielding 5.5%.
• Bond B: A callable corporate bond, meaning the issuer has the right to redeem the bond before maturity, yielding 6.0%.

Let's assume the current 5-year U.S. Treasury yield (considered the risk-free rate) is 3.0%.

First, we calculate a simple credit spread (or nominal spread) for both:

• Bond A Spread: 5.5% - 3.0% = 2.5% or 250 basis points.
• Bond B Spread: 6.0% - 3.0% = 3.0% or 300 basis points.

Superficially, Bond B offers a higher spread. However, Bond B has an embedded call option, which benefits the issuer. This option effectively makes Bond B less attractive to the investor because their potential upside is limited if interest rates fall and the bond is called. The Adjusted Annualized Spread accounts for this.

Let's say, after running a complex model that considers future interest rate paths and the probability of the call option being exercised, the option cost for Bond B is determined to be 70 basis points.

To calculate Bond B's Adjusted Annualized Spread (OAS), we would subtract this option cost from a comparable spread like the Z-spread (for simplicity, if we assume the Z-spread for Bond B, before adjusting for the option, is 300 bps):

Now, comparing the "adjusted" spreads:

• Bond A (option-free, so its simple credit spread is effectively its OAS): 250 bps
• Bond B (callable, OAS): 230 bps

Even though Bond B initially had a higher nominal yield and spread, its Adjusted Annualized Spread is lower once the value of the issuer's call option is factored in. This indicates that Bond A provides a higher yield premium for its credit and liquidity risks, making it potentially more attractive on an option-adjusted basis. This example highlights how the Adjusted Annualized Spread provides a more "apples-to-apples" comparison when evaluating bond valuation for securities with embedded features.

Practical Applications

The Adjusted Annualized Spread (OAS) is an indispensable tool in the world of fixed income securities for a variety of professionals. Its primary application lies in enabling investors and analysts to compare the relative attractiveness of bonds, particularly those with embedded options. By stripping out the influence of these options, OAS provides a clearer picture of the compensation received for pure credit and liquidity risk.

For portfolio managers, OAS helps in identifying undervalued or overvalued bonds, allowing for more informed allocation decisions within a diversified bond portfolio. For instance, an investment-grade corporate bond with a surprisingly high OAS might signal a good buying opportunity if the underlying credit quality is sound. Financial institutions and traders heavily rely on OAS models for risk management and pricing complex derivatives. Data providers like Bloomberg Terminal also calculate and disseminate OAS for various bond indices, which professionals use for market analysis and benchmarking.¹⁷, ¹⁸

Regulatory bodies also emphasize transparency in bond markets. The U.S. Securities and Exchange Commission (SEC), for example, stresses the importance of accurate and complete disclosure in municipal bond markets to help investors make informed decisions.¹⁶ While OAS isn't a direct regulatory requirement for disclosure, the underlying principles of understanding all components of a bond's yield spread, including the impact of embedded options, align with the SEC's emphasis on transparency. The Federal Reserve Bank of St. Louis's FRED database provides historical data for Option-Adjusted Spreads across various corporate bond indices, offering valuable insights into market conditions and risk premiums over time.¹⁵

Limitations and Criticisms

Despite its sophistication, the Adjusted Annualized Spread (OAS) has several limitations and criticisms that investors should consider. A primary concern is its model dependence. The calculation of OAS relies heavily on the assumptions built into the interest rate model and the volatility assumptions used to price the embedded option. Different models or different volatility inputs can produce varying OAS values for the same bond, leading to inconsistencies.¹⁴

Another criticism is that OAS, while adjusting for embedded options, still represents a theoretical spread. It assumes rational exercise of the options (e.g., an issuer will call a bond if it is economically advantageous). In reality, issuers might not always act optimally due to various factors, including financial covenants, reputational considerations, or operational constraints, which can affect the actual cash flows received by the investor.

Furthermore, market conditions can significantly influence spreads, sometimes in ways not fully captured by models. For instance, during periods of heightened market stress or economic uncertainty, credit spreads, including those that are option-adjusted, tend to widen as investors demand higher compensation for perceived risks.¹³ Conversely, in strong economic environments, spreads can tighten significantly.¹² Some analyses suggest that even when spreads appear tight, the underlying quality of bonds (like high-yield bonds) may have improved, complicating direct comparisons based solely on spread levels.¹¹ Factors like liquidity also play a role, with less liquid bonds often commanding wider spreads to compensate investors for the difficulty of trading them.¹⁰

Finally, while the OAS aims to isolate credit and liquidity risks, some argue that it can still be influenced by market technicals (supply and demand dynamics) or broader macroeconomic factors, making it challenging to attribute its entire value solely to the bond's intrinsic risks. The Bank for International Settlements (BIS) published analysis, for example, on how central bank interventions, like the Federal Reserve's corporate bond buying program during the COVID-19 pandemic, significantly lowered credit spreads, often through a reduction in credit risk premia rather than solely default risk, indicating the influence of non-fundamental factors.⁹

Adjusted Annualized Spread vs. Zero-Volatility Spread (Z-spread)

The Adjusted Annualized Spread (OAS) and the Zero-Volatility Spread (Z-spread) are both measures used in fixed income to express the yield premium of a bond over a benchmark yield curve. However, their fundamental difference lies in how they account for embedded options.

The Z-spread is the constant spread that, when added to each point on a benchmark Treasury yield curve (or other risk-free curve), makes the present value of a bond's cash flows equal to its market price. The key characteristic of the Z-spread is that it does not consider the impact of any embedded options within the bond. It assumes a static cash flow stream, regardless of future interest rate movements. As such, the Z-spread reflects compensation for credit risk, liquidity risk, and any other non-option risks, plus the implicit value of any embedded options.⁷, ⁸

In contrast, the Adjusted Annualized Spread (OAS) takes the Z-spread a step further by explicitly accounting for the value of embedded options. It uses an interest rate model (e.g., a binomial or Monte Carlo model) to simulate various future interest rate paths and determines how the bond's cash flows would change if the option were exercised. The OAS is then the constant spread that, when added to the benchmark rates in this dynamic framework, equates the bond's theoretical value to its market price. Essentially, OAS adjusts the Z-spread to remove the portion of the spread attributable to the embedded option, providing a cleaner measure of compensation solely for the bond's fundamental credit and liquidity risks.⁶

For instance, a callable bond (where the issuer can redeem it early) will have an OAS lower than its Z-spread because the call option benefits the issuer, making the bond less valuable to the investor on an option-adjusted basis.⁴, ⁵ Conversely, a putable bond (where the investor can sell it back to the issuer early) will have an OAS higher than its Z-spread, as the put option benefits the investor.³ Therefore, the OAS is generally considered a more accurate tool for comparing bonds with embedded options, as it allows for a more "apples-to-apples" comparison of their underlying risk premiums.

FAQs

What does a higher Adjusted Annualized Spread mean for an investor?

A higher Adjusted Annualized Spread generally indicates that a bond is offering more yield compensation for its underlying credit and liquidity risks, after accounting for any embedded options. If compared to a similar bond, a higher OAS might suggest it is relatively undervalued or "cheap" in the market.²

Is the Adjusted Annualized Spread applicable to all types of bonds?

The Adjusted Annualized Spread is most relevant and insightful for bonds that contain embedded options, such as callable bonds, putable bonds, or mortgage-backed securities (MBS). For plain vanilla (option-free) bonds, the Z-spread is often sufficient, as there are no options to adjust for, and in theory, the OAS would be equal to the Z-spread if volatility were zero.¹

How does interest rate volatility affect the Adjusted Annualized Spread?

Interest rate volatility significantly impacts the calculation of the Adjusted Annualized Spread. Higher volatility increases the value of embedded options. For example, in a callable bond, higher volatility makes the issuer's call option more valuable, which typically leads to a lower OAS for the investor. Conversely, for a putable bond, higher volatility makes the investor's put option more valuable, which would result in a higher OAS.

Can the Adjusted Annualized Spread predict future bond returns?

While the Adjusted Annualized Spread provides a valuable measure of a bond's relative value at a given point in time, it does not directly predict future bond returns. Bond returns are influenced by many factors, including changes in interest rates, credit quality, market liquidity, and broader economic conditions. OAS helps in assessing the yield premium received for risks, but actual returns depend on how those risks materialize and market prices evolve.