Accumulated oas option adjusted spread

What Is Option-Adjusted Spread (OAS)?

The Option-Adjusted Spread (OAS) is a sophisticated measure used in fixed-income analysis to evaluate the additional yield an investor receives for holding a fixed-income security that contains embedded options. It quantifies the spread over a risk-free rate, typically the Treasury yield curve, after accounting for the potential impact of these embedded features on the bond's cash flows. As a core concept within bond valuation, OAS provides a more accurate assessment of a bond's yield relative to its inherent risks, distinguishing between compensation for credit risk and compensation for the risks associated with the embedded options. This metric is particularly vital for evaluating complex instruments like mortgage-backed securities (MBS) or callable bonds, where future cash flows are not fixed but depend on various market conditions.

History and Origin

The concept of the Option-Adjusted Spread emerged in the 1980s, a period marked by increasing complexity in financial markets and heightened interest rate volatility.²⁴ Its development was closely tied to the proliferation of mortgage-backed securities and other structured products, which introduced embedded options like prepayment rights for borrowers.²³ Traditional yield measures proved inadequate for valuing these securities accurately because they did not account for the dynamic nature of cash flows influenced by such options. As computing power advanced in the 1990s, more sophisticated valuation models, including those necessary for OAS calculations, became feasible. This enabled fixed-income analysts to better assess risk and perform relative value comparisons across a wider range of debt instruments.²²

Key Takeaways

• The Option-Adjusted Spread (OAS) is a measure of the yield spread over a benchmark yield curve for bonds with embedded options.
• It adjusts for the value of embedded options, providing a clearer measure of a bond's credit risk by separating it from option-related risks.
• OAS is particularly useful for valuing complex securities like mortgage-backed securities (MBS) and callable bonds, where cash flows are uncertain due to borrower or issuer options.
• The calculation of OAS involves complex financial models, such as binomial trees or Monte Carlo simulation, to account for various interest rate scenarios and option exercise probabilities.
• A higher OAS generally indicates a higher expected return for the additional risks assumed, making it a key tool for comparing the relative value of different fixed-income investments.

Formula and Calculation

The calculation of Option-Adjusted Spread (OAS) is complex and typically involves iterative numerical methods. Conceptually, OAS represents the constant spread that, when added to every point on the appropriate risk-free rate (e.g., Treasury) yield curve, equates the theoretical price of a security (derived from a dynamic pricing model that accounts for embedded options) to its observed market price.

While the precise calculation relies on complex models, the relationship between OAS, Z-spread, and the cost of the embedded option can be expressed simply:

Where:

• OAS is the Option-Adjusted Spread, expressed in basis points.
• Z-spread (Zero-Volatility Spread) is the constant spread that, when added to the benchmark spot rate curve, makes the present value of a bond's cash flows equal to its market price, without considering embedded options.
• Option Cost is the value of the embedded option(s) in the bond, expressed in basis points. This cost reflects the benefit of the option to its holder (issuer for a callable bond, investor for a putable bond).²¹

For a callable bond, the option cost is positive from the issuer's perspective, effectively reducing the OAS compared to the Z-spread, as the investor is compensated for the issuer's right to call the bond early. For a putable bond, the option cost is negative from the issuer's perspective (a benefit to the investor), leading to a higher OAS than the Z-spread.²⁰

Interpreting the Option-Adjusted Spread

Interpreting the Option-Adjusted Spread (OAS) involves understanding what the resulting numeric value signifies in the context of a bond's pricing and risk. A positive OAS indicates that the bond offers a yield higher than the risk-free rate after adjusting for the impact of its embedded options. This additional yield compensates investors for various risks, primarily credit risk, but also potentially illiquidity or other unmodeled risks.¹⁹

When comparing two bonds, a higher OAS (assuming similar credit quality and other characteristics) typically suggests that the bond is relatively undervalued or offers a greater expected return for a given level of risk, especially if the embedded options are properly accounted for in the model. Conversely, a lower OAS might indicate that a bond is relatively overvalued or offers less compensation for its risks.¹⁸ Investors use OAS to assess if they are adequately compensated for the unique risks posed by options, such as prepayment risk in mortgage-backed securities or call risk in callable bonds.

Hypothetical Example

Consider two hypothetical bonds, Bond A and Bond B, both with a face value of $1,000, a 5-year maturity, and a market price of $980. The prevailing risk-free rate for 5-year Treasury bonds is 3%.

• Bond A is a plain vanilla corporate bond with no embedded options. Its Z-spread is calculated to be 150 basis points. Since there are no embedded options, its Option Cost is 0.

  • OAS (Bond A) = 150 bps - 0 bps = 150 bps.

• Bond B is a callable bond issued by a similar corporation, with the issuer having the right to call the bond after 2 years if interest rates fall significantly. Its Z-spread is calculated to be 180 basis points. Due to the embedded call option, a financial model estimates the Option Cost to the investor (benefit to the issuer) as 40 basis points.

  • OAS (Bond B) = 180 bps - 40 bps = 140 bps.

In this example, while Bond B initially appears to offer a higher spread over the Treasury curve (180 bps Z-spread vs. 150 bps Z-spread for Bond A), its Option-Adjusted Spread of 140 bps is lower than Bond A's 150 bps. This indicates that once the value of the embedded call option (which favors the issuer) is factored in, Bond A offers a comparatively higher risk-adjusted return for its credit risk and other non-option related risks. Investors would use this insight in their bond valuation process to determine which bond offers better value.

Practical Applications

The Option-Adjusted Spread (OAS) is a critical tool with diverse applications in the world of fixed-income analysis. Its ability to dissect the components of a bond's yield spread makes it invaluable for various financial professionals:

• Relative Value Analysis: OAS allows investors to compare the attractiveness of different bonds, particularly those with varying embedded options. By adjusting for these options, it provides a more "apples-to-apples" comparison of the underlying credit risk and other non-option risks. For instance, comparing the OAS of a callable bond to a non-callable bond helps reveal which security offers superior risk-adjusted compensation.¹⁷,¹⁶
• Portfolio Management: Portfolio managers use OAS to identify undervalued or overvalued securities. A bond with a higher OAS relative to comparable securities might be considered cheap, signaling a potential buying opportunity. Conversely, a low OAS might suggest an overpriced bond.¹⁵ This metric helps guide asset allocation decisions within fixed-income portfolios.
• Risk Management: OAS assists in managing interest rate risk and prepayment risk. By understanding how embedded options affect a bond's sensitivity to interest rate changes, analysts can better model potential future cash flows and adjust their hedges or portfolio exposures accordingly.¹⁴ The effective duration of a bond, which accounts for cash flow changes due to embedded options, is often a byproduct of the models used to calculate OAS.¹³
• Pricing and Trading: For market makers and traders, OAS is essential for accurately pricing complex fixed-income instruments, especially mortgage-backed securities. It helps determine a fair price by quantifying the spread that compensates for all inherent risks, excluding the option's influence.¹²

Limitations and Criticisms

Despite its widespread use and theoretical advantages, the Option-Adjusted Spread (OAS) has several limitations and has faced criticisms:

• Model Dependence: The accuracy of OAS is highly dependent on the underlying financial model used for its calculation. These models, often employing complex techniques like Monte Carlo simulation or binomial trees, rely on various assumptions, particularly regarding future interest rate volatility and prepayment risk. If these assumptions are flawed or do not reflect actual market behavior, the resulting OAS can be inaccurate. Different models or even different inputs (e.g., volatility assumptions) within the same model can yield different OAS values for the same bond, impacting relative value assessments.¹¹,¹⁰
• Lack of Standardization: There is no universal standard for calculating OAS. Different market participants may use proprietary models or different methodologies and assumptions, leading to inconsistencies in OAS values. This lack of standardization can make it challenging to compare OAS figures across different institutions or to use them as a universal benchmark.⁹
• Difficulty in Interpretation: While OAS aims to provide a "true" spread net of option effects, its interpretation can sometimes be misleading. It is an averaged number across many simulated interest rate paths and may not fully capture the behavior of a security under specific, unfavorable market scenarios.⁸ Furthermore, some models may not fully account for all types of embedded options (e.g., default options) or other market factors like liquidity, potentially leading to a distorted picture of true risk compensation.⁷
• Historical Data Reliance: OAS calculations often rely on historical data for estimating parameters like volatility and prepayment rates. However, past behavior may not perfectly predict future market conditions or borrower behavior, especially during periods of significant economic change or market stress.

These limitations highlight that while OAS is a powerful analytical tool, it should not be used in isolation. Financial professionals often combine OAS analysis with other metrics and qualitative assessments to make more informed bond valuation and investment decisions.⁶

Option-Adjusted Spread vs. Z-spread

The Option-Adjusted Spread (OAS) and the Z-spread are both measures of credit risk and other non-benchmark yield components, but they differ fundamentally in how they account for embedded options within a bond.

The Z-spread, or Zero-Volatility Spread, represents the constant spread that, when added to each point on a benchmark yield curve (typically the Treasury spot rate curve), discounts a bond's projected cash flows to its observed market price.⁵ It is a static measure that assumes fixed cash flows and does not consider any changes to these cash flows that might arise from embedded options, such as call or put provisions. In essence, the Z-spread incorporates all forms of spread (credit, liquidity, optionality) without separating them.

In contrast, the Option-Adjusted Spread (OAS) refines the Z-spread by explicitly accounting for the value of these embedded options. OAS uses a dynamic pricing model that simulates numerous interest rate paths and potential option exercises, aiming to remove the portion of the spread attributable to the options themselves. For a callable bond, where the issuer has the right to redeem the bond early, the option reduces the value to the investor, so the OAS will be lower than the Z-spread. Conversely, for a putable bond, where the investor has the right to sell the bond back to the issuer, the option benefits the investor, making the OAS higher than the Z-spread.⁴

The key distinction is that OAS seeks to isolate the spread component that solely reflects the bond's fundamental credit risk and other non-option related factors, providing a more "option-free" measure for comparative analysis.³

FAQs

What types of bonds is OAS most useful for?

OAS is most useful for valuing bonds that have embedded options, such as callable bonds (where the issuer can redeem early), putable bonds (where the investor can sell early), and especially mortgage-backed securities (MBS), which have complex prepayment risk due to borrowers' ability to refinance their mortgages.

How does interest rate volatility affect OAS?

Interest rate volatility significantly impacts OAS. For bonds with embedded options, higher volatility generally increases the value of the option. For a callable bond, higher volatility increases the issuer's incentive to call the bond, which is detrimental to the investor, thus typically leading to a lower OAS. For a putable bond, higher volatility makes the put option more valuable to the investor, resulting in a higher OAS.²

Can OAS be negative?

Theoretically, OAS can be negative, although this is rare in practice and often suggests a mispricing in the market or issues with the valuation model's assumptions. A negative OAS would imply that the bond's yield is below the risk-free rate even after accounting for embedded options and credit risk. Such a scenario would typically be an arbitrage opportunity, indicating the bond is significantly overvalued.¹

Is a higher OAS always better?

Generally, for bonds of similar characteristics and credit risk, a higher OAS is considered better from an investor's perspective. It implies that the investor is receiving more compensation (yield) for the risks taken, after adjusting for the impact of embedded options. However, it is crucial to ensure that the higher OAS isn't simply a reflection of higher uncompensated risks not fully captured by the model or significant liquidity risk.