Adjusted discounted spread

What Is Option-Adjusted Spread?

The Option-Adjusted Spread (OAS) is a sophisticated measure used in fixed income valuation to quantify the additional yield an investor demands for taking on the risks associated with a bond that contains embedded options. Unlike simpler spread measures, the OAS accounts for how these options, such as the right of an issuer to call a bond early or an investor to put a bond back to the issuer, can impact a security's future cash flows and overall value²⁵. It falls under the broader category of financial modeling and is particularly relevant for complex fixed income securities like mortgage-backed securities (MBS) and callable bonds. The Option-Adjusted Spread essentially represents the spread over a benchmark yield curve that compensates investors for both credit and liquidity risks, after isolating the impact of any embedded options²⁴.

History and Origin

The concept of accounting for embedded options in bond valuation became increasingly important with the proliferation of complex fixed-income instruments, particularly mortgage-backed securities (MBS) in the 1980s and 1990s. These securities introduced significant prepayment risk, where underlying mortgage holders could prepay their loans, dramatically altering the cash flow stream to MBS investors. Traditional yield measures and simpler spreads could not adequately capture the value or cost of these embedded prepayment options.

As such, financial engineers and quantitative analysts developed more advanced valuation models, including Monte Carlo simulations and binomial trees, to project a bond's cash flows under various interest rate scenarios. The Option-Adjusted Spread emerged as a way to derive a spread that was "option-free," allowing for a more accurate comparison of bonds with differing embedded options. This evolution reflected a growing need for sophisticated tools to analyze and price securities in an increasingly complex bond market. The development of robust yield curve models by institutions like the European Central Bank has been fundamental to the accuracy of OAS calculations, providing the necessary framework for simulating interest rate paths²³.

Key Takeaways

• Option-Adjusted Spread (OAS) quantifies the yield spread on a bond with embedded options over a risk-free benchmark, adjusting for the value of those options.
• It is a dynamic measure that considers how changes in interest rates can affect the exercise of embedded options and, consequently, the bond's cash flows.
• OAS helps investors compare the relative value of fixed-income securities, especially those with features like call or put options, by stripping out the impact of optionality.
• The calculation of OAS typically involves complex models like Monte Carlo simulations, which project cash flows across numerous possible interest rate scenarios.
• A higher Option-Adjusted Spread generally indicates a greater risk-adjusted return for the investor, assuming the underlying valuation model is sound.

Formula and Calculation

The Option-Adjusted Spread (OAS) does not have a single, simple algebraic formula like a yield to maturity or a static spread. Instead, it is derived through an iterative process using complex financial modeling techniques, most commonly binomial tree models or Monte Carlo simulations. The core idea is to find the constant spread that, when added to every point on the benchmark spot rate curve (typically the Treasury yield curve), makes the theoretical value of the bond's projected cash flows equal to its observed market price, while explicitly accounting for the optionality.

The general relationship can be conceptualized as:

Where:

• (\text{Market Price}) = The current observed market price of the bond.
• (\text{Expected Cash Flow}_t) = The projected cash flow at time (t), determined by simulating various interest rate paths and accounting for the likelihood and impact of the embedded option being exercised (e.g., a callable bond being called or a putable bond being put)²².
• (\text{Spot Rate}_t) = The benchmark (e.g., U.S. Treasury) spot rate for maturity (t), derived from the prevailing yield curve.
• (\text{OAS}) = The Option-Adjusted Spread, which is the value being solved for.
• (N) = The number of cash flow periods.

The iterative process involves:

1. Generating a large number of possible interest rate paths using a stochastic interest rate model.
2. For each path, determining the bond's cash flows by factoring in the embedded options. For example, if interest rates fall significantly, a callable bond might be called, ending its cash flows early.
3. Discounting these cash flows back to the present using the benchmark spot rates plus an assumed spread.
4. Averaging the present values across all simulated paths.
5. Adjusting the assumed spread (the OAS) until the average present value equals the bond's current market price.

This calculation inherently incorporates interest rate volatility into the valuation, as higher volatility increases the value of embedded options and thus impacts the Option-Adjusted Spread.

Interpreting the Option-Adjusted Spread

The Option-Adjusted Spread provides a more accurate assessment of a bond's value and risk relative to a benchmark by separating the premium for credit and liquidity risk from the impact of embedded options. A higher Option-Adjusted Spread generally indicates that the bond offers a greater return for the risks it carries, excluding the risks related to its embedded options²¹. This makes it a crucial tool for comparing bonds with different structural complexities.

For instance, if Bond A has an OAS of 100 basis points and Bond B has an OAS of 80 basis points, and both are otherwise comparable in terms of credit quality and maturity, Bond A is considered more attractive on a risk-adjusted basis. This is because it offers an additional 20 basis points of yield for the underlying credit and liquidity risks after removing the effect of any embedded options. Investors use the OAS to determine if a bond's listed price is worthwhile given the risks, allowing them to assess whether they are adequately compensated for the non-option-related risks. It helps in identifying potentially undervalued or overvalued securities by providing a "cleaner" spread measure.

Hypothetical Example

Consider an investor, Sarah, who is evaluating two mortgage-backed securities (MBS) that have similar credit ratings and maturities but different underlying mortgage pools, which could lead to different prepayment risk characteristics. MBS A has an observed market price of $980 and MBS B has an observed market price of $975. Both are benchmarked against the current Treasury yield curve.

Sarah uses a financial model that simulates 1,000 possible interest rate paths for each MBS, taking into account how changes in rates would influence homeowner prepayment behavior. For each path, the model calculates the expected cash flows and discounts them back to the present.

After running the simulations:

• For MBS A, the model finds that a constant spread of 120 basis points (1.20%) added to the Treasury spot rates makes the average present value of its cash flows equal to its market price of $980.
• For MBS B, the model determines that a constant spread of 105 basis points (1.05%) is required to equate its average present value to its market price of $975.

In this scenario, MBS A has an Option-Adjusted Spread of 120 basis points, while MBS B has an OAS of 105 basis points. Despite MBS B having a slightly lower market price, MBS A offers a higher OAS. This suggests that, after adjusting for the embedded prepayment options, MBS A provides a greater yield premium for the non-option risks (like credit risk and liquidity risk) compared to MBS B. Therefore, Sarah might conclude that MBS A offers better value for the risks she is undertaking. This analysis, based on a discounted cash flow approach, helps Sarah make a more informed investment decision.

Practical Applications

The Option-Adjusted Spread (OAS) is widely used by institutional investors, portfolio managers, and quantitative analysts in several key areas within fixed income securities analysis.

One primary application is in relative value analysis. Investors use OAS to compare bonds with embedded options, such as callable bonds, putable bonds, and mortgage-backed securities (MBS), to comparable option-free bonds or to each other. By removing the impact of optionality, OAS provides a "truer" spread that reflects only the compensation for credit and liquidity risks, allowing for more apples-to-apples comparisons across different bond structures. This helps portfolio managers identify bonds that may be undervalued or overvalued relative to their inherent risks²⁰.

OAS is also crucial in risk management. It helps to assess how a bond's value might react to changes in market interest rate volatility. Because the OAS calculation inherently incorporates volatility, it provides insights into the bond's behavior under different market conditions. For example, an MBS OAS will reflect the sensitivity of its cash flows to interest rate changes through prepayments.

Furthermore, market participants and policymakers monitor aggregate OAS levels across various bond sectors. For instance, the ICE BofA US High Yield Index Option-Adjusted Spread, published by the Federal Reserve Bank of St. Louis, provides insights into the perceived risk and investor sentiment in the high-yield bond market¹⁹. Widening credit spreads, including those adjusted for options, often signal increased economic uncertainty or concerns about corporate creditworthiness, while narrowing spreads suggest optimism¹⁸. Regulatory bodies also have an interest in spread transparency for investor protection. The Securities and Exchange Commission (SEC), in conjunction with bodies like FINRA, has discussed the importance of disclosing yield spreads to assist investors in making relative value comparisons in fixed-income markets, although specific OAS disclosure requirements for retail confirmations are more complex due to the model-dependent nature of OAS¹⁶, ¹⁷. FINRA Rule 2232, for instance, focuses on broader fixed income confirmation disclosures but highlights the regulatory emphasis on transparency in bond markets¹⁵.

Limitations and Criticisms

While the Option-Adjusted Spread (OAS) is a powerful tool, it has several limitations and criticisms that investors should consider. A primary concern is its model dependency. The calculation of OAS relies heavily on the specific financial modeling framework and assumptions used, particularly regarding future interest rate volatility and prepayment speeds¹⁴. Different models or different assumptions within the same model can produce varying OAS values for the same security, making direct comparisons across analyses from different sources challenging. The complexity of these models means that their outputs are only as reliable as their inputs and underlying assumptions.

Another criticism is that the OAS, by design, attempts to isolate the value of embedded options. However, separating these option values perfectly from other risks, such as credit risk and liquidity risk, can be difficult in practice¹³. The interaction between interest rate changes, credit quality, and market liquidity can be complex, and a model may not fully capture these interdependencies. For example, in times of market stress, both credit spreads and interest rate volatility might increase simultaneously, making it hard to disentangle their individual effects on a bond's price and, consequently, its OAS¹².

Furthermore, OAS models often rely on historical data to calibrate parameters, such as interest rate movements or prepayment patterns. However, past performance is not indicative of future results, and market conditions can change, rendering historical assumptions less relevant. Unexpected events or shifts in economic regimes can significantly impact the behavior of embedded options and the overall bond market, which may not be adequately captured by models based on historical averages¹¹. Therefore, while OAS provides valuable insights, it should be used in conjunction with other metrics and a comprehensive understanding of market dynamics and the specific security's characteristics.

Option-Adjusted Spread vs. Z-spread

The Option-Adjusted Spread (OAS) and the Z-spread (Zero-Volatility Spread) are both measures of spread over a benchmark yield curve, but they differ fundamentally in how they account for embedded options in a bond. This distinction is crucial for accurate bond valuation and relative value analysis.

The Z-spread, also known as the static spread, is the constant spread that, when added to each point on the benchmark spot rate curve (typically the Treasury yield curve), makes the discounted present value of a bond's cash flows equal to its market price¹⁰. Crucially, the Z-spread does not take into account any embedded options. It assumes that the bond's cash flows are fixed and deterministic, regardless of future interest rate movements. Therefore, the Z-spread reflects compensation for all non-Treasury risks, including credit risk, liquidity risk, and any implicit cost or benefit from embedded options⁹.

In contrast, the Option-Adjusted Spread (OAS) specifically adjusts the Z-spread to account for the value of embedded options. The OAS calculation explicitly models how future cash flows might change due to the exercise of these options under various interest rate scenarios⁸. The value of the embedded option is effectively "removed" or "adjusted for" to arrive at the Option-Adjusted Spread.

For a callable bond, where the issuer has the right to redeem the bond early (an option valuable to the issuer, detrimental to the investor), the OAS will be lower than the Z-spread. This is because the option costs the investor money (reduces the bond's value), and the OAS subtracts this option cost from the overall spread⁷.
Conversely, for a putable bond, where the investor has the right to sell the bond back to the issuer (an option valuable to the investor), the OAS will be higher than the Z-spread. The value of the put option benefits the investor, and the OAS adds this option benefit back to the spread⁶.

In essence, the Z-spread reflects the total spread over the Treasury curve without considering optionality, while the OAS provides the spread that compensates for non-option risks, making it a more refined measure for securities with embedded options. The relationship can be simplified as: Z-spread = OAS + Option Cost (for callable bonds) or Z-spread = OAS - Option Value (for putable bonds)⁵.

FAQs

What type of bonds is Option-Adjusted Spread used for?

The Option-Adjusted Spread (OAS) is primarily used for fixed income securities that have embedded options. These include bonds with call provisions (callable bonds), put provisions (putable bonds), and especially mortgage-backed securities (MBS), which have embedded prepayment options⁴. It is less relevant for "plain vanilla" bonds that have no such features.

How does Option-Adjusted Spread account for risk?

OAS accounts for risk by providing a spread over a risk-free rate (like U.S. Treasuries) that specifically compensates investors for the bond's credit risk and [liquidity risk], after explicitly modeling and adjusting for the impact of any embedded options. By doing so, it isolates the non-option related risks, offering a more precise risk-adjusted return metric², ³.

Why is Option-Adjusted Spread considered a dynamic measure?

OAS is considered dynamic because its calculation involves simulating various future interest rate volatility paths and predicting how embedded options might be exercised in those different scenarios. This contrasts with static measures that only consider a single yield or spread without accounting for potential changes in cash flows due to future market movements.

Can Option-Adjusted Spread be negative?

Theoretically, the Option-Adjusted Spread can be negative, although it is uncommon. A negative OAS would imply that the bond is trading at a yield lower than the risk-free rate, even after accounting for embedded options. This could happen if the embedded option (e.g., a highly valuable put option) is so beneficial to the investor that it significantly outweighs the credit risk and other risks, or if the bond is severely overvalued in the market.

Is Option-Adjusted Spread perfect for bond analysis?

No, the Option-Adjusted Spread is not perfect, though it is a very useful tool. Its accuracy depends heavily on the quality and assumptions of the underlying financial modeling used to project interest rates and cash flows¹. Different models can produce different OAS values. It should always be used in conjunction with other analytical tools and a thorough understanding of the specific bond and market conditions.