# Option-Adjusted Spread (OAS)

The **Option-Adjusted Spread (OAS)** is a concept in fixed-income securities analysis, particularly in evaluating bonds with embedded options, such as callable or putable bonds.

It represents the spread that traders receive over a benchmark yield curve, adjusted for the value of embedded options.

## Key Takeaways – Option-Adjusted Spread (OAS)

Risk-Adjusted Comparison

- OAS allows traders to fairly compare bonds with different embedded options by adjusting for option value.
- This helps identify undervalued or overvalued securities across various fixed-income products.
Market Sensitivity

- OAS fluctuates with changes in interest rates, volatility, and credit spreads.
Versatile Metric

- OAS applies to a wide range of securities, from corporate bonds to complex structured products.
- It’s essential for relative value analysis, risk management, and portfolio allocation decisions in fixed-income trading.

## Key Components

### Definition and Purpose

OAS is the extra yield a bond offers over a benchmark, after adjusting for any built-in options. It helps compare bonds fairly by accounting for these options.

It provides a more accurate measure of the risk and return of a bond by accounting for the optionality feature.

### Benchmark Yield Curve

Typically, the benchmark yield curve is the risk-free Treasury yield curve or a swap curve.

The choice of the benchmark affects the OAS calculation and interpretation.

### Embedded Options

**Call Option –**Allows the issuer to redeem the bond before maturity at specified call dates and prices.**Put Option –**Allows the bondholder to sell the bond back to the issuer before maturity at specified put dates and prices.**Effect of Options –**These options affect the bond’s cash flows, making the bond’s yield and price more complex to analyze.

## Calculation

### Option-Free Value

Calculate the present value of the bond’s cash flows using the benchmark yield curve, ignoring the option.

### Valuation of Options

Use an interest rate model (e.g., binomial trees, Monte Carlo simulation) to estimate the value of the embedded option.

### OAS Determination

Adjust the spread over the benchmark yield curve so that the present value of the adjusted cash flows (considering optionality) equals the market price of the bond.

OAS= Z-Spread – Option Cost

Where:

**Z-Spread =**The constant spread that makes the present value of cash flows equal to the market price.**Option Cost =**The estimated value of the embedded option.

## Interpretation

### Positive OAS

A higher OAS indicates that the bond is offering a premium over the benchmark yield curve.

This suggest higher risk or better compensation for the risk after accounting for the optionality.

### Comparative Analysis

Comparing OAS among similar bonds helps traders identify undervalued or overvalued securities after accounting for differences in embedded options.

### Risk and Return

The OAS provides insight into the risk-adjusted return of a bond.

This helps traders make more informed decisions about the bond’s attractiveness relative to other investments.

## Practical Applications

### Portfolio Management

Portfolio managers use OAS to assess the relative value of bonds within a portfolio, especially when managing interest rate risk and credit risk.

### Trading Strategies

Traders use OAS to identify arbitrage or relative value opportunities by comparing the OAS of different bonds with similar credit quality and maturity.

### Risk Management

OAS helps in quantifying and managing the interest rate risk and optionality risk in fixed-income portfolios.

## Practical Examples

Consider a 5-year callable corporate bond with a 4% coupon, currently trading at $102.

The benchmark Treasury yield is 2%, and the Z-spread is 150 basis points (3.5% discount rate).

To calculate OAS:

- Calculate bond value using Treasury curve + Z-spread = $103.20 (using the 3.5% discount rate)
- Estimate option value using an interest rate model = $1.20 (equivalent to 30 basis points in spread terms)
- Adjust spread until model price matches market price: 120 basis points

OAS= Z-spread – Option Value in spread terms OAS = 150 bps – 30 bps = 120 bps

This example illustrates how OAS accounts for the embedded call option, resulting in a lower spread than the Z-spread.

## Market Conditions and OAS

Changing market conditions significantly impact OAS calculations and interpretations.

**Interest rate volatility**affects option values, thereby influencing OAS.**Higher volatility**typically increases option values, reducing OAS.**Credit spread changes**also impact OAS; widening spreads often lead to higher OAS, reflecting increased risk.**Market liquidity**conditions can affect bond pricing, indirectly influencing OAS.**Economic cycles and monetary policy**shifts can alter interest rate expectations, affecting OAS calculations.- Furthermore, sudden
**market shocks or crises**can lead to rapid OAS changes, reflecting greater unknowns (and wider distributions of expected outcomes).

Analysts must consider these dynamic market factors when interpreting OAS to make informed investment decisions.

## Limitations and Challenges

OAS has several limitations and challenges.

### Model-Dependent

Firstly, it’s heavily model-dependent, relying on assumptions about future interest rate paths.

Different models can yield varying results, making comparisons difficult.

The accuracy of OAS calculations is particularly sensitive to the interest rate model chosen.

### Options Aren’t Always Easy to Evaluate

Estimating option values accurately is challenging, especially for complex or exotic options.

Market illiquidity can further complicate fair value estimations.

OAS also assumes constant spreads over the bond’s life, which may not hold true in reality.

Moreover, OAS doesn’t account for other risk factors like credit risk changes.

### Computationally Intensive

OAS calculations can be computationally intensive, requiring sophisticated software and expertise to implement correctly.

## OAS vs. Other Spread Measures

OAS differs from other spread measures like nominal spread or static spread.

### Nominal Spread

Nominal spread, the simplest measure, is the difference between a bond’s yield and the yield of a risk-free benchmark.

### Static Spread

Static spread (Z-spread) is constant over the yield curve but doesn’t account for embedded options.

### OAS’s Advantage

OAS’s advantage is its consideration of option value, providing a more accurate risk-adjusted spread.

This makes OAS useful for securities with embedded options.

However, OAS is more complex to calculate and interpret.

As mentioned above, it’s also model-dependent, which can lead to inconsistencies.

While nominal and static spreads are easier to calculate and understand, they may oversimplify for complex securities.

This makes OAS preferable in many cases despite its challenges.

## OAS for Different Types of Securities

OAS is versatile and applies to various fixed-income securities beyond callable and putable bonds.

### MBS

For mortgage-backed securities (MBS), OAS accounts for prepayment options, which is important given homeowners’ ability to refinance.

### CMBS

In commercial mortgage-backed securities (CMBS), OAS considers both prepayment and extension risks.

### ABS

For asset-backed securities (ABS), OAS incorporates early amortization features.

### Convertible Bonds

Convertible bonds use OAS to value the conversion option.

### CDOs

Even for more exotic structures like collateralized debt obligations (CDOs), OAS helps in valuing complex cash flow structures.

In each case, OAS provides a risk-adjusted spread measure, which allows for more accurate comparisons across different security types and structures.

## Historical Context

OAS emerged in the 1980s as financial markets grew more complex and interest rate volatility increased.

Its development coincided with the rise of mortgage-backed securities and other structured products, which required more sophisticated valuation methods.

OAS addressed the limitations of simpler spread measures in handling embedded options.

The concept gained prominence in the 1990s as computing power increased, enabling more complex calculations.

OAS became important in modern fixed-income analysis, allowing for better risk assessment and relative value comparisons.

Its importance grew further with the expansion of the structured products market in the 2000s, becoming a standard tool for portfolio managers, traders, and risk managers in modern fixed-income markets.

## OAS and Credit Risk

OAS is closely related to credit risk assessment in fixed-income securities.

A higher OAS generally indicates higher credit risk, as traders demand more compensation for potential default.

Credit analysts use OAS to compare bonds of similar credit quality but different structures.

Changes in OAS over time can signal shifts in perceived credit risk.

For example, widening OAS might indicate deteriorating credit conditions.

OAS also helps in analyzing the credit risk premium by comparing it to credit default swap (CDS) spreads.

In credit portfolio management, OAS aids in identifying relative value opportunities and potential mispricing.

However, OAS incorporates other risks besides credit risk, so analysts need to consider additional factors in credit analysis.

## OAS in Asset Allocation

OAS is important in asset allocation decisions across fixed-income sectors.

Portfolio managers use OAS to compare risk-adjusted returns of different securities, helping to identify relative value opportunities.

Higher OAS may indicate potentially undervalued securities, while lower OAS might suggest overvaluation.

OAS helps traders in sector rotation strategies, guiding shifts between corporate bonds, MBS, ABS, and other sectors based on relative spreads.

It’s useful in allocating between securities with different embedded options.

OAS also helps in maintaining desired portfolio characteristics, such as duration and convexity, while maximizing risk-adjusted returns.

However, managers need to consider other factors alongside OAS, such as liquidity, credit quality, and overall portfolio objectives, to make sophisticated allocation decisions.

## OAS Sensitivity

OAS sensitivity refers to how OAS changes in response to various market factors.

### Rate Changes

Interest rate changes significantly impact OAS – generally, as rates rise, OAS tends to widen for callable bonds due to decreased call risk.

### Volatility Changes

Volatility changes also affect OAS – higher volatility typically reduces OAS for callable bonds.

### Credit Spread Movements

Credit spread movements influence OAS, with widening credit spreads often leading to higher OAS.

### OAS Duration

The concept of OAS duration measures the sensitivity of a bond’s price to changes in OAS, similar to how duration measures price sensitivity to yield changes.

### OAS Convexity

OAS convexity captures the non-linear relationship between price and OAS changes.

Understanding these sensitivities is important for risk management and relative value analysis in fixed-income portfolios.

## Regulatory Considerations

OAS has important regulatory implications in the financial industry.

Risk reporting requirements often include OAS as a measure of interest rate and option risk.

Basel III and other capital adequacy frameworks consider OAS in understanding the risk of fixed-income portfolios.

Regulators may use OAS in stress testing scenarios to evaluate banks’ resilience to interest rate shocks.

In some jurisdictions, OAS is part of the fair value hierarchy for financial reporting purposes.

Nevertheless, the model-dependent nature of OAS can raise concerns about consistency and comparability across institutions.

Regulators may require transparency in OAS calculation methodologies.

## Global Perspectives

OAS application and interpretation can vary across global markets due to differences in market structures, interest rate regimes, and regulatory environments.

In developed markets, OAS is widely used and generally consistent in application.

However, emerging markets may face challenges in OAS calculation due to less liquid benchmark yield curves or more volatile interest rate environments.

The choice of benchmark yield curve can differ. US markets typically use Treasury curves. In European markets it’s more common to use swap curves.

Japan’s low interest rate environment in modern history presents unique challenges for OAS interpretation.

In some markets, credit risk may have a more significant role in OAS. In others, liquidity risk might be more prominent.

Understanding these global differences is important for international fixed-income traders and global portfolio managers to develop a nuanced understanding.

## Conclusion

The option-adjusted spread incorporates the value of embedded options into the yield spread, providing a nuanced measure of a bond’s return relative to its risk.

Its use is important in the valuation and comparison of bonds with embedded options.