# What is an Option-Adjusted Spread (OAS)?

An option-adjusted spread is the difference between the yield of a security that pays fixed interest payments and the current U.S. Treasury rates, which represents the rate of return on a risk-free investment.

## 🤔 Understanding an option-adjusted spread

An option-adjusted spread is used for bonds with embedded options (features that allow the bond issuer or holder to take a particular action in the future). The option-adjusted spread represents the spread after adjusting for, or removing, the bond’s option. The option-adjusted spread allows investors to see the impact the embedded option can have on the bond and how it affects the value of the bond. Embedded options create additional risk, and looking at this spread can indicate to investors whether the security is worth the listed price when taking those risks into account. Option-adjusted spreads frequently determine the value of mortgage-backed securities (bonds derived from pool of mortgages).

An example of when an option-adjusted spread might be used is in the case of a callable bond. Callable bonds have an embedded option — in this case, it’s a call option. This option allows the bond issuer to retire a bond before its maturity date, something an issuer might do if interest rates decline. An investor considering investing in callable bonds might use the option-adjusted spread to analyze the value of that security.

## Takeaway

An option-adjusted spread is like converting oranges into apples…

Comparing bonds with embedded options to their traditional counterparts is like comparing apples to oranges — it’s just not a good comparison. The option-adjusted spread helps to level that playing field to allow investors to examine them more easily… apples-to-apples.

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## What is the purpose of an OAS?

The purpose of an option-adjusted spread (OAS) is to help investors to compare the yield of fixed-income securities with embedded options, such as a call option that allows the issuer to call back the offering. One example of this type of offering is a callable bond. In this case, the issuer of the bond can retire a bond before its maturity date, something an issuer might do if interest rates decline.

Using the option-adjusted spread can give potential investors a better idea of the value of a security and whether it is a worthwhile investment for them. This method is more accurate than merely looking at the expected return on a bond until it matures.

So how would this be used practically? Well, an investor is going to expect a lower price and higher yield on a bond with an embedded option to compensate for the issuer’s call option. In the case of a bond with no embedded option, however, an investor would expect the price to be higher and the yield lower. An investor would use the option-adjusted spread to compare one bond with an embedded option to another with an embedded option. The one with the higher range will have a lower price. For example, let’s say an investor is comparing two mortgage-backed securities, both with the same estimated maturity. The investor calculates the OAS of the two, ultimately finding that one has a higher OAS and lower price. The investor decides this security is a better deal due to the higher potential yield.

## How does volatility affect embedded options?

With a traditional bond, you can use the yield to maturity (YTM) to measure the overall return an investor who buys a bond at the market price is expected to earn if that investor holds the bond until maturity. However, YTM is not a good measure to use when a bond has an embedded option. When a bond has an embedded call option, the issuer has the right to call back the bond before maturity.

The option-adjusted spread takes this potential into account. It accounts for volatility - The measure of the range of returns you might see for a security. Securities with higher volatility usually have a higher risk.

There are two types of volatility to consider for investments with embedded options. The first is changing interest rates. If the interest rate drops, callable bond issuers (often) are more likely to call bonds , in which case they call the debt. The other risk is prepayment, which is the risk that borrowers will prematurely repay their debts. In general, advanced payments go up as interest rates go down, and vice versa.

Volatility is ultimately significant for determining the option-adjusted spread. As volatility increases, the spread decreases.

## What are mortgage-backed securities?

Option-adjusted spreads are often used when it comes to mortgage-backed securities. In fact, this is when we most often see option-adjusted spreads because most corporate bonds do not have embedded options.

A mortgage-backed security is an investment bundle of home loans. Mortgage loans are purchased from banks, mortgage companies, and other originators and then assembled into pools by a governmental, quasi-governmental, or private entity. The entity then issues securities that represent claims on the principal and interest payments made by borrowers on the loans in the pool, a process known as securitization.

There are two primary types of mortgage-backed securities:

- Pass-throughs: the most common type of mortgage-backed security, where the homeowners make their mortgage payments, and the money in the pool is passed through to the investors on a pro-rata basis.
- Collateralized mortgage obligations: a slightly more complicated type of mortgage-backed security — It’s a fixed-income security backed by multiple pools (also called tranches) of mortgage securities or loans.

You may remember that mortgage-backed securities played a significant role in the financial crisis that began in 2007. The demand for mortgage-backed securities was increasing as home prices were rising, and so banks began to lower their lending standards. This trend led to a decrease in the quality of mortgages in those securities.

Despite their role in the financial crisis, mortgage-backed securities are still an investment option today. The federal government regulates these securities to help prevent further crisis.

## What is a duration?

Duration is an estimate of how sensitive the price of a bond is to interest rates. Effective duration references bonds that have embedded options. The duration measures the amount of time it takes for the investor to be paid back for the price of the bond. This period is not the same as the amount of time it takes for the bond to reach maturity.

Effective duration is ultimately measuring how much the price of a bond declines as the interest rate goes up. It’s helpful for investors when quantifying the risk of fluctuating interest rates.

## How do you calculate OAS?

Determining an option-adjusted spread (OAS) involves a very complex calculation — There are a lot of factors involved. Let’s talk about some of the most critical information to know about the calculation of an option-adjusted spread.

### What is the Z-spread?

Several factors go into determining the option-adjusted spread of a security. But before we go into that calculation, we should talk about the zero-volatility spread, more commonly referred to as the Z-spread. The Z-spread is another tool that goes into determining the value of a security. And while the two spreads have some similarities, it’s important not to confuse the two.

The Z-spread, also known as the static spread, does not take into account the value of embedded options like the option-adjusted spread does. Instead, it is a constant spread between the current cash flow value of a bond and the U.S. Treasury spot rate yield curve (a yield curve created using Treasury spot rates).

The Z-spread is the yield you will get from a bond above the return you’d get for the same maturity Treasury bond. The calculation is very complex and requires a lot of trial and error — It takes into account the current bond price and any interest accrued, the bond coupon payment, the spot rate at each maturity.

The formula looks like this:

P = {C(1) / (1 + (r(1) + Z) / 2) ^ (2 x n)} + {C(2) / (1 + (r(2) + Z) / 2) ^ (2 x n)} + {C(n) / (1 + (r(n) + Z) / 2) ^ (2 x n)}

In this formula, P is the bond’s current price plus accrued interest, C(x) is the bond coupon payment, r(x) is the spot rate at each maturity, Z is the Z-spread, T is the bond’s cash flow at maturity, and n is the relevant time.

### How to determine OAS

Now that we’ve figured out what a Z-spread is and how to determine it, we’ll have an easier time breaking down how to identify an option-adjusted spread. The option-adjusted spread starts with the Z-spread and adjusts it to account for the embedded option.

Like the Z-spread, the calculation for determining an option-adjusted spread is very complicated. It takes the Z-spread, and further discounts the value to account for any embedded options. The calculation takes into historical data account to predict interest rates and prepayment rates. Option-adjusted spreads are usually measured in basis points (aka bps).

Often used to calculate option-adjusted spreads is the Monte Carlo model, which is used to calculate the value of options with lots of uncertain or complicated features. It uses hundreds of yield-curve scenarios to make the calculation.

The formula looks like this: OAS = Z Spread - Embedded Option.

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