8.

This LOS is essentially the same as LOS 1.B.l. The static spread (or Z-spread) is the spread not over the Treasury’s YTM, but over each of the spot rates in a given Treasury term structure. In other words, the same spread is added to all risk-free spot rates. The Z-spread is inherently more accurate (and will usually differ from) the nominal spread since it is based upon the arbitrage-free spot rates, rather than a given YTM.

o: Explain the option-adjusted spread for a bond with an embedded option and explain the option cost.

The option adjusted spread (OAS) is used when a bond has embedded options. The OAS can be though of as the difference between the static or Z-spread and the option cost. For the exam, remember the following relationship between the static spread (Z-spread), the OAS, and the embedded option cost:

Z-Spread – OAS = Option Cost in % Terms.

Also remember that you use the Z-spread for risky bonds that do not contain call options in an attempt to improve on the shortcomings of the na?ve or nominal spread. If the bond has an embedded option and the cash flows of the bond are dependent on the future path of interest rates, then remove the option from the spread by using the OAS.

p: Illustrate why the nominal spread hides the option risk for bonds with embedded options.

It is worth noting that a large Z-spread value can result from either component. Therefore, a large Z-spread could be the result of a large option cost implying that the investor may not be receiving as much compensation for default and other risks as may be initially perceived.

q: Explain a forward rate.

Spot interest rates as derived above are the result of market participant’s tolerance for risk and their collective view regarding the future path of interest rates. If we assume that these results are purely a function of expectations (called the expectations theory of the term structure of interest rates), we can use spot rates to estimate the market's consensus on future interest rates.

r: Explain and illustrate the relationship between short-term forward rates and spot rates.

Spot interest rates as derived above are the result of market participant’s tolerance for risk and their collective view regarding the future path of interest rates. Suppose that you have a two-year time horizon and are offered the choice between locking in a 2-year spot rate of 8.167 percent or investing at the 1-year spot rate of 4 percent and rolling over your investment at the end of the year into another 1-year security. If the difference between the 1 and 2-year rates is purely a function of expectations regarding future interest rates, you should be indifferent between these two alternatives. You expect that you derive the same result regardless of which one you choose, since market participant’s expectations are perfectly factored in to the 2-year rate.

s: Compute spot rates from forward rates and forward rates from spot rates.

This LOS is essentially the same as LOS 1.B.l. The static spread (or Z-spread) is the spread not over the Treasury’s YTM, but over each of the spot rates in a given Treasury term structure. In other words, the same spread is added to all risk-free spot rates. The Z-spread is inherently more accurate (and will usually differ from) the nominal spread since it is based upon the arbitrage-free spot rates, rather than a given YTM.

o: Explain the option-adjusted spread for a bond with an embedded option and explain the option cost.

The option adjusted spread (OAS) is used when a bond has embedded options. The OAS can be though of as the difference between the static or Z-spread and the option cost. For the exam, remember the following relationship between the static spread (Z-spread), the OAS, and the embedded option cost:

Z-Spread – OAS = Option Cost in % Terms.

Also remember that you use the Z-spread for risky bonds that do not contain call options in an attempt to improve on the shortcomings of the na?ve or nominal spread. If the bond has an embedded option and the cash flows of the bond are dependent on the future path of interest rates, then remove the option from the spread by using the OAS.

p: Illustrate why the nominal spread hides the option risk for bonds with embedded options.

It is worth noting that a large Z-spread value can result from either component. Therefore, a large Z-spread could be the result of a large option cost implying that the investor may not be receiving as much compensation for default and other risks as may be initially perceived.

q: Explain a forward rate.

Spot interest rates as derived above are the result of market participant’s tolerance for risk and their collective view regarding the future path of interest rates. If we assume that these results are purely a function of expectations (called the expectations theory of the term structure of interest rates), we can use spot rates to estimate the market's consensus on future interest rates.

r: Explain and illustrate the relationship between short-term forward rates and spot rates.

Spot interest rates as derived above are the result of market participant’s tolerance for risk and their collective view regarding the future path of interest rates. Suppose that you have a two-year time horizon and are offered the choice between locking in a 2-year spot rate of 8.167 percent or investing at the 1-year spot rate of 4 percent and rolling over your investment at the end of the year into another 1-year security. If the difference between the 1 and 2-year rates is purely a function of expectations regarding future interest rates, you should be indifferent between these two alternatives. You expect that you derive the same result regardless of which one you choose, since market participant’s expectations are perfectly factored in to the 2-year rate.

s: Compute spot rates from forward rates and forward rates from spot rates.