Reading 65: Yield Measures, Spot Rates, and Forward Rates LO junior, adjusted, accounts, face, 2010

honeycfa

LOS g: Describe how the option-adjusted spread accounts for the option cost in a bond with an embedded option.

Kwagmyre Investments, Ltd., hold two bonds: a callable bond issued by Mudd Manufacturing Inc. and a putable bond issued by Precarious Builders. Both bonds have option adjusted spreads (OAS) of 135 basis points (bp). Kevin Grisly, a junior analyst at the firm, makes the following statements (each statement is independent). Apparently, Grisly could benefit from a CFA review course, because the only statement that could be accurate is:

A) The spread over the spot rates for a Treasury security similar to Mudd's bond is 145 bp.

B) Given a nominal spread for Precarious Builders of 110 bp, the option cost is -25 bp.

C) The Z-spread for Mudd's bond is based on the YTM.

---

The “spread over the spot rates for a Treasury security similar to Mudd’s bond” refers to the Z-spread on the bond. For a callable bond, the OAS < Z-spread, so this could be a true statement because 135bp < 145 bp.

The other statements are false. The option cost is calculated using the OAS and the Z-spread, not the nominal spread. The static spread (or Z-spread) is the spread over each of the spot rates in a given Treasury term structure, not the spread over the Treasury’s YTM.

Following is a more detailed discussion:

The option-adjusted spread (OAS) is used when a bond has embedded options. The OAS can be thought 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

Remember the following option value relationships:

• For embedded short calls (e.g. callable bonds): option value > 0 (you receive compensation for writing the option to the issuer), and the OAS < Z-spread. In other words, you require more yield on the callable bond than for an option-free bond.
• For embedded long puts (e.g. putable bonds): option value < 0 (i.e., you must pay for the option), and the OAS > Z-spread. In other words, you require a lower yield on the putable bond than for an option-free bond.

 

honeycfa

An analyst has gathered the following information:

• Bond A is an 11% annual coupon bond currently trading at 106.385 and matures in 3 years. The yield-to-maturity (YTM) for Bond A is 8.50%.

• The YTM for a Treasury bond that matures in 3-years is 7.65%.

• 1, 2, and 3-year spot rates are 5.0%, 6.5% and 8.25%, respectively.

Which of the following statements regarding spreads on bond A is TRUE?

A) The nominal spread is approximately 85 basis points.

B) The nominal spread is approximately 25 basis points.

C) The Z-spread is approximately 85 basis points.

---

The nominal spread is 8.50% ? 7.65% = 0.85%. Note that the Z-spread, calculated by trial and error, is approximately 48 basis points.

honeycfa

Which of the following statements on spreads is FALSE?

A) The Z-spread will equal the nominal spread if the term structure of interest rates is flat.

B) The option-adjusted spread (OAS) is the difference between the Z-spread and the option cost.

C) The Z-spread may be used for bonds that contain call options.

---

The Z-spread is used for risky bonds that do NOT contain call options in an attempt to improve on the shortcomings of the nominal spread. The other statements are correct.

honeycfa

The following information is available for two bonds:

• Bond X is callable and has an option-adjusted spread (OAS) of 55bp. Similar bonds have a Z-spread of 68bp and a nominal spread of 60bp.

• Bond Y is putable and has an OAS of 100bp. Similar bonds have a Z-spread of 78bp and a nominal spread of 66bp.

The embedded option cost for Bond:

A) X is 13bp.

B) X is 5bp.

C) X is 8bp.

---

Option cost (Bond X) = Z-spread – OAS = 68bp – 55bp = 13bp
Option cost (Bond Y) = Z-spread – OAS = 78bp – 100bp = - 22bp