Reading 66: Yield Measures, Spot Rates, and Forward Rates-LOS 2011, face, accounts, center, option

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Session 16: Fixed Income: Analysis and Valuation
Reading 66: Yield Measures, Spot Rates, and Forward Rates

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

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

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

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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.

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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 CORRECT?

A) The nominal spread is approximately 25 basis points.

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

C) The nominal spread is approximately 85 basis points.

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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.

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Which of the following statements on spreads is NOT correct?

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

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

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

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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.

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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 5bp.

B) X is 13bp.

C) X is 8bp.

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

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