Kingpin804

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.

Kingpin804

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.

Kingpin804

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

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

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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 spreadover 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.

Kingpin804

Assume that an option-free 5% coupon bond with annual coupon payments has two years to maturity. A callable bond that is the same in every respect as the option-free bond is priced at 91.76. With the term structure flat at 6% what is the value of the embedded call option?

A) -8.24.

B) 4.58.

C) 6.41.

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The option value is the difference between the option-free bond price and the corresponding callable bond price.
The value of the option free bond is computed as follows: PMT = 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign).
The option value = 98.17 – 91.76 = 6.41.

Kingpin804

Assume an option-free 5% coupon bond with annual coupon payments has two years remaining to maturity. A putable bond that is the same in every respect as the option-free bond is priced at 101.76. With the term structure flat at 6% what is the value of the embedded put option?

A) 1.76.

B) 3.59.

C) -3.59.

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The value of the embedded put option of the putable bond is the difference between the price of the putable bond and the price of the option-free bond.
The value of the option-free bond is computed as follows: PMT = 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign).
The option value = 101.79 − 98.17 = 3.59.

Kingpin804

The six-year spot rate is 7% and the five-year spot rate is 6%. The implied one-year forward rate five years from now is closest to:

A) 6.5%.

B) 12.0%.

C) 5.0%.

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1r5= [(1 + R6)6 / (1 + R5)5] - 1 = [(1.07)6/(1.06)5] – 1 = [1.5 / 1.338] - 1 = 0.12

Kingpin804

Suppose the 3-year spot rate is 12.1% and the 2-year spot rate is 11.3%. Which of the following statements concerning forward and spot rates is most accurate? The 1-year:

A) forward rate two years from today is 13.2%.

B) forward rate one year from today is 13.7%.

C) forward rate two years from today is 13.7%.

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The equation for the three-year spot rate, Z3, is (1 + Z1)(1 + 1f1)(1 + 1f2) = (1 + Z3)3. Also, (1 + Z1)(1 + 1f1) = (1 + Z2)2. So, (1 + 1f2) = (1 + Z3)3 / (1 + Z2)2, computed as: (1 + 0.121)3 / (1 + 0.113)2 = 1.137. Thus, 1f2 = 0.137, or 13.7%.

Kingpin804

Given the following spot and forward rates, how much should an investor pay for each $100 of a 3-year, annual zero-coupon bond?

• One-year spot rate is 3.75%
• The 1-year forward rate 1 year from today is 9.50%
• The 1-year forward rate 2 years from today is 15.80%

The investor should pay approximately:

A) $76.

B) $44.

C) $83.

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The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate. Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate.
Using the formula: (1 + Z3)3 = (1 + 1f0)(1 + 1f1)(1 + 1f2)
where Z = spot rate and nfm = the n year rate m periods from today, (1f0 = the 1 year spot rate now).

(1 + Z3)3 = (1.0375) × (1.095) × (1.158)
Z3 = 1.3155601/3 − 1 = 0.095730, or 9.57%

Then, the value of the zero coupon bond = 100 / (1.09573)3 = 76.01, or approximately $76,
or, using a financial calculator, N = 3; I/Y = 9.57; FV = 1,000; PMT = 0; CPT → PV = 76.20 or approximately $76.

Kingpin804

Given the following spot and forward rates, how much should an investor pay for a 3-year, annual zero-coupon bond with a face value of $1,000?

• One-year spot rate at 3.5%
• The 1-year forward rate 1 year from today is 11.5%
• The 1-year forward rate 2 years from today is 19.75%

The investor should pay approximately:

A) $724.

B) $720.

C) $884.

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The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate. Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate.

Using the formula: (1 + Z3)3 = (1 + 1f0) × (1 + 1f1) × (1 + 1f2)

Where Z = spot rate and nfm = The n year rate m periods from today, (1f0 = the 1 year spot rate now)

(1 + Z3)3 = (1.035) × (1.115) × (1.1975)
Z3 = 1.38191/3 − 1 = 0.11386, or 11.39%

Then, the value of the zero coupon bond = 1,000 / (1.1139)3 = 723.62, or approximately $724.
or, using a financial calculator, N = 3; I/Y = 11.39; FV = 1,000; PMT = 0; CPT → PV = 723.54, or approximately $724.

Kingpin804

Given the one-year spot rate S1 = 0.06 and the implied 1-year forward rates one, two, and three years from now of: 1f1 = 0.062; 1f2 = 0.063; 1f3 = 0.065, what is the theoretical 4-year spot rate?

A) 6.75%.

B) 6.00%.

C) 6.25%.

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S4 = [ (1.06) (1.062) (1.063) (1.065) ].25 − 1 = 6.25%.