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%.

Kingpin804

The one-year spot rate is 6% and the one-year forward rates starting in one, two and three years respectively are 6.5%, 6.8% and 7%. What is the four-year spot rate?

A) 6.51%.

B) 6.58%.

C) 6.57%.

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The four-year spot rate is computed as follows:
Four-year spot rate = [(1 + 0.06)(1 + 0.065)(1 + 0.068)(1 + 0.07) ]1/4 – 1 = 6.57%

Kingpin804

Given that the one-year spot rate is 5.76% and the 1.5-year spot rate is 6.11%, assuming semiannual compounding what is the six-month forward rate starting one year from now?

A) 7.04%.

B) 6.81%.

C) 6.97%.

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The forward rate is computed as follows: