Podcast
Questions and Answers
Jorge Fullen is evaluating a 7%, 10-year bond that is callable at par in 5 years. Coupon payments can be reinvested at an annual rate of 7%, and the current price of the bond is $1,065.00 per $1,000 of face value. The bond pays interest semiannually. Should Fullen consider the yield to first call (YTC) or the yield to maturity (YTM) in making his purchase decision?
Jorge Fullen is evaluating a 7%, 10-year bond that is callable at par in 5 years. Coupon payments can be reinvested at an annual rate of 7%, and the current price of the bond is $1,065.00 per $1,000 of face value. The bond pays interest semiannually. Should Fullen consider the yield to first call (YTC) or the yield to maturity (YTM) in making his purchase decision?
- YTC, since YTC is less than YTM. (correct)
- YTM, since YTM is greater than YTC.
- YTC, since YTC is greater than YTM.
Neuman Company has bonds outstanding with five years to maturity that trade at a spread of +240 basis points above the five-year government bond yield. Neuman also has five-year bonds outstanding that are identical in all respects except that they are convertible into 30 shares of Neuman common stock. At which of the following spreads are the convertible bonds most likely to trade?
Neuman Company has bonds outstanding with five years to maturity that trade at a spread of +240 basis points above the five-year government bond yield. Neuman also has five-year bonds outstanding that are identical in all respects except that they are convertible into 30 shares of Neuman common stock. At which of the following spreads are the convertible bonds most likely to trade?
- +270 basis points.
- +330 basis points.
- +210 basis points. (correct)
A 20-year bond pays an annual coupon of 6% and has a par value of $1,000. If its current yield is 7%, its yield to maturity is closest to:
A 20-year bond pays an annual coupon of 6% and has a par value of $1,000. If its current yield is 7%, its yield to maturity is closest to:
- 7.0%.
- 7.4%. (correct)
- 8.6%.
A 15-year, 10% annual coupon bond is sold for $1,150. It can be called at the end of 5 years for $1,100. What is the bond's yield to call (YTC)?
A 15-year, 10% annual coupon bond is sold for $1,150. It can be called at the end of 5 years for $1,100. What is the bond's yield to call (YTC)?
Which of the following is the most accurate statement about stated and effective annual interest rates?
Which of the following is the most accurate statement about stated and effective annual interest rates?
A 10% annual coupon, $1,000 par value bond that matures in 5 years is priced at 92.8. Its yield to maturity is closest to:
A 10% annual coupon, $1,000 par value bond that matures in 5 years is priced at 92.8. Its yield to maturity is closest to:
Consider a 5-year, semiannual, 10% coupon bond with a maturity value of 1,000 selling for $1,081.11. The first call date is 3 years from now and the call price is $1,030. What is the yield-to-call?
Consider a 5-year, semiannual, 10% coupon bond with a maturity value of 1,000 selling for $1,081.11. The first call date is 3 years from now and the call price is $1,030. What is the yield-to-call?
A coupon bond pays annual interest, has a par value of $1,000, matures in 4 years, has a coupon rate of $100, and a yield to maturity of 12%. The current yield on this bond is:
A coupon bond pays annual interest, has a par value of $1,000, matures in 4 years, has a coupon rate of $100, and a yield to maturity of 12%. The current yield on this bond is:
A major brokerage house is currently selling an investment product that offers an 8% rate of return, compounded monthly. Based on this information, it follows that this investment has:
A major brokerage house is currently selling an investment product that offers an 8% rate of return, compounded monthly. Based on this information, it follows that this investment has:
A disadvantage of G-spreads and I-spreads is that they are theoretically correct only if the spot yield curve is:
A disadvantage of G-spreads and I-spreads is that they are theoretically correct only if the spot yield curve is:
McClintock 8% coupon bonds maturing in 10 years are currently trading at 97.55. These bonds are option-free and pay coupons semiannually. The McClintock bonds have a:
McClintock 8% coupon bonds maturing in 10 years are currently trading at 97.55. These bonds are option-free and pay coupons semiannually. The McClintock bonds have a:
Calculate the current yield and the yield-to-first call on a bond with the following characteristics:
- 5 years to maturity
- $1,000 face value
- 8.75% semi-annual coupon
- Priced to yield 9.25%
- Callable at $1,025 in two years
Select the option with the correct Current Yield and Yield-to-Call.
Calculate the current yield and the yield-to-first call on a bond with the following characteristics:
- 5 years to maturity
- $1,000 face value
- 8.75% semi-annual coupon
- Priced to yield 9.25%
- Callable at $1,025 in two years
Select the option with the correct Current Yield and Yield-to-Call.
Tony Ly is a Treasury Manager with Deeter Holdings, a large consumer products holding company. The Assistant Treasurer has asked Ly to calculate the current yield and the Yield-to-first Call on a bond the company holds that has the following characteristics:
- 7 years to maturity
- $1,000 face value
- 7.0% semi-annual coupon
- Priced to yield 9.0%
- Callable at $1,060 in two years
If Ly calculates correctly, the current yield (CY) and yield to call (YTC) are approximately:
Tony Ly is a Treasury Manager with Deeter Holdings, a large consumer products holding company. The Assistant Treasurer has asked Ly to calculate the current yield and the Yield-to-first Call on a bond the company holds that has the following characteristics:
- 7 years to maturity
- $1,000 face value
- 7.0% semi-annual coupon
- Priced to yield 9.0%
- Callable at $1,060 in two years
If Ly calculates correctly, the current yield (CY) and yield to call (YTC) are approximately:
A $1,000 bond with an annual coupon rate of 10% has 10 years to maturity and is currently priced at $800. The bond's yield-to-maturity is closest to:
A $1,000 bond with an annual coupon rate of 10% has 10 years to maturity and is currently priced at $800. The bond's yield-to-maturity is closest to:
Other things equal, as the number of compounding periods increases, what is the effect on the effective annual rate (EAR)?
Other things equal, as the number of compounding periods increases, what is the effect on the effective annual rate (EAR)?
An 11% coupon bond with annual payments and 10 years to maturity is callable in 3 years at a call price of $1,100. If the bond is selling today for 975, the yield to call is:
An 11% coupon bond with annual payments and 10 years to maturity is callable in 3 years at a call price of $1,100. If the bond is selling today for 975, the yield to call is:
If an investment has an APR of 18% and is compounded quarterly, its effective annual rate (EAR) is closest to:
If an investment has an APR of 18% and is compounded quarterly, its effective annual rate (EAR) is closest to:
A 20-year, 9% annual coupon bond selling for $1,098.96 offers a yield of:
A 20-year, 9% annual coupon bond selling for $1,098.96 offers a yield of:
A fixed coupon callable bond issued by Protohype Inc. is trading with a yield to maturity of 6.4%. Compared to this YTM, the bond's option-adjusted yield will be:
A fixed coupon callable bond issued by Protohype Inc. is trading with a yield to maturity of 6.4%. Compared to this YTM, the bond's option-adjusted yield will be:
What is the equivalent annual-pay yield for a bond with a semiannual-bond basis yield of 5.6%?
What is the equivalent annual-pay yield for a bond with a semiannual-bond basis yield of 5.6%?
An interpolated spread (I-spread) for a bond is a yield spread relative to:
An interpolated spread (I-spread) for a bond is a yield spread relative to:
A Treasury bond due in one-year has a yield of 8.5%. A Treasury bond due in 5 years has a yield of 9.3%. A bond issued by Galaxy Motors due in 5 years has a yield of 9.9%. A bond issued by Exe due in one year has a yield of 9.4%. The yield spreads on the bonds issued by Exe and Galaxy Motors are:
A Treasury bond due in one-year has a yield of 8.5%. A Treasury bond due in 5 years has a yield of 9.3%. A bond issued by Galaxy Motors due in 5 years has a yield of 9.9%. A bond issued by Exe due in one year has a yield of 9.4%. The yield spreads on the bonds issued by Exe and Galaxy Motors are:
A single yield used to discount all of a bond's cash flows when calculating its price is most accurately described as the bond's:
A single yield used to discount all of a bond's cash flows when calculating its price is most accurately described as the bond's:
A 6% bond paying coupons semi-annually has 10 years until maturity. The bond currently trades at 111.5. Its yield to maturity is closest to:
A 6% bond paying coupons semi-annually has 10 years until maturity. The bond currently trades at 111.5. Its yield to maturity is closest to:
Venenata Foods has a 10-year bond outstanding with an annual coupon of 6.5%. If the bond is currently priced at $1,089.25, which of the following is closest to the semiannual-bond basis yield?
Venenata Foods has a 10-year bond outstanding with an annual coupon of 6.5%. If the bond is currently priced at $1,089.25, which of the following is closest to the semiannual-bond basis yield?
A local bank advertises that it will pay interest at the rate of 4.5%, compounded monthly, on regular savings accounts. What is the effective rate of interest that the bank is paying on these accounts?
A local bank advertises that it will pay interest at the rate of 4.5%, compounded monthly, on regular savings accounts. What is the effective rate of interest that the bank is paying on these accounts?
Which of the following adjustments is most likely to be made to the day count convention when calculating corporate bond yield spreads to government bond yields?
Which of the following adjustments is most likely to be made to the day count convention when calculating corporate bond yield spreads to government bond yields?
A $1,000 par value, 10%, semiannual, 20-year debenture bond is currently selling for $1,100. What is this bond's current yield and will the current yield be higher or lower than the yield to maturity?
A $1,000 par value, 10%, semiannual, 20-year debenture bond is currently selling for $1,100. What is this bond's current yield and will the current yield be higher or lower than the yield to maturity?
A stated annual interest rate of 9% compounded semiannually results in an effective annual rate closest to:
A stated annual interest rate of 9% compounded semiannually results in an effective annual rate closest to:
What is the current yield for a 5% three-year bond whose price is $93.19?
What is the current yield for a 5% three-year bond whose price is $93.19?
A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is:
A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is:
What is the yield to call on a bond that has an 8% coupon paid annually, $1,000 face value, 10 years to maturity and is first callable in 6 years? The current market price is $1,100. The call price is the face value plus 1-year's interest.
What is the yield to call on a bond that has an 8% coupon paid annually, $1,000 face value, 10 years to maturity and is first callable in 6 years? The current market price is $1,100. The call price is the face value plus 1-year's interest.
If a $1,000 bond has a 14% coupon rate and a current price of 950, what is the current yield?
If a $1,000 bond has a 14% coupon rate and a current price of 950, what is the current yield?
Harmon Moving has a 13.25% coupon semiannual coupon bond currently trading in the market at $1,229.50. The bond has eight years remaining until maturity, but only two years until first call on the issue at 107.50% of $1,000 par value. Which of the following is closest to the yield to first call on the bond?
Harmon Moving has a 13.25% coupon semiannual coupon bond currently trading in the market at $1,229.50. The bond has eight years remaining until maturity, but only two years until first call on the issue at 107.50% of $1,000 par value. Which of the following is closest to the yield to first call on the bond?
An investor purchases a 5-year, A-rated, 7.95% coupon, semiannual-pay corporate bond at a yield to maturity of 8.20%. The bond is callable at 102 in three years. The bond's yield to call is closest to:
An investor purchases a 5-year, A-rated, 7.95% coupon, semiannual-pay corporate bond at a yield to maturity of 8.20%. The bond is callable at 102 in three years. The bond's yield to call is closest to:
If a callable bond has an option-adjusted spread (OAS) of 75 basis points, this most likely suggests:
If a callable bond has an option-adjusted spread (OAS) of 75 basis points, this most likely suggests:
The bonds of Grinder Corp. trade at a G-spread of 150 basis points above comparable maturity U.S. Treasury securities. The option adjusted spread (OAS) on the Grinder bonds is 75 basis points. Using this information, and assuming that the Treasury yield curve is flat:
The bonds of Grinder Corp. trade at a G-spread of 150 basis points above comparable maturity U.S. Treasury securities. The option adjusted spread (OAS) on the Grinder bonds is 75 basis points. Using this information, and assuming that the Treasury yield curve is flat:
A 20-year, $1,000 face value, 10% semi-annual coupon bond is selling for $875. The bond's yield to maturity is:
A 20-year, $1,000 face value, 10% semi-annual coupon bond is selling for $875. The bond's yield to maturity is:
A five-year bond with a 7.75% semiannual coupon currently trades at 101.245% of a par value of $1,000. Which of the following is closest to the current yield on the bond?
A five-year bond with a 7.75% semiannual coupon currently trades at 101.245% of a par value of $1,000. Which of the following is closest to the current yield on the bond?
Bond X is a noncallable corporate bond maturing in ten years. Bond Y is also a corporate bond maturing in ten years, but Bond Y is callable at any time beginning three years from now. Both bonds carry a credit rating of AA. Based on this information:
Bond X is a noncallable corporate bond maturing in ten years. Bond Y is also a corporate bond maturing in ten years, but Bond Y is callable at any time beginning three years from now. Both bonds carry a credit rating of AA. Based on this information:
A stated interest rate of 9% compounded quarterly results in an effective annual rate closest to:
A stated interest rate of 9% compounded quarterly results in an effective annual rate closest to:
Which of the following describes the yield to worst? The:
Which of the following describes the yield to worst? The:
A semiannual-pay bond is callable in five years at $1,080. The bond has an 8% coupon and 15 years to maturity. If an investor pays $895 for the bond today, the yield to call is closest to:
A semiannual-pay bond is callable in five years at $1,080. The bond has an 8% coupon and 15 years to maturity. If an investor pays $895 for the bond today, the yield to call is closest to:
Consider a bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100. The yield to maturity is closest to:
Consider a bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100. The yield to maturity is closest to:
What is the yield to maturity (YTM) on a semiannual-bond basis of a 20-year, U.S. zero-coupon bond selling for $300?
What is the yield to maturity (YTM) on a semiannual-bond basis of a 20-year, U.S. zero-coupon bond selling for $300?
What is the effective annual rate if the stated rate is 12% compounded quarterly?
What is the effective annual rate if the stated rate is 12% compounded quarterly?
A 12% coupon bond with semiannual payments is callable in 5 years. The call price is $1,120. If the bond is selling today for $1,110, what is the yield-to-call?
A 12% coupon bond with semiannual payments is callable in 5 years. The call price is $1,120. If the bond is selling today for $1,110, what is the yield-to-call?
The zero volatility spread (Z-spread) is the spread that:
The zero volatility spread (Z-spread) is the spread that:
A bond with a 12% semiannual coupon is currently trading at 102.25 per 100 of face value and has seven years to maturity. Which of the following is closest to the yield to maturity (YTM) on the bond?
A bond with a 12% semiannual coupon is currently trading at 102.25 per 100 of face value and has seven years to maturity. Which of the following is closest to the yield to maturity (YTM) on the bond?
Consider a bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100. The yield to call is closest to:
Consider a bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100. The yield to call is closest to:
For a callable bond, the option-adjusted spread (OAS):
For a callable bond, the option-adjusted spread (OAS):
A 20-year, 9% semi-annual coupon bond selling for $914.20 offers a yield to maturity of:
A 20-year, 9% semi-annual coupon bond selling for $914.20 offers a yield to maturity of:
A $1,000 par value, 10% annual coupon bond with 15 years to maturity is priced at $951. The bond's yield to maturity is:
A $1,000 par value, 10% annual coupon bond with 15 years to maturity is priced at $951. The bond's yield to maturity is:
A 20 year, 8% semi-annual coupon, $1,000 par value bond is selling for $1,100. The bond is callable in 4 years at $1,080. What is the bond's yield to call?
A 20 year, 8% semi-annual coupon, $1,000 par value bond is selling for $1,100. The bond is callable in 4 years at $1,080. What is the bond's yield to call?
A 20-year, 10% semi-annual coupon bond selling for $925 has a yield to maturity (YTM) of:
A 20-year, 10% semi-annual coupon bond selling for $925 has a yield to maturity (YTM) of:
A 30-year, 10% annual coupon bond is sold at par. It can be called at the end of 10 years for $1,100. What is the bond's yield to call (YTC)?
A 30-year, 10% annual coupon bond is sold at par. It can be called at the end of 10 years for $1,100. What is the bond's yield to call (YTC)?
Flashcards
YTC vs. YTM Decision
YTC vs. YTM Decision
Yield to call (YTC) should be used because amortizing the premium over a shorter period results in a lower, more conservative return.
Convertible Bond Spreads
Convertible Bond Spreads
Convertible bonds trade at a lower spread due to the value of the conversion option for the bondholder.
Current Yield
Current Yield
Annual interest divided by the current market price of the bond.
Effective Annual Rate (EAR)
Effective Annual Rate (EAR)
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Yields on Discount Bonds
Yields on Discount Bonds
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Periodic Interest Rate
Periodic Interest Rate
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G-spreads and I-spreads Accuracy
G-spreads and I-spreads Accuracy
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Compounding Frequency Impact
Compounding Frequency Impact
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Option-Adjusted Yield
Option-Adjusted Yield
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I-Spread Definition
I-Spread Definition
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Yield to Maturity (YTM)
Yield to Maturity (YTM)
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Yield to Call (YTC)
Yield to Call (YTC)
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Bond Yield Basis Adjustment
Bond Yield Basis Adjustment
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Current Yield Formula
Current Yield Formula
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Yield to Call (YTC) Defined
Yield to Call (YTC) Defined
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Calculation of Yield to Maturity
Calculation of Yield to Maturity
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Option-Adjusted Spread (OAS)
Option-Adjusted Spread (OAS)
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Zero-Volatility Spread (Z-Spread)
Zero-Volatility Spread (Z-Spread)
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Callable Bond
Callable Bond
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Periodic Rate
Periodic Rate
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Yields on Discount Bonds.
Yields on Discount Bonds.
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Yield-to-Worst
Yield-to-Worst
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Yield Spread
Yield Spread
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Coupon Rate
Coupon Rate
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OAS vs. Z-Spread (Callable Bonds)
OAS vs. Z-Spread (Callable Bonds)
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Compounding
Compounding
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Callable Yield
Callable Yield
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Bond Yield (Semiannual Basis)
Bond Yield (Semiannual Basis)
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Capital of France (example flashcard)
Capital of France (example flashcard)
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Study Notes
- Current yield = annual coupon payment/price of the bond.
- If a bond's price is $1,100 and the annual coupon is $100, the current yield is 9.09%.
- If a bond is selling at a premium, the Yield to Maturity (YTM) must be less than the coupon rate; therefore the current yield is greater than the YTM.
- The YTM calculation: FV = 1,000; PV = -1,100; N = 40; PMT = 50; CPT → I = 4.46 × 2 = 8.92.
- A stated annual interest rate of 9% compounded semi-annually results in an effective annual rate of 9.2%.
- The effective six-month rate is 9%/2 = 4.5%.
- The effective annual rate is calculated as: EAR = (1 + period rate)^Periods in a year – 1 = (1 + 4.5%)^2 – 1 = 9.2%.
- The current yield for a 5% three-year bond whose price is $93.19 is 5.37%.
- Calculation: Current yield = 5% x 100 / $93.19 = 5.37%.
- A local bank offers an account that pays 8%, compounded quarterly with the effective annual rate of interest of 8.24%.
- Effective annual rate= (1 + periodic rate)^m – 1 = (1.02)^4 – 1 = 8.24%.
- The yield to call on a bond with an 8% coupon paid annually, $1,000 face value, 10 years to maturity and first callable in 6 years, with a market price of $1,100, has a call price of face value plus 1 year's interest; the yield to call: 7.02%.
- Calculation: N = 6; PV = -1,100.00; PMT = 80; FV = 1,080; Compute I/Y = 7.02%.
- If a $1,000 bond has a 14% coupon rate and a current price of 950, the current yield is 14.74%.
- Calculation: (0.14)(1,000) = $140 coupon; 140/950 × 100 = 14.74.
- A Harmon Moving bond has a 13.25% coupon semiannual coupon bond trading at $1,229.50. It has eight years remaining, but only two years until first call at 107.50% of $1,000 par value; the yield to first call on the bond is 4.72%.
- Calculation: FV = $1,075; N = 2 × 2 = 4; PMT = $66.25; PV = -1,229.50, CPT → I/Y = 2.36%, annualized as (2.36)(2) = 4.72%.
- An investor purchases a 5-year, A-rated, 7.95% coupon, semiannual-pay corporate bond at a yield to maturity of 8.20%. The bond is callable at 102 in three years, the bond's yield to call is 8.9%.
- Calculation: First determine the price paid for the bond: N = 5 × 2 = 10; I/Y = 8.20 / 2 = 4.10; PMT = 7.95 / 2 = 3.975; FV = 100; CPT PV = -98.99; Use the value, and the call price and date to determine the yield to call: N = 3 × 2 = 6; PMT = 7.95 / 2 = 3.975; PV = -98.99; FV = 102; CPT I/Y = 4.4686 × 2 = 8.937%.
- If a callable bond has an option-adjusted spread (OAS) of 75 basis points, the bond has a zero-volatility spread greater than 75 basis points.
- For a bond with an embedded call option, the OAS is less than its zero-volatility spread by the option cost, and so the zero-volatility spread is greater than the OAS for callable bonds.
- If the embedded call option has any value to the issuer, the zero-volatility spread is greater than 75 basis points where the OAS is 75 basis points.
- The option-adjusted spread doesn't include any compensation for the volatility risk related to the option.
- The option cost is the difference between the bond's zero-volatility spread (not the nominal spread) and its OAS.
- The bonds of Grinder Corp. trade at a G-spread of 150 basis points and an option adjusted spread (OAS) is 75 basis points, with a flat treasury yield curve; the option cost is 75 basis points.
- Option cost is the difference between the zero volatility spread and the OAS, or 150 – 75 = 75 bp.
- A 20-year, $1,000 face value, 10% semiannual coupon bond selling for $875 has a yield to maturity of 11.62%.
- Calculation: N = 40 (2 × 20 years); PMT = 50 (0.10 × 1,000) / 2; PV = -875; FV = 1,000; CPT → I/Y = 5.811 × 2 (for annual rate) = 11.62%.
- A five-year bond with a 7.75% semiannual coupon currently trades at 101.245% of a par value of $1,000 has a current yield on the bond of 7.65%.
- The annual coupon = ($1,000)(0.0775) = $77.50., meaning the current yield = ($77.50) / ($1,012.45) = 0.0765 = 7.65%.
- Bond Y which is callable will have the higher Z-spread due to the call option embedded in the bond.
- For callable Bond Y, the option-adjusted spread is less than the Z-spread, and since Bond X is noncallable, the Z-spread and the OAS will be the same.
- A stated interest rate of 9% compounded quarterly has an effective annual rate of 9.3%.
- Calculation: Quarterly rate = 0.09 / 4 = 0.0225, thus the effective annual rate EAR = (1 + 0.0225)^4 – 1 = 0.09308, or 9.308%.
- The yield to worst describes the lowest of all possible yields to call.
- Yield to worst involves the calculation of yield to call for every possible call date, determining the lowest expected return.
- A semiannual-pay bond is callable in five years at $1,080 with an 8% coupon and 15 years to maturity, if an investor pays $895; the yield to call is 12.1%.
- Calculation: N = 10; PV = -895; PMT = 80 / 2 = 40; FV = 1080; CPT → I/Y = 6.035 × 2 = 12.07%.
- For a bond selling for $1,150, with 28 years to maturity, that pays 12% annual coupon, and is callable in 8 years for $1,100; the yield to maturity is 10.34%.
- Calculation: N = 28; PMT = 120; PV = -1,150; FV = 1,000; CPT I/Y = 10.3432.
- On a semiannual-bond basis of a 20-year, U.S. zero-coupon bond selling for $300, the yield to maturity (YTM) is 6.11%.
- Calculation: N = 40; PV = -300; FV = 1,000; CPT → I = 3.055 × 2 = 6.11.
- If the stated rate is 12% compounded quarterly, the effective annual rate is 12.55%.
- Calculation: If the stated rate is 12%, then the effective quarterly (period) rate is 12% / 4 = 3%. Effective annual rate = [1 + (0.12 / 4)]^4 – 1 = 12.55%.
- A 12% coupon bond with semiannual payments is callable in 5 years at $1,120. If the bond is selling today for $1,110, the yield-to-call is 10.95%.
- Calculation: PMT = 60; N = 10; FV = 1,120; PV = -1,110; CPT → 1 = 5.47546; (5.47546)(2) = 10.95.
- The zero volatility spread (Z-spread) is the spread that is added to each spot rate on the government yield curve that will cause the present value of the bond's cash flows to equal its market price.
- The zero volatility spread (Z-spread) is the interest rate that is added to each zero-coupon bond spot rate that will cause the present value of the risky bond's cash flows to equal its market value.
- The nominal spread is the spread that is added to the YTM of a similar maturity government bond that will then equal the YTM of the risky bond.
- A bond with a 12% semiannual coupon is trading at 102.25 per 100 of face value and has seven years to maturity; the yield to maturity (YTM) is 11.52%.
- Calculation: Enter PV = -$1,022.50; PMT = $60; N = 14; FV = $1,000; CPT → I/Y = 5.76%, so (5.76)(2) = 11.52%.
- A bond selling for $1,150, with 28 years to maturity, that pays a 12% annual coupon, and is callable in 8 years for $1,100, the yield to call is 10.05%.
- Calculation: N = 8; PMT = 120; PV = -1,150; FV = 1,100; CPT I/Y = 10.0554.
- For a callable bond, the option-adjusted spread (OAS) is less than the zero-volatility spread.
- A 20-year, 9% semi-annual coupon bond selling for $914.20 offers a yield to maturity of 10%.
- Calculation: N = 40; PMT = 45; PV = -914.20; FV = 1,000; CPT → I/Y = 5%, YTM = 5% × 2 = 10%.
- A $1,000 par value, 10% annual coupon bond with 15 years to maturity priced at $951 has a yield to maturity greater than its current yield.
- The bond's YTM calculation: N = 15; PMT = 100; PV = -951; FV = 1,000; CPT I/Y = 10.67%, and the current yield = annual coupon payment / bond price; CY = 100/$951 = 0.1051 or 10.51%.
- A 20 year, 8% semi-annual coupon, $1,000 par value bond is selling for $1,100 and is callable in 4 years at $1,080, the bond's yield to call is 6.87%.
- Calculation: n = 4(2) = 8; PMT = 80/2 = 40; PV = -1,100; FV = 1,080 Compute YTC = 3.435(2) = 6.87%.
- A 20-year, 10% semi-annual coupon bond selling for $925 has a yield to maturity (YTM) of 10.93%.
- Calculation: N = 40, PMT = 50, PV = -925, FV = 1,000, CPT I/Y = 5.4653 × 2 = 10.9305.
- A 30-year, 10% annual coupon bond is sold at par and can be called at the end of 10 years for $1,100; what is the bond's yield to call (YTC) 10.6%.
- Calculation: N = 10; PMT = 100; PV = -1,000; FV = 1,100; CPT → I = 10.6.
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