Deck 9: Valuation and Analysis of Bonds With Embedded Options

Question 1

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-The value of Bond 7 is closest to:

A) 99.697% of par.
B) 99.936% of par.
C) 101.153% of par.

Answer 1

99.697% of par.

Question 2

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-The effective duration of Bond 6 is:

A) lower than or equal to 1.
B) higher than 1 but lower than 3.
C) higher than 3.

Answer 2

lower than or equal to 1.

Question 3

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-All else being equal, if the shape of the yield curve changes from upward sloping to flat- tening, the value of the option embedded in Bond 2 will most likely:

A) decrease.
B) remain unchanged.
C) increase.

Answer 3

increase.

Question 4

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-Based on Exhibit 1, Rayes would most likely conclude that relative to Bond 1, Bond 2 is:

A) overpriced.
B) fairly priced.
C) underpriced.

Question 5

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-The value of Bond 3 is closest to:

A) 102.103% of par.
B) 103.688% of par.
C) 103.744% of par.

Question 6

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-The minimum value of Bond 9 is equal to the greater of:

A) the conversion value of Bond 9 and the current value of Bond 10.
B) the current value of Bond 10 and a call option on whorton's common stock.
C) the conversion value of Bond 9 and a call option on whorton's common stock.

Question 7

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-The value of Bond 8 is closest to:

A) 98.116% of par.
B) 100.000% of par.
C) 100.485% of par.

Question 8

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-A fall in interest rates would most likely result in:

A) a decrease in the effective duration of Bond 3.
B) Bond 3 having more upside potential than Bond 2.
C) a change in the effective convexity of Bond 3 from positive to negative.

Question 9

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-if the market price of Pro Star's common stock falls from its level on 19 october 20X0, the price of the convertible bond will most likely:

A) fall at the same rate as Pro Star's stock price.
B) fall but at a slightly lower rate than Pro Star's stock price.
C) be unaffected until Pro Star's stock price reaches the conversion price.

Question 10

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-The value of Bond 9 is equal to the value of Bond 10:

A) plus the value of a put option on whorton's common stock.
B) plus the value of a call option on whorton's common stock.
C) minus the value of a call option on whorton's common stock.

Question 11

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-The conversion price of the bond in Exhibit 3 is closest to:

A) $26.67.
B) $32.26.
C) $34.19.

Question 12

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-in Exhibit 2, the bond whose effective duration will lengthen if interest rates rise is:

A) Bond 3.
B) Bond 4.
C) Bond 5.

Question 13

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-The factor that is currently least likely to affect the risk-return characteristics of Bond 9 is:

A) interest rate movements.
B) whorton's credit spreads.
C) whorton's common stock price movements.

Question 14

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-The value of Bond 2 is closest to:

A) 102.103% of par.
B) 103.121% of par.
C) 103.744% of par.

Question 15

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-The bond that would most likely protect investors against a significant increase in interest rates is:

A) Bond 1.
B) Bond 2.
C) Bond 3.

Question 16

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-All else being equal, a rise in interest rates will most likely result in the value of the option embedded in Bond 3:

A) decreasing.
B) remaining unchanged.
C) increasing.

Question 17

The following information relates to Questions 20-27John Smith, an investment adviser, meets with lydia Carter to discuss her pending retirement
and potential changes to her investment portfolio. domestic economic activity has been weak-ening recently, and Smith's outlook is that equity market values will be lower during the next year. He would like Carter to consider reducing her equity exposure in favor of adding more fixed-income securities to the portfolio.Government yields have remained low for an extended period, and Smith suggests con-sidering investment-grade corporate bonds to provide additional yield above government debt issues. in light of recent poor employment figures and two consecutive quarters of negative GdP growth, the consensus forecast among economists is that the central bank, at its next meeting this month, will take actions that will lead to lower interest rates.
Smith and Carter review par, spot, and one-year forward rates (Exhibit 1) and four fixed- rate investment-grade bonds issued by Alpha Corporation that are being considered for invest-ment (Exhibit 2).
$$\begin{array}{l}\text { EXHIBTT } 1 \text { Par, Spot, and One-Year Forward Rates (annual coupon payments) }\\\begin{array} { l c c c } \hline \text { Maturity (Years) } & \text { Par Rate (\%) } & \text { Spot Rate (\%) } & \text { One-Year Forward (\%) } \\\hline 1 & 1.0000 & 1.0000 & 1.0000 \\2 & 1.2000 & 1.2012 & 1.4028 \\3 & 1.2500 & 1.2515 & 1.3522 \\\hline\end{array}\end{array}$$
EXHIBIT 2 Selected Fixed-Rate Bonds of Alpha Corporation
$\begin{array}{lcl}\hline \text { Bond } & \text { Annual Coupon } & \text { Type of Bond } \\\hline \text { Bond 1 } & 1.5500 \% & \text { Straight bond } \\\text { Bond 2 } & 1.5500 \% & \text { Convertible bond: currently trading out of the money } \\\text { Bond 3 } & 1.5500 \% & \text { Putable bond: putable at par one year and two years from now } \\\text { Bond 4 } & 1.5500 \% & \text { Callable bond: callable at par without any lockout periods }\\\hline\end{array}$
Note: All bonds in Exhibit 2 have remaining maturities of exactly three years.
Carter tells Smith that the local news media have been reporting that housing starts,exports, and demand for consumer credit are all relatively strong, even in light of other poor macroeconomic indicators. Smith explains that the divergence in economic data leads him to believe that volatility in interest rates will increase. Smith also states that he recently read a report issued by Brown and Company forecasting that the yield curve could invert within the next six months. Smith develops a binomial interest rate tree with a 15% interest rate volatility assumption to assess the value of Alpha Corporation's bonds. Exhibit 3 presents the interest rate tree.

Carter asks Smith about the possibility of nalyzing bonds that have lower credit rat-ings than the investment-grade Alpha bonds. Smith discusses four other corporate bonds with Carter. Exhibit 4 presents selected data on the four bonds. EXHiBiT 4 Selected information on fixed-Rate Bonds for Beta, Gamma, delta, and Rho
$\text { Corporations }$
$\begin{array}{lllc}\hline\text { Bond } & \text { Issuer } & \text { Bond Features } & \text { Credit Rating } \\\hline \text { Bond 5 } & \text { Beta Corporation } & \text { Coupon 1.70\% } & \text { B } \\& & \text { Callable in Year 2 } & \\& &\text { OAS of } 45 \text { bps } & \\\text { Bond 6 } & \text { Gamma Corporation } & \text { Coupon 1.70\% } \\& & \text { Callable in Year 2 } & \\&& \text { OAS of 65 bps } \\\text { Bond 7 } & \text { Delta Corporation } & \text { Coupon 1.70\% }&\text { B }\\ & & \text { Callable in Year 2 } & \\& & \text { OAS of } 85\\\text { Bond 8 }& \text { Rho Corporation } & \text { Coupon 1.70\% } & \text { CCC } \\&&\text {Callable in Year 2}\\&&\text {OAS of \( 105 \mathrm{bps} \)}\\\hline\end{array}$
Notes: All bonds have remaining maturities of three years. oAS stands for option-adjusted spread.

-Based on Exhibit 2, and assuming that the forecast for interest rates and Smith's outlook for equity returns are validated, which bond's option is most likely to be exercised?

A) Bond 2
B) Bond 3
C) Bond 4

Question 18

The following information relates to Questions 11-19
Rayes investment Advisers specializes in fixed-income portfolio management. Meg Rayes, the owner of the firm, would like to add bonds with embedded options to the firm's bond port-folio. Rayes has asked Mingfang Hsu, one of the firm's analysts, to assist her in selecting and analyzing bonds for possible inclusion in the firm's bond portfolio.Hsu first selects two corporate bonds that are callable at par and have the same character-istics in terms of maturity, credit quality and call dates. Hsu uses the option-adjusted spread(oAS) approach to analyse the bonds, assuming an interest rate volatility of 10%. The resultsof his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu's Analysis Using the OAS Approach
$\begin{array}{l}\text { Analysis Using the OAS Approach }\\\begin{array}{lc}\hline \text { Bond } & \text { OAS (in bps) } \\\hline \text { Bond 1 } & 25.5 \\\text { Bond 2 } & 30.3 \\\hline\end{array}\end{array}$

Hsu then selects the four bonds issued by Rw, inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds 4 and 5 are identical to Bond3, an option-free bond, except that they each include an embedded option.
$$\begin{array}{l}\text { EXHIBIT } 2 \text { Bonds Issued by RW, Inc. }\\\begin{array} { l l l } \hline \text { Bond } &{ \text { Coupon } } & { \text { Special Provision } } \\\hline \text { Bond } 3 & 4.00 \% \text { annual } & \\\text { Bond } 4 & 4.00 \% \text { annual } & \text { Callable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 5 & 4.00 \% \text { annual } & \text { Putable at par at the end of years } 1 \text { and } 2 \\\text { Bond } 6 & \text { One-year Libor annually, } \\&\text { set in arrears }\\\hline\end{array}\end{array}$$
To value and analyze Rw's bonds, Hsu uses an estimated interest rate volatility of 15% and constructs the binomial interest rate tree provided in Exhibit 3.

Rayes asks Hsu to determine the sensitivity of Bond 4's price to a 20 bps parallel shift ofthe benchmark yield curve. The results of Hsu's calculations are shown in Exhibit 4.EXHiBiT 4 Summary Results of Hsu's Analysis about the Sensitivity of Bond 4's Price to a ParallelShift of the Benchmark yield Curve Magnitude of the Parallel Shift in the Benchmark yield Curve +20 bps ?20 bps full Price of Bond 4 (% of par) 100.478 101.238 Hsu also selects the two floating-rate bonds issued by Varlep, plc given in Exhibit 5. These
bonds have a maturity of three years and the same credit rating.
$$\begin{array}{l}\text { EXHIBIT } 5 \text { Floating-Rate Bonds Issued by Varlep, plc }\\\begin{array} { l l } \text { Bond } & \text { Coupon } \\\hline \text { Bond } 7 & \text { One-year Libor annually, set in arrears, capped at } 5.00 \% \\\text { Bond } 8 & \text { One-year Libor annually, set in arrears, floored at } 3.50 \% \\\hline\end{array}\end{array}$$
To value Varlep's bonds, Hsu constructs the binomial interest rate tree provided inExhibit 6.

last, Hsu selects the two bonds issued by whorton, inc. given in Exhibit 7. These bonds are close to their maturity date and are identical, except that Bond 9 includes a conversion option. whorton's common stock is currently trading at $30 per share.
$$\begin{array}{l}\text { EXH???? } 7 \text { Bonds Issued by Whorton, Inc. }\\\begin{array} { l l } \text { Bond } & \text { Type of Bond } \\\hline \text { Bond } 9 & \text { Convertible bond with a conversion price of } \$ 50 \\\text { Bond } 10 & \text { Identical to Bond } 9 \text { except that it does not include a conversion option } \\\hline\end{array}\end{array}$$

-The effective duration of Bond 4 is closest to:

A) 0.76.
B) 1.88.
C) 3.77.

Question 19

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-The call feature of Bond 2 is best described as:

A) European style.
B) American style.
C) Bermudan style.

Question 20

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \\\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \\\\\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \\&&&\text { and on 1 October 20X2 } \begin{array}{l}\\\end{array} \\\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \\ &&&\text { and on 1 October 20X2 }\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c } \text { Issue Date: } & 6 \text { December 20X0 } \\\hline \text { Maturity Date: } & 6 \text { December 20X4 } \\\text { Coupon Rate: } & 2 \% \\\text { Issue Price: } & \$ 1,000 \\\text { Conversion Ratio: } & 31\\\hline\end{array}$

-All else being equal, if ferguson assumes an interest rate volatility of 15% instead of 10%, the bond that would most likely increase in value is:

A) Bond 1.
B) Bond 2.
C) Bond 3.

Question 21

Based on Exhibit 4, the arbitrage-free value of the Ri bond is closest to:

A) €814.
B) €1,056.
C) €1,108.

Question 22

Based on Exhibit 2, the current price of Bond 1 is most likely greater than the current price of:

A) Bond 2.
B) Bond 3.
C) Bond 4.

Question 23

Based on the information in Exhibit 1 and Exhibit 2, the value of the embedded option in Bond 4 is closest to:

A) nil.
B) 0.1906.
C) 0.3343.

Question 24

if benchmark yields were to fall, which bond in Exhibit 1 would most likely experience a decline in effective duration?

A) Ai bond
B) Bi bond
C) CE bond

Question 25

which bond in Exhibit 1 most likely has the lowest effective convexity?

A) Ai bond
B) Bi bond
C) CE bond

Question 26

if the Brown and Company forecast comes true, which of the following is most likely to occur? The value of the embedded option in:

A) Bond 3 decreases.
B) Bond 4 decreases.
C) both Bond 3 and Bond 4 increase.

Question 27

The following information relates to Questions 28-36Jules Bianchi is a bond analyst for Maneval investments, inc. Bianchi gathers data on three
corporate bonds, as shown in Exhibit 1.EXHiBiT 1 Selected Bond dataissuer Coupon Rate Price Bond description Ayrault, inc. (Ai) 5.25% 100.200 Callable at par in one year and twoyears from today Blum, inc. (Bi) 5.25% 101.300 option-free Cresson Enterprises (CE) 5.25% 102.100 Putable at par in one year from todayNote: Each bond has a remaining maturity of three years, annual coupon payments, and a credit rating of BBB.
To assess the interest rate risk of the three bonds, Bianchi constructs two binomial interest rate trees based on a 10% interest rate volatility assumption and a current one-year rate of 1%.Panel A of Exhibit 2 provides an interest rate tree assuming the benchmark yield curve shifts down by 30 bps, and Panel B provides an interest rate tree assuming the benchmark yield curve
shifts up by 30 bps. Bianchi determines that the Ai bond is currently trading at an option-ad-justed spread (oAS) of 13.95 bps relative to the enchmark yield curve.EXHiBiT 2 Binomial interest Rate Trees
$\text { Panet a interest Kates shit Down by so bps }$


$\text { Panel B: Interest Rates Shift Up by } 30 \text { bps }$

Armand Gillette, a convertible bond analyst, stops by Bianchi's office to discuss two con-vertible bonds. one is issued by delille Enterprises (dE) and the other is issued by Raffarin incorporated (Ri). Selected data for the two bonds are presented in Exhibits 3 and 4.
EXHIBIT 3 Selected Data for DE Convertible Bond
$\begin{array}{ll}\hline\text { Issue price } & € 1,000 \text { at par } \\\text { Conversion period } & 13 \text { September } 20X 5 \text { to } 12 \text { September 20X8 } \\\text { Initial conversion price } & € 10.00 \text { per share } \\\text { Threshold dividend } & € 0.50 \text { per share } \\\text { Change of control conversion price } & € 8.00 \text { per share } \\\text { Common stock share price on issue date } & € 8.70 \\\text { Share price on 17 September 20X5 } & € 9.10 \\\text { Convertible bond price on } 17 \text { September 20X5 } & € 1,123\\\hline\end{array}$

EXHIBIT 4 Selected Data for RI Convertible Bond
$\begin{array}{llcc} \hline\text {Straight bond value } &€ 978 \\ \text { Value of embedded issuer call option} &€ 43 \\ \text { Value of embedded investor put option } &€ 26\\ \text { Value of embedded call option on issuer's stock } & € 147\\ \text { Conversion price } &€ 12.50 \\ \hline\text {Current common stock share price } &€ 11.75\\\end{array}$

Gillette makes the following comments to Bianchi:
• "The dE bond does not contain any call or put options but the Ri bond contains both an embedded call option and a put option. i expect that delille Enterprises will soon announce a common stock dividend of €0.70 per share."
• "My belief is that, over the next year, Raffarin's share price will appreciate toward the con-version price but not exceed it."

-Based on Exhibits 1 and 2, the effective duration for the Ai bond is closest to:

A) 1.98.
B) 2.15.
C) 2.73.

Question 28

Based on Exhibit 1, for the Bi bond, one-sided:

A) up-duration will be greater than one-sided down-duration.
B) down-duration will be greater than one-sided up-duration.
C) up-duration and one-sided down-duration will be about equal.

Question 29

Based on Exhibit 2 and Exhibit 3, the market price of Bond 4 is closest to:

A) 100.4578.
B) 100.5123.
C) 100.8790.

Question 30

Based on Exhibit 1, which key rate duration is the largest for the Bi bond?

A) one-year key rate duration
B) Two-year key rate duration
C) Three-year key rate duration

Question 31

Based on Exhibit 4 and Gillette's forecast regarding Raffarin's share price, the return on the Ri bond over the next year is most likely to be:

A) lower than the return on Raffarin's common shares.
B) the same as the return on Raffarin's common shares.
C) higher than the return on Raffarin's common shares.

Question 32

if Smith's interest rate volatility forecast turns out to be true, which bond in Exhibit 2 is likely to experience the greatest price increase?

A) Bond 2
B) Bond 3
C) Bond 4

Question 33

Based on Exhibit 3, the market conversion premium per share for the dE bond on 17 September 20X5 is closest to:

A) €0.90.
B) €2.13.
C) €2.53.

Question 34

Assuming the forecast for interest rates is proven accurate, which bond in Exhibit 2 will likely experience the smallest price increase?

A) Bond 1
B) Bond 3
C) Bond 4

Question 35

Based on Exhibit 3, if delille Enterprises pays the dividend expected by Gillette, the con- version price of the dE bond will:

A) be adjusted downward.
B) not be adjusted.
C) be adjusted upward.

Question 36

which of the following conclusions regarding the bonds in Exhibit 4 is correct?

A) Bond 5 is relatively cheaper than Bond 6.
B) Bond 7 is relatively cheaper than Bond 6.
C) Bond 8 is relatively cheaper than Bond 7.