Exam 9: Valuation and Analysis of Bonds With Embedded Options

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

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 Analysis Using the OAS Approach Bond OAS (in bps) Bond 1 25.5 Bond 2 30.3 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. EXHIBIT 2 Bonds Issued by RW, Inc. Bond Coupon Special Provision Bond 3 4.00\% annual Bond 4 4.00\% annual Callable at par at the end of years 1 and 2 Bond 5 4.00\% annual Putable at par at the end of years 1 and 2 Bond 6 One-year Libor annually, set in arrears 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. EXHIBIT 5 Floating-Rate Bonds Issued by Varlep, plc Bond Coupon Bond 7 One-year Libor annually, set in arrears, capped at 5.00\% Bond 8 One-year Libor annually, set in arrears, floored at 3.50\% 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. EXHІВАТ 7 Bonds Issued by Whorton, Inc. Bond Type of Bond Bond 9 Convertible bond with a conversion price of \ 50 Bond 10 Identical to Bond 9 except that it does not include a conversion option -The value of Bond 9 is equal to the value of Bond 10:

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. Bond Maturity Coupon Type of Bond Bond 1 1 October 20X3 4.40\% annual Option-free Bond 2 1 October 20X3 4.40\% annual Callable at par on 1 October 20X1 and on 1 October 20X2 Bond 3 1 October 20X3 4.40\% annual Putable at par on 1 October 20X1 and on 1 October 20X2 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. Issue Date: 6 December 20X0 Maturity Date: 6 December 20X4 Coupon Rate: 2\% Issue Price: \ 1,000 Conversion Ratio: 31 -The value of Bond 2 is closest to:

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

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

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 Analysis Using the OAS Approach Bond OAS (in bps) Bond 1 25.5 Bond 2 30.3 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. EXHIBIT 2 Bonds Issued by RW, Inc. Bond Coupon Special Provision Bond 3 4.00\% annual Bond 4 4.00\% annual Callable at par at the end of years 1 and 2 Bond 5 4.00\% annual Putable at par at the end of years 1 and 2 Bond 6 One-year Libor annually, set in arrears 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. EXHIBIT 5 Floating-Rate Bonds Issued by Varlep, plc Bond Coupon Bond 7 One-year Libor annually, set in arrears, capped at 5.00\% Bond 8 One-year Libor annually, set in arrears, floored at 3.50\% 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. EXHІВАТ 7 Bonds Issued by Whorton, Inc. Bond Type of Bond Bond 9 Convertible bond with a conversion price of \ 50 Bond 10 Identical to Bond 9 except that it does not include a conversion option -The factor that is currently least likely to affect the risk-return characteristics of Bond 9 is:

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

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. Bond Maturity Coupon Type of Bond Bond 1 1 October 20X3 4.40\% annual Option-free Bond 2 1 October 20X3 4.40\% annual Callable at par on 1 October 20X1 and on 1 October 20X2 Bond 3 1 October 20X3 4.40\% annual Putable at par on 1 October 20X1 and on 1 October 20X2 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. Issue Date: 6 December 20X0 Maturity Date: 6 December 20X4 Coupon Rate: 2\% Issue Price: \ 1,000 Conversion Ratio: 31 -All else being equal, a rise in interest rates will most likely result in the value of the option embedded in Bond 3:

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:

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

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

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

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?

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. Bond Maturity Coupon Type of Bond Bond 1 1 October 20X3 4.40\% annual Option-free Bond 2 1 October 20X3 4.40\% annual Callable at par on 1 October 20X1 and on 1 October 20X2 Bond 3 1 October 20X3 4.40\% annual Putable at par on 1 October 20X1 and on 1 October 20X2 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. Issue Date: 6 December 20X0 Maturity Date: 6 December 20X4 Coupon Rate: 2\% Issue Price: \ 1,000 Conversion Ratio: 31 -The conversion price of the bond in Exhibit 3 is closest to:

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

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. Bond Maturity Coupon Type of Bond Bond 1 1 October 20X3 4.40\% annual Option-free Bond 2 1 October 20X3 4.40\% annual Callable at par on 1 October 20X1 and on 1 October 20X2 Bond 3 1 October 20X3 4.40\% annual Putable at par on 1 October 20X1 and on 1 October 20X2 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. Issue Date: 6 December 20X0 Maturity Date: 6 December 20X4 Coupon Rate: 2\% Issue Price: \ 1,000 Conversion Ratio: 31 -The bond that would most likely protect investors against a significant increase in interest rates is:

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. Bond Maturity Coupon Type of Bond Bond 1 1 October 20X3 4.40\% annual Option-free Bond 2 1 October 20X3 4.40\% annual Callable at par on 1 October 20X1 and on 1 October 20X2 Bond 3 1 October 20X3 4.40\% annual Putable at par on 1 October 20X1 and on 1 October 20X2 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. Issue Date: 6 December 20X0 Maturity Date: 6 December 20X4 Coupon Rate: 2\% Issue Price: \ 1,000 Conversion Ratio: 31 -The value of Bond 3 is closest to:

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 Issue price 1,000 at par Conversion period 13 September 20X5 to 12 September 20X8 Initial conversion price 10.00 per share Threshold dividend 0.50 per share Change of control conversion price 8.00 per share Common stock share price on issue date 8.70 Share price on 17 September 20X5 9.10 Convertible bond price on 17 September 20X5 1,123 EXHIBIT 4 Selected Data for RI Convertible Bond Straight bond value 978 Value of embedded issuer call option 43 Value of embedded investor put option 26 Value of embedded call option on issuer's stock 147 Conversion price 12.50 Current common stock share price 11.75 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:

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 Analysis Using the OAS Approach Bond OAS (in bps) Bond 1 25.5 Bond 2 30.3 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. EXHIBIT 2 Bonds Issued by RW, Inc. Bond Coupon Special Provision Bond 3 4.00\% annual Bond 4 4.00\% annual Callable at par at the end of years 1 and 2 Bond 5 4.00\% annual Putable at par at the end of years 1 and 2 Bond 6 One-year Libor annually, set in arrears 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. EXHIBIT 5 Floating-Rate Bonds Issued by Varlep, plc Bond Coupon Bond 7 One-year Libor annually, set in arrears, capped at 5.00\% Bond 8 One-year Libor annually, set in arrears, floored at 3.50\% 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. EXHІВАТ 7 Bonds Issued by Whorton, Inc. Bond Type of Bond Bond 9 Convertible bond with a conversion price of \ 50 Bond 10 Identical to Bond 9 except that it does not include a conversion option -Based on Exhibit 1, Rayes would most likely conclude that relative to Bond 1, Bond 2 is:

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 Analysis Using the OAS Approach Bond OAS (in bps) Bond 1 25.5 Bond 2 30.3 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. EXHIBIT 2 Bonds Issued by RW, Inc. Bond Coupon Special Provision Bond 3 4.00\% annual Bond 4 4.00\% annual Callable at par at the end of years 1 and 2 Bond 5 4.00\% annual Putable at par at the end of years 1 and 2 Bond 6 One-year Libor annually, set in arrears 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. EXHIBIT 5 Floating-Rate Bonds Issued by Varlep, plc Bond Coupon Bond 7 One-year Libor annually, set in arrears, capped at 5.00\% Bond 8 One-year Libor annually, set in arrears, floored at 3.50\% 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. EXHІВАТ 7 Bonds Issued by Whorton, Inc. Bond Type of Bond Bond 9 Convertible bond with a conversion price of \ 50 Bond 10 Identical to Bond 9 except that it does not include a conversion option -The effective duration of Bond 6 is: