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The following information relates to Questions 1–9 Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies

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The following information relates to Questions 1–9

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%, respectively. Based on an estimated interest rate volatility of 10%, Ferguson constructs the binomial interest rate tree shown in Exhibit 2.

EXHIBIT 2 Binomial Interest Rate Tree

Year 0	Year 1	Year 2
		4.6470%
	3.5930%
2.2500%		3.8046%
	2.9417%	3.1150%

 

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 Pro Star, Inc.

Issue Date:	6 December 20X0
Maturity Date:	6 December 20X4
Coupon Rate:	2%
Issue Price:	$1,000
Conversion Ration:	31

 

1. The call feature of Bond 2 is best described as:

A. European style.

B. American style.

C. Bermudan style.

2. 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.

3. 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.

4. The value of Bond 2 is closest to:

A. 102.103% of par.

B. 103.121% of par.

C. 103.744% of par.

5. The value of Bond 3 is closest to:

A. 102.103% of par.

B. 103.688% of par.

C. 103.744% of par.

6. 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.

7. 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.

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

A. decrease.

B. remain unchanged.

C. increase.

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

A. $26.67.

B. $32.26.

C. $34.19.

The following information relates to Questions 10–15

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 portfolio. 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 characteristics 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 results of his analysis are presented in Exhibit 1.

EXHIBIT 1 Summary Results of Hsu’s

Analysis Using the OAS Approach

Bind	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 Bond 3, 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.

EXHIBIT 3 Binomial Interest Rate Tree Used to Value RW’s Bonds

Year 0	Year 1	Year 2
		5.3340%
	4.6343%
2.5000%		3.9515%
	3.4331%
		2.9274%

 

Rayes asks Hsu to determine the sensitivity of Bond 4’s price to a 20 bps parallel shift of the 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 Parallel Shift 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 in

Exhibit 6.

EXHIBIT 6 Binomial Interest Rate Tree Used to Value Varlep’s Bonds

Year 0                                   Year 1                                   Year 2

                                                                                          6.3679%

                                             4.5027%                                          

3.0000%                                                                           5.0092%

                                            3.5419%

                                                                                           3.9404%

10. Based on Exhibit 1, Rayes would most likely conclude that relative to Bond 1, Bond 2 1S:

A. overpriced.

B. fairly priced.

C. underpriced.

11. 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.

12. In Exhibit 2, the bond whose effective duration will lengthen if interest rates rise 1s:

A. Bond 3.

B. Bond 4.

C. Bond 5.

13. The effective duration of Bond 4 is closest to:

A. 0.76.

B. 1.88.

C. 3.77.

14. The value of Bond 7 is closest to:

A. 99.697% of par.

B. 99.936% of par.

C. 101.153% of par.

15. The value of Bond 8 is closest to:

A. 98.116% of par.

B. 100.000% of par.

C. 100.485% of par.