45
CHAPTER 9
VALUATION AND ANALYSIS:
BONDS WITH
EMBEDDED OPTIONS
PROBLEMS
fie following information relates to Questions 1–101
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. e 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
e 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.
1
is question set was developed by Danny Hassett, CFA (Arlington, TX, USA) and Ioannis Georgiou,
CFA (Cyprus).
46 Part I: Learning Objectives, Summary Overview, and Problems
EXHIBIT 2 Binomial Interest Rate Tree
Year 0
2.5000%
Year 1
3.5930%
2.9417%
Year 2
4.6470%
3.8046%
3.1150%
On 19 October 20X0, Ferguson analyzes the convertible bond issued by Pro Star given
in Exhibit 3. at day, the market prices of Pro Star’s convertible bond and common stock are
$1,060 and $37.50, respectively.
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
1. e call feature of Bond #2 is best described as:
A. European style.
B. American style.
C. Bermudan style.
2. e 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. e value of Bond #2 is closest to:
A. 102.103% of par.
B. 103.121% of par.
C. 103.744% of par.
5. e 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.
Chapter 9 Valuation and Analysis: Bonds with Embedded Options 47
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 at-
tening, the value of the option embedded in Bond #2 will most likely:
A. decrease.
B. remain unchanged.
C. increase.
9. e conversion price of the bond in Exhibit 3 is closest to:
A. $26.67.
B. $32.26.
C. $34.19.
10. 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.
fie following information relates to Question 11–192
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%. e results
of his analysis are presented in Exhibit 1.
EXHIBIT 1 Summary Results of Hsu’s
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. ese 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.
2
is question set was developed by Dan Reeder, CFA (Shawnee, OK, USA) and Ioannis Georgiou, CFA
(Cyprus).
48 Part I: Learning Objectives, Summary Overview, and Problems
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
2.5000%
Year 1
4.6343%
3.4331%
Year 2
5.3340%
3.9515%
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. e 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 oating-rate bonds issued by Varlep, plc given in Exhibit 5. ese
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, oored at 3.50%
To value Varlep’s bonds, Hsu constructs the binomial interest rate tree provided in
Exhibit 6.
Chapter 9 Valuation and Analysis: Bonds with Embedded Options 49
EXHIBIT 6 Binomial Interest Rate Tree Used to Value Varlep’s Bonds
Year 0
3.0000%
Year 1
4.5027%
3.5419%
Year 2
6.3679%
5.0092%
3.9404%
Last, Hsu selects the two bonds issued by Whorton, Inc. given in Exhibit 7. ese 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.
EXHIBIT 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
11. Based on Exhibit 1, Rayes would most likely conclude that relative to Bond #1, Bond #2 is:
A. overpriced.
B. fairly priced.
C. underpriced.
12. e 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.
13. In Exhibit 2, the bond whose effective duration will lengthen if interest rates rise is:
A. Bond #3.
B. Bond #4.
C. Bond #5.
14. e effective duration of Bond #4 is closest to:
A. 0.76.
B. 1.88.
C. 3.77.
15. e value of Bond #7 is closest to:
A. 99.697% of par.
B. 99.936% of par.
C. 101.153% of par.
16. e value of Bond #8 is closest to:
A. 98.116% of par.
B. 100.000% of par.
C. 100.485% of par.
50 Part I: Learning Objectives, Summary Overview, and Problems
17. e 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.
18. e 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.
19. e factor that is currently least likely to affect the risk-return characteristics of Bond #9is:
A. Interest rate movements.
B. Whorton’s credit spreads.
C. Whorton’s common stock price movements.